diff --git a/.idea/workspace.xml b/.idea/workspace.xml
index 6465a84..3f3e67c 100644
--- a/.idea/workspace.xml
+++ b/.idea/workspace.xml
@@ -2,20 +2,10 @@
 <project version="4">
   <component name="ChangeListManager">
     <list default="true" id="b82c504b-cebe-4b95-a526-6942af548f40" name="Default" comment="">
-      <change beforePath="" afterPath="$PROJECT_DIR$/src/InvariantSets.py" />
-      <change beforePath="$PROJECT_DIR$/.idea/workspace.xml" afterPath="$PROJECT_DIR$/.idea/workspace.xml" />
-      <change beforePath="$PROJECT_DIR$/src/A.csv" afterPath="$PROJECT_DIR$/src/A.csv" />
-      <change beforePath="$PROJECT_DIR$/src/B.csv" afterPath="$PROJECT_DIR$/src/B.csv" />
       <change beforePath="$PROJECT_DIR$/src/LMPC_PathFollowing.npz" afterPath="$PROJECT_DIR$/src/LMPC_PathFollowing.npz" />
-      <change beforePath="$PROJECT_DIR$/src/MPC_PathFollowing.npz" afterPath="$PROJECT_DIR$/src/MPC_PathFollowing.npz" />
-      <change beforePath="$PROJECT_DIR$/src/MPC_tv_PathFollowing.npz" afterPath="$PROJECT_DIR$/src/MPC_tv_PathFollowing.npz" />
-      <change beforePath="$PROJECT_DIR$/src/PID_PathFollowing.npz" afterPath="$PROJECT_DIR$/src/PID_PathFollowing.npz" />
-      <change beforePath="$PROJECT_DIR$/src/SS.csv" afterPath="" />
-      <change beforePath="$PROJECT_DIR$/src/SS0.csv" afterPath="" />
-      <change beforePath="$PROJECT_DIR$/src/fnc/SysID.py" afterPath="$PROJECT_DIR$/src/fnc/SysID.py" />
-      <change beforePath="$PROJECT_DIR$/src/fnc/SysModel.py" afterPath="$PROJECT_DIR$/src/fnc/SysModel.py" />
+      <change beforePath="$PROJECT_DIR$/src/Qfun.csv" afterPath="$PROJECT_DIR$/src/Qfun.csv" />
+      <change beforePath="$PROJECT_DIR$/src/fnc/LMPC.py" afterPath="$PROJECT_DIR$/src/fnc/LMPC.py" />
       <change beforePath="$PROJECT_DIR$/src/main.py" afterPath="$PROJECT_DIR$/src/main.py" />
-      <change beforePath="$PROJECT_DIR$/src/x.csv" afterPath="" />
     </list>
     <option name="EXCLUDED_CONVERTED_TO_IGNORED" value="true" />
     <option name="TRACKING_ENABLED" value="true" />
@@ -32,8 +22,18 @@
       <file leaf-file-name="main.py" pinned="false" current-in-tab="true">
         <entry file="file://$PROJECT_DIR$/src/main.py">
           <provider selected="true" editor-type-id="text-editor">
-            <state relative-caret-position="327">
-              <caret line="70" column="0" lean-forward="false" selection-start-line="70" selection-start-column="0" selection-end-line="70" selection-end-column="0" />
+            <state relative-caret-position="791">
+              <caret line="454" column="26" lean-forward="false" selection-start-line="454" selection-start-column="26" selection-end-line="454" selection-end-column="26" />
+              <folding />
+            </state>
+          </provider>
+        </entry>
+      </file>
+      <file leaf-file-name="LMPC.py" pinned="false" current-in-tab="false">
+        <entry file="file://$PROJECT_DIR$/src/fnc/LMPC.py">
+          <provider selected="true" editor-type-id="text-editor">
+            <state relative-caret-position="217">
+              <caret line="25" column="45" lean-forward="false" selection-start-line="25" selection-start-column="45" selection-end-line="25" selection-end-column="45" />
               <folding />
             </state>
           </provider>
@@ -42,8 +42,8 @@
       <file leaf-file-name="InvariantSets.py" pinned="false" current-in-tab="false">
         <entry file="file://$PROJECT_DIR$/src/InvariantSets.py">
           <provider selected="true" editor-type-id="text-editor">
-            <state relative-caret-position="855">
-              <caret line="57" column="20" lean-forward="false" selection-start-line="57" selection-start-column="20" selection-end-line="57" selection-end-column="20" />
+            <state relative-caret-position="474">
+              <caret line="63" column="0" lean-forward="false" selection-start-line="63" selection-start-column="0" selection-end-line="81" selection-end-column="24" />
               <folding>
                 <element signature="e#0#18#0" expanded="true" />
               </folding>
@@ -54,9 +54,11 @@
       <file leaf-file-name="FTOCP.py" pinned="false" current-in-tab="false">
         <entry file="file://$PROJECT_DIR$/src/fnc/FTOCP.py">
           <provider selected="true" editor-type-id="text-editor">
-            <state relative-caret-position="1635">
-              <caret line="109" column="30" lean-forward="false" selection-start-line="109" selection-start-column="24" selection-end-line="109" selection-end-column="30" />
-              <folding />
+            <state relative-caret-position="206">
+              <caret line="137" column="53" lean-forward="false" selection-start-line="137" selection-start-column="51" selection-end-line="137" selection-end-column="53" />
+              <folding>
+                <marker date="1524887748000" expanded="true" signature="51:95" ph="..." />
+              </folding>
             </state>
           </provider>
         </entry>
@@ -64,8 +66,8 @@
       <file leaf-file-name="SysModel.py" pinned="false" current-in-tab="false">
         <entry file="file://$PROJECT_DIR$/src/fnc/SysModel.py">
           <provider selected="true" editor-type-id="text-editor">
-            <state relative-caret-position="660">
-              <caret line="97" column="36" lean-forward="false" selection-start-line="97" selection-start-column="36" selection-end-line="97" selection-end-column="36" />
+            <state relative-caret-position="1200">
+              <caret line="80" column="27" lean-forward="false" selection-start-line="80" selection-start-column="27" selection-end-line="80" selection-end-column="27" />
               <folding />
             </state>
           </provider>
@@ -74,8 +76,8 @@
       <file leaf-file-name="Track.py" pinned="false" current-in-tab="false">
         <entry file="file://$PROJECT_DIR$/src/fnc/Track.py">
           <provider selected="true" editor-type-id="text-editor">
-            <state relative-caret-position="780">
-              <caret line="52" column="22" lean-forward="false" selection-start-line="52" selection-start-column="22" selection-end-line="52" selection-end-column="31" />
+            <state relative-caret-position="-1774">
+              <caret line="4" column="0" lean-forward="false" selection-start-line="4" selection-start-column="0" selection-end-line="4" selection-end-column="0" />
               <folding />
             </state>
           </provider>
@@ -84,9 +86,11 @@
       <file leaf-file-name="SysID.py" pinned="false" current-in-tab="false">
         <entry file="file://$PROJECT_DIR$/src/fnc/SysID.py">
           <provider selected="true" editor-type-id="text-editor">
-            <state relative-caret-position="3060">
-              <caret line="204" column="87" lean-forward="false" selection-start-line="204" selection-start-column="87" selection-end-line="204" selection-end-column="87" />
-              <folding />
+            <state relative-caret-position="270">
+              <caret line="18" column="13" lean-forward="false" selection-start-line="18" selection-start-column="13" selection-end-line="18" selection-end-column="13" />
+              <folding>
+                <marker date="1524887748000" expanded="true" signature="294:317" ph="..." />
+              </folding>
             </state>
           </provider>
         </entry>
@@ -102,22 +106,6 @@
   </component>
   <component name="FindInProjectRecents">
     <findStrings>
-      <find>cu</find>
-      <find>la</find>
-      <find>b</find>
-      <find>q</find>
-      <find>LMPC_BuildMatEqConst</find>
-      <find>vt</find>
-      <find>N</find>
-      <find>npG</find>
-      <find>L</find>
-      <find>b_termConstr</find>
-      <find>A</find>
-      <find>savetxt</find>
-      <find>xPred</find>
-      <find>-1</find>
-      <find>vst</find>
-      <find>Linearization</find>
       <find>solver</find>
       <find>Track</find>
       <find>EstimateABC</find>
@@ -129,6 +117,25 @@
       <find>np.append</find>
       <find>cvs</find>
       <find>csv</find>
+      <find>BuildMatIneqConst</find>
+      <find>SS</find>
+      <find>A</find>
+      <find>A_cl</find>
+      <find>G.csv</find>
+      <find>E</find>
+      <find>GetPred</find>
+      <find>LMPC_BuildMatEqConst</find>
+      <find>shape</find>
+      <find>depsi_ey</find>
+      <find>s is negative, here the state</find>
+      <find>linalg</find>
+      <find>LMPC_TermConstr</find>
+      <find>RunLMPC</find>
+      <find>Curvature</find>
+      <find>vt</find>
+      <find>Ke</find>
+      <find>Qslack</find>
+      <find>negative</find>
     </findStrings>
   </component>
   <component name="Git.Settings">
@@ -139,21 +146,21 @@
       <list>
         <option value="$PROJECT_DIR$/src/fnc/LocalLinearRegrassion.py" />
         <option value="$PROJECT_DIR$/src/fnc/LocalLinearRegression.py" />
+        <option value="$PROJECT_DIR$/src/fnc/SysModel.py" />
+        <option value="$PROJECT_DIR$/src/InvariantSets.py" />
         <option value="$PROJECT_DIR$/src/fnc/FTOCP.py" />
         <option value="$PROJECT_DIR$/src/fnc/Track.py" />
-        <option value="$PROJECT_DIR$/src/fnc/LMPC.py" />
-        <option value="$PROJECT_DIR$/src/fnc/SysModel.py" />
         <option value="$PROJECT_DIR$/src/fnc/SysID.py" />
-        <option value="$PROJECT_DIR$/src/InvariantSets.py" />
+        <option value="$PROJECT_DIR$/src/fnc/LMPC.py" />
         <option value="$PROJECT_DIR$/src/main.py" />
       </list>
     </option>
   </component>
   <component name="ProjectFrameBounds">
-    <option name="x" value="-1665" />
+    <option name="x" value="-1638" />
     <option name="y" value="-150" />
-    <option name="width" value="1665" />
-    <option name="height" value="1049" />
+    <option name="width" value="1583" />
+    <option name="height" value="1050" />
   </component>
   <component name="ProjectView">
     <navigator currentView="ProjectPane" proportions="" version="1">
@@ -178,6 +185,11 @@
               <item name="RacingLMPC" type="b2602c69:ProjectViewProjectNode" />
               <item name="RacingLMPC" type="462c0819:PsiDirectoryNode" />
             </path>
+            <path>
+              <item name="RacingLMPC" type="b2602c69:ProjectViewProjectNode" />
+              <item name="RacingLMPC" type="462c0819:PsiDirectoryNode" />
+              <item name="Matlab" type="462c0819:PsiDirectoryNode" />
+            </path>
             <path>
               <item name="RacingLMPC" type="b2602c69:ProjectViewProjectNode" />
               <item name="RacingLMPC" type="462c0819:PsiDirectoryNode" />
@@ -189,6 +201,15 @@
               <item name="src" type="462c0819:PsiDirectoryNode" />
               <item name="fnc" type="462c0819:PsiDirectoryNode" />
             </path>
+            <path>
+              <item name="RacingLMPC" type="b2602c69:ProjectViewProjectNode" />
+              <item name="External Libraries" type="cb654da1:ExternalLibrariesNode" />
+            </path>
+            <path>
+              <item name="RacingLMPC" type="b2602c69:ProjectViewProjectNode" />
+              <item name="External Libraries" type="cb654da1:ExternalLibrariesNode" />
+              <item name="&lt; Python 2.7 &gt;" type="70bed36:NamedLibraryElementNode" />
+            </path>
           </expand>
           <select />
         </subPane>
@@ -253,26 +274,38 @@
     <servers />
   </component>
   <component name="ToolWindowManager">
-    <frame x="-1665" y="-150" width="1665" height="1049" extended-state="0" />
-    <editor active="true" />
+    <frame x="0" y="23" width="1440" height="873" extended-state="6" />
     <layout>
-      <window_info id="Project" active="false" anchor="left" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="true" show_stripe_button="true" weight="0.15085158" sideWeight="0.48809522" order="0" side_tool="false" content_ui="combo" />
+      <window_info id="Project" active="false" anchor="left" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="true" show_stripe_button="true" weight="0.17477097" sideWeight="0.48809522" order="0" side_tool="false" content_ui="combo" />
       <window_info id="TODO" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.33" sideWeight="0.5" order="6" side_tool="false" content_ui="tabs" />
       <window_info id="Event Log" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.33" sideWeight="0.5" order="7" side_tool="true" content_ui="tabs" />
-      <window_info id="Run" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="true" show_stripe_button="true" weight="0.29454926" sideWeight="0.5" order="2" side_tool="false" content_ui="tabs" />
+      <window_info id="Inspection Results" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.32943678" sideWeight="0.5" order="-1" side_tool="false" content_ui="tabs" />
+      <window_info id="Find" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.33" sideWeight="0.5" order="1" side_tool="false" content_ui="tabs" />
+      <window_info id="Run" active="true" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="true" show_stripe_button="true" weight="0.27763495" sideWeight="0.5" order="2" side_tool="false" content_ui="tabs" />
       <window_info id="Version Control" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.33" sideWeight="0.5" order="7" side_tool="false" content_ui="tabs" />
       <window_info id="Python Console" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.33" sideWeight="0.5" order="7" side_tool="false" content_ui="tabs" />
       <window_info id="Structure" active="false" anchor="left" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.25" sideWeight="0.5" order="1" side_tool="false" content_ui="tabs" />
       <window_info id="Terminal" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.33" sideWeight="0.5" order="7" side_tool="false" content_ui="tabs" />
-      <window_info id="Debug" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.39203355" sideWeight="0.5" order="3" side_tool="false" content_ui="tabs" />
+      <window_info id="Debug" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.39057592" sideWeight="0.5" order="3" side_tool="false" content_ui="tabs" />
       <window_info id="Favorites" active="false" anchor="left" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.17477097" sideWeight="0.5119048" order="2" side_tool="true" content_ui="tabs" />
       <window_info id="Cvs" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.25" sideWeight="0.5" order="4" side_tool="false" content_ui="tabs" />
+      <window_info id="TODO" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.33" sideWeight="0.5" order="6" side_tool="false" content_ui="tabs" />
       <window_info id="Message" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.33" sideWeight="0.5" order="0" side_tool="false" content_ui="tabs" />
       <window_info id="Commander" active="false" anchor="right" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.4" sideWeight="0.5" order="0" side_tool="false" content_ui="tabs" />
+      <window_info id="Event Log" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.33" sideWeight="0.5" order="7" side_tool="true" content_ui="tabs" />
       <window_info id="Inspection" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.4" sideWeight="0.5" order="5" side_tool="false" content_ui="tabs" />
+      <window_info id="Run" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="true" show_stripe_button="true" weight="0.29454926" sideWeight="0.5" order="2" side_tool="false" content_ui="tabs" />
+      <window_info id="Version Control" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.33" sideWeight="0.5" order="7" side_tool="false" content_ui="tabs" />
+      <window_info id="Python Console" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.33" sideWeight="0.5" order="7" side_tool="false" content_ui="tabs" />
+      <window_info id="Terminal" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.33" sideWeight="0.5" order="7" side_tool="false" content_ui="tabs" />
       <window_info id="Hierarchy" active="false" anchor="right" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.25" sideWeight="0.5" order="2" side_tool="false" content_ui="combo" />
+      <window_info id="Project" active="false" anchor="left" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="true" show_stripe_button="true" weight="0.1587708" sideWeight="0.48809522" order="0" side_tool="false" content_ui="combo" />
+      <window_info id="Inspection Results" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.32943678" sideWeight="0.5" order="13" side_tool="false" content_ui="tabs" />
       <window_info id="Find" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.33" sideWeight="0.5" order="1" side_tool="false" content_ui="tabs" />
+      <window_info id="Structure" active="false" anchor="left" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.25" sideWeight="0.5" order="1" side_tool="false" content_ui="tabs" />
       <window_info id="Ant Build" active="false" anchor="right" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.25" sideWeight="0.5" order="1" side_tool="false" content_ui="tabs" />
+      <window_info id="Debug" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.39203355" sideWeight="0.5" order="3" side_tool="false" content_ui="tabs" />
+      <window_info id="Favorites" active="false" anchor="left" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.17477097" sideWeight="0.5119048" order="2" side_tool="true" content_ui="tabs" />
     </layout>
     <layout-to-restore>
       <window_info id="TODO" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.33" sideWeight="0.5" order="6" side_tool="false" content_ui="tabs" />
@@ -309,7 +342,7 @@
           </properties>
         </breakpoint>
       </default-breakpoints>
-      <option name="time" value="10" />
+      <option name="time" value="12" />
     </breakpoint-manager>
     <watches-manager />
   </component>
@@ -326,7 +359,9 @@
       <provider selected="true" editor-type-id="text-editor">
         <state relative-caret-position="345">
           <caret line="23" column="34" lean-forward="true" selection-start-line="23" selection-start-column="34" selection-end-line="23" selection-end-column="34" />
-          <folding />
+          <folding>
+            <marker date="1524887748000" expanded="true" signature="51:95" ph="..." />
+          </folding>
         </state>
       </provider>
     </entry>
@@ -350,7 +385,9 @@
       <provider selected="true" editor-type-id="text-editor">
         <state relative-caret-position="330">
           <caret line="22" column="20" lean-forward="true" selection-start-line="22" selection-start-column="20" selection-end-line="22" selection-end-column="20" />
-          <folding />
+          <folding>
+            <marker date="1524887748000" expanded="true" signature="294:317" ph="..." />
+          </folding>
         </state>
       </provider>
     </entry>
@@ -366,7 +403,9 @@
       <provider selected="true" editor-type-id="text-editor">
         <state relative-caret-position="840">
           <caret line="56" column="24" lean-forward="false" selection-start-line="56" selection-start-column="24" selection-end-line="56" selection-end-column="24" />
-          <folding />
+          <folding>
+            <marker date="1524887748000" expanded="true" signature="51:95" ph="..." />
+          </folding>
         </state>
       </provider>
     </entry>
@@ -390,7 +429,9 @@
       <provider selected="true" editor-type-id="text-editor">
         <state relative-caret-position="840">
           <caret line="56" column="0" lean-forward="true" selection-start-line="56" selection-start-column="0" selection-end-line="56" selection-end-column="0" />
-          <folding />
+          <folding>
+            <marker date="1524887748000" expanded="true" signature="294:317" ph="..." />
+          </folding>
         </state>
       </provider>
     </entry>
@@ -422,7 +463,9 @@
       <provider selected="true" editor-type-id="text-editor">
         <state relative-caret-position="345">
           <caret line="23" column="52" lean-forward="true" selection-start-line="23" selection-start-column="52" selection-end-line="23" selection-end-column="52" />
-          <folding />
+          <folding>
+            <marker date="1524887748000" expanded="true" signature="294:317" ph="..." />
+          </folding>
         </state>
       </provider>
     </entry>
@@ -430,7 +473,9 @@
       <provider selected="true" editor-type-id="text-editor">
         <state relative-caret-position="885">
           <caret line="59" column="22" lean-forward="false" selection-start-line="59" selection-start-column="22" selection-end-line="59" selection-end-column="22" />
-          <folding />
+          <folding>
+            <marker date="1524887748000" expanded="true" signature="51:95" ph="..." />
+          </folding>
         </state>
       </provider>
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@@ -462,7 +507,9 @@
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+          <folding>
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+          <folding>
+            <marker date="1524887748000" expanded="true" signature="51:95" ph="..." />
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+          <folding>
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+          <folding>
+            <marker date="1524887748000" expanded="true" signature="294:317" ph="..." />
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@@ -526,7 +579,9 @@
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+          <folding>
+            <marker date="1524887748000" expanded="true" signature="51:95" ph="..." />
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+          <folding>
+            <marker date="1524887748000" expanded="true" signature="294:317" ph="..." />
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@@ -627,23 +684,8 @@
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     </entry>
     <entry file="file://$PROJECT_DIR$/src/fnc/LocalLinearRegrassion.py" />
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-    </entry>
     <entry file="file://$PROJECT_DIR$/src/fnc/LocalLinearRegression.py" />
     <entry file="file://$USER_HOME$/Desktop/SysID.py" />
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-      <provider selected="true" editor-type-id="text-editor">
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@@ -651,51 +693,71 @@
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       </provider>
     </entry>
-    <entry file="file://$PROJECT_DIR$/src/fnc/LMPC.py">
+    <entry file="file:///Library/Python/2.7/site-packages/cvxopt/coneprog.py">
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diff --git a/Matlab/Lower_d.csv b/Matlab/Lower_d.csv
new file mode 100644
index 0000000..e7d8d47
--- /dev/null
+++ b/Matlab/Lower_d.csv
@@ -0,0 +1,6 @@
+-0.07927
+-0.023019
+-0.22604
+-0.030566
+0
+0
diff --git a/Matlab/Upper_d.csv b/Matlab/Upper_d.csv
new file mode 100644
index 0000000..00cecb6
--- /dev/null
+++ b/Matlab/Upper_d.csv
@@ -0,0 +1,6 @@
+0.11777
+0.014249
+0.17482
+0.038472
+0.24926
+0.041378
diff --git a/Matlab/Workspace.mat b/Matlab/Workspace.mat
index 78cd4d3..688cc31 100644
Binary files a/Matlab/Workspace.mat and b/Matlab/Workspace.mat differ
diff --git a/Matlab/main.m b/Matlab/main.m
index d20e153..48f5721 100644
--- a/Matlab/main.m
+++ b/Matlab/main.m
@@ -28,7 +28,7 @@
 BasisVector = W.V'
 NumBasic = size(BasisVector,2)
 %%
-SampledPoint = []
+SampledPoint = [zeros(6,1)]
 
 for i = 1:5000
     Point = zeros(6, 1);
@@ -112,4 +112,7 @@
 
 %%
 save('Workspace')
-[(sum(Checking))/size(Checking,1) (sum(Checking1))/size(Checking1,1)]
\ No newline at end of file
+[(sum(Checking))/size(Checking,1) (sum(Checking1))/size(Checking1,1)]
+
+csvwrite('Lower_d.csv',Lower_d)
+csvwrite('Upper_d.csv',Upper_d)
diff --git a/src/A.csv b/src/A.csv
index edf475b..7c4f12b 100644
--- a/src/A.csv
+++ b/src/A.csv
@@ -1,6 +1,6 @@
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--0.001194,0.051213,-0.000968,0.000619,0.000002,-0.000945
--0.034577,-0.023278,0.051117,0.024999,0.000252,0.075960
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diff --git a/src/B.csv b/src/B.csv
index 3532033..f4dd396 100644
--- a/src/B.csv
+++ b/src/B.csv
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-0.030004,0.118322
-0.255475,0.005134
-2.461203,0.036751
-0.181724,0.001875
-0.000450,0.007761
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diff --git a/src/Error.csv b/src/Error.csv
index 91ff2fd..b5e84ef 100644
--- a/src/Error.csv
+++ b/src/Error.csv
@@ -1,2 +1,2 @@
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--0.065760,-0.052656,-0.604120,-0.059533,-0.014188,-0.005731
+0.207061,0.024163,0.317387,0.054273,0.014816,0.005224
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diff --git a/src/LMPC_PathFollowing.npz b/src/LMPC_PathFollowing.npz
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diff --git a/src/MPC_PathFollowing.npz b/src/MPC_PathFollowing.npz
index 6369f9a..9682559 100644
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diff --git a/src/MPC_tv_PathFollowing.npz b/src/MPC_tv_PathFollowing.npz
index 1c76fb6..4ba464e 100644
Binary files a/src/MPC_tv_PathFollowing.npz and b/src/MPC_tv_PathFollowing.npz differ
diff --git a/src/PID_PathFollowing.npz b/src/PID_PathFollowing.npz
index a467c5a..4ea49a3 100644
Binary files a/src/PID_PathFollowing.npz and b/src/PID_PathFollowing.npz differ
diff --git a/src/Qfun.csv b/src/Qfun.csv
new file mode 100644
index 0000000..acc5259
--- /dev/null
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diff --git a/src/Sel_xQfun.csv b/src/Sel_xQfun.csv
new file mode 100644
index 0000000..123fe42
--- /dev/null
+++ b/src/Sel_xQfun.csv
@@ -0,0 +1,40 @@
+-12.000000
+-13.000000
+-14.000000
+-15.000000
+-16.000000
+-17.000000
+-18.000000
+-19.000000
+-20.000000
+-21.000000
+-22.000000
+-23.000000
+-24.000000
+-25.000000
+-26.000000
+-27.000000
+-28.000000
+-29.000000
+-30.000000
+-31.000000
+-9.000000
+-10.000000
+-11.000000
+-12.000000
+-13.000000
+-14.000000
+-15.000000
+-16.000000
+-17.000000
+-18.000000
+-19.000000
+-20.000000
+-21.000000
+-22.000000
+-23.000000
+-24.000000
+-25.000000
+-26.000000
+-27.000000
+-28.000000
diff --git a/src/fnc/FTOCP.py b/src/fnc/FTOCP.py
index 358483a..75786b5 100644
--- a/src/fnc/FTOCP.py
+++ b/src/fnc/FTOCP.py
@@ -1,5 +1,5 @@
 def FTOCP(M, q, G, L, E, F, b, x0, np, qp, matrix):
-    res_cons = qp(M, matrix(q), F, matrix(b), G, E * matrix(x0) + L)
+    res_cons = qp(M, matrix(q), F, matrix(b+np.dot(E, x0)), G,  matrix(L))
     if res_cons['status'] == 'optimal':
         feasible = 1
     else:
@@ -18,40 +18,43 @@ def BuildMatEqConst(A, B, C, N, n, d, np, spmatrix, TimeVarying):
     # We are going to build our optimization vector z \in \mathbb{R}^((N+1) \dot n \dot N \dot d), note that this vector
     # stucks the predicted trajectory x_{k|t} \forall k = t, \ldots, t+N+1 over the horizon and
     # the predicte input u_{k|t} \forall k = t, \ldots, t+N over the horizon
-    Gx = np.eye(n * (N + 1))
-    Gu = np.zeros((n * (N + 1), d * (N)))
+    Gx = np.eye(n * (N+1))
+    Gu = np.zeros((n * (N+1), d * (N)))
 
-    E = np.zeros((n * (N + 1), n))
-    E[np.arange(n)] = np.eye(n)
+    Ltot = np.zeros((n * (N+1), 1))
 
-    L = np.zeros((n * (N + 1), 1))
+    Etot = np.zeros((n * (N + 1), n))
+    Etot[np.arange(n)] = np.eye(n)
 
     for i in range(0, N):
-        ind1 = n + i * n + np.arange(n)
+        ind1 =  n + i * n + np.arange(n)
         ind2x = i * n + np.arange(n)
         ind2u = i * d + np.arange(d)
 
         if TimeVarying == 0:
             Gx[np.ix_(ind1, ind2x)] = -A
             Gu[np.ix_(ind1, ind2u)] = -B
-            L[ind1, :]              =  C
+            Ltot[ind1, :]           =  C
         else:
             Gx[np.ix_(ind1, ind2x)] = -A[i]
             Gu[np.ix_(ind1, ind2u)] = -B[i]
-            L[ind1, :]              =  C[i]
+            Ltot[ind1, :]           =  C[i]
 
-    G = np.hstack((Gx, Gu))
+    Gtot = np.hstack((Gx, Gu))
+
+    # Now select the rows related with model dynamics
+    G = Gtot[n:Gtot.shape[0], :]
+    L = Ltot[n:Ltot.shape[0]]
 
     # np.savetxt('G_MPC.csv', G, delimiter=',', fmt='%f')
     # np.savetxt('E_MPC.csv', E, delimiter=',', fmt='%f')
 
     G_sparse = spmatrix(G[np.nonzero(G)], np.nonzero(G)[0], np.nonzero(G)[1], G.shape)
-    E_sparse = spmatrix(E[np.nonzero(E)], np.nonzero(E)[0], np.nonzero(E)[1], E.shape)
     L_sparse = spmatrix(L[np.nonzero(L)], np.nonzero(L)[0], np.nonzero(L)[1], L.shape)
 
-    return G_sparse, E_sparse, L_sparse
+    return G_sparse, L_sparse
 
-def BuildMatIneqConst(N, n, np, linalg, spmatrix):
+def BuildMatIneqConst(N, n, np, linalg, spmatrix, Ke, Error_Bounds):
     # Buil the matrices for the state constraint in each region. In the region i we want Fx[i]x <= bx[b]
     Fx = np.array([[ 1., 0., 0., 0., 0., 0.],
                    [ 0., 0., 0., 0., 0., 1.],
@@ -62,6 +65,14 @@ def BuildMatIneqConst(N, n, np, linalg, spmatrix):
                    [ 2.]])# max ey
 
     # Buil the matrices for the input constraint in each region. In the region i we want Fx[i]x <= bx[b]
+    Fux = np.array([-Ke[0, :],  # Need to take into account  u_tot = -Kx + u
+                     Ke[0, :],  # Need to take into account -u_tot =  Kx - u
+                    -Ke[1, :],  # Need to take into account  u_tot = -Kx + u
+                     Ke[1, :]]) # Need to take into account -u_tot =  Kx - u
+
+    print "Fux ", np.squeeze(Fux)
+    print "Fx ", Fx
+
     Fu = np.array([[ 1., 0.],
                    [-1., 0.],
                    [ 0., 1.],
@@ -85,17 +96,44 @@ def BuildMatIneqConst(N, n, np, linalg, spmatrix):
     Futot = linalg.block_diag(*rep_b)
     butot = np.tile(np.squeeze(bu), N)
 
+    rep_c = [np.squeeze(Fux)] * (N)       # This parts considers that u_tot = -Kx + u
+    Mat1  = linalg.block_diag(*rep_c)
+    NoTerminalConstr_x_N = np.zeros((np.shape(Mat1)[0],n)) # No need to consider x_N as there is not u_N
+    Fxutot = np.hstack((Mat1, NoTerminalConstr_x_N))
+
+
     # Let's stack all together
     rFxtot, cFxtot = np.shape(Fxtot)
     rFutot, cFutot = np.shape(Futot)
     Dummy1 = np.hstack( (Fxtot                    , np.zeros((rFxtot,cFutot))))
-    Dummy2 = np.hstack( (np.zeros((rFutot,cFxtot)), Futot))
-    F = np.vstack( ( Dummy1, Dummy2) )
-    b = np.hstack((bxtot, butot))
+    Dummy2 = np.hstack( (Fxutot                   , Futot))
+    F_horizon = np.vstack( ( Dummy1, Dummy2) )
+    b_horizon = np.hstack((bxtot, butot))
+
+
+    # Now constraint x(t) - x_0 \in O_e, basically -x(t) + Lower_bound <= -x_0 <= -x(t) + Upper_bound
+    # --> -x_0 <= -x(t) + Upper_bound, x_0 <= x(t) - Lower_bound)
+    F_0 = np.zeros((2*n, F_horizon.shape[1]))
+    F_0[0:n,0:n]    = -np.eye(n)
+    F_0[n:2*n, 0:n] =  np.eye(n)
+
+    F = np.vstack((F_0, F_horizon))
+    Lower_bound = Error_Bounds[0]
+    Upper_bound = Error_Bounds[1]
+    b = np.hstack((Upper_bound, -Lower_bound, b_horizon))
+
+    E = np.zeros((F.shape[0], n))
+    E[0:n,0:n]   = -np.eye(n)
+    E[n:2*n,0:n] =  np.eye(n)
+
+    # np.savetxt('F_MPC.csv', F, delimiter=',', fmt='%f')
+    # np.savetxt('b_MPC.csv', b, delimiter=',', fmt='%f')
+    # np.savetxt('E_MPC.csv', E, delimiter=',', fmt='%f')
+
 
 
     F_sparse = spmatrix(F[np.nonzero(F)], np.nonzero(F)[0], np.nonzero(F)[1], F.shape)
-    return F_sparse, b
+    return F_sparse, b, E
 
 def BuildMatCost(Q, R, P, N, linalg, np, spmatrix, vt):
 
diff --git a/src/fnc/FTOCP.pyc b/src/fnc/FTOCP.pyc
index 5680488..2009a86 100644
Binary files a/src/fnc/FTOCP.pyc and b/src/fnc/FTOCP.pyc differ
diff --git a/src/fnc/LMPC.py b/src/fnc/LMPC.py
index b9102a1..046fa2a 100644
--- a/src/fnc/LMPC.py
+++ b/src/fnc/LMPC.py
@@ -1,21 +1,29 @@
-def LMPC(npG, L, npE, F, b, x0, np, qp, matrix, datetime, la, SS, Qfun, N, n, d, spmatrix, numSS_Points, Qslack, Q_LMPC, R_LMPC, it, swifth):
+def LMPC(npG, L, npE, E_LMPC, F, b, z0, x0, np, qp, matrix, datetime, la, zSS, xSS, Qfun, N, n, d, spmatrix, numSS_Points, Qslack, Q_LMPC, R_LMPC, it, swifth):
 
-    SS_Points1, Sel_Qfun1 = SelectPoints(SS, Qfun, it-1, x0, numSS_Points/2, np, la, swifth)
-    SS_Points2, Sel_Qfun2 = SelectPoints(SS, Qfun, it-2, x0, numSS_Points/2, np, la, swifth)
+    zSS_Points1, _ = SelectPoints(zSS, Qfun, it-1, z0, numSS_Points/2, np, la, swifth)
+    zSS_Points2, _ = SelectPoints(zSS, Qfun, it-2, z0, numSS_Points/2, np, la, swifth)
 
-    SS_Points = np.hstack((SS_Points1, SS_Points2))
+    zSS_Points = np.hstack((zSS_Points1, zSS_Points2))
 
-    Sel_Qfun = np.hstack((Sel_Qfun1, Sel_Qfun2))
+    xSS_Points1, Sel_xQfun1 = SelectPoints(xSS, Qfun, it-1, x0, numSS_Points/2, np, la, swifth)
+    xSS_Points2, Sel_xQfun2 = SelectPoints(xSS, Qfun, it-2, x0, numSS_Points/2, np, la, swifth)
 
+    xSS_Points = np.hstack((xSS_Points1, xSS_Points2))
 
-    G, E = LMPC_TermConstr(npG, npE, N, n, d, np, spmatrix, SS_Points)
+    Sel_xQfun = np.hstack((Sel_xQfun1, Sel_xQfun2))
 
-    M, q = LMPC_BuildMatCost(Sel_Qfun, numSS_Points, N, np, spmatrix, Qslack, Q_LMPC, R_LMPC)
+
+    G, E = LMPC_TermConstr(npG, npE, N, n, d, np, spmatrix, zSS_Points, xSS_Points)
+
+    M, q = LMPC_BuildMatCost(Sel_xQfun, numSS_Points, N, np, spmatrix, Qslack, Q_LMPC, R_LMPC)
 
     startTimer = datetime.datetime.now()
-    Sol, feasible = LMPC_FTOCP(M, q, G, L, E, F, b, x0, np, qp, matrix)
-    xPred, uPred, lambdPred, slack = LMPC_GetPred(Sol, n,d,N, np)
+    Sol, feasible = LMPC_FTOCP(M, q, G, L, E, E_LMPC, F, b, x0, np, qp, matrix)
+    zPred, uPred, xPred, lambdPred, slack = LMPC_GetPred(Sol, n,d,N, np)
 
+    if x0[4] > 18.5:
+        np.savetxt('xSS_Points.csv', xSS_Points, delimiter=',', fmt='%f')
+        np.savetxt('Sel_xQfun.csv', Sel_xQfun, delimiter=',', fmt='%f')
     # print SS_Points.shape, lambdPred.shape
     # print "Term Costr \n", np.dot(SS_Points, lambdPred),"\n", xPred[:,-1], "\n", xPred.T
     # print "Here lambda ", lambdPred, lambdPred.shape, np.dot(np.ones(lambdPred.shape[0]), lambdPred)
@@ -58,29 +66,44 @@ def ComputeCost(x, u, np, TrackLength):
     return Cost
 
 
-def LMPC_TermConstr(G, E, N ,n ,d ,np, spmatrix, SS_Points):
+def LMPC_TermConstr(G, E, N ,n ,d ,np, spmatrix, zSS_Points, xSS_Points):
     # Update the matrices for the Equality constraint in the LMPC. Now we need an extra row to constraint the terminal point to be equal to a point in SS
     # The equality constraint has now the form: G_LMPC*z = E_LMPC*x0 + TermPoint.
     # Note that the vector TermPoint is updated to constraint the predicted trajectory into a point in SS. This is done in the FTOCP_LMPC function
 
-    TermCons = np.zeros((n, (N + 1) * n + N * d))
-    TermCons[:, N * n:(N + 1) * n] = np.eye(n)
+    TermCons_z = np.zeros((n, 2 * (N + 1) * n + N * d))
+    TermCons_z[:,  N * n:(N + 1) * n] = np.eye(n)  # Constrain the terminal point for z
+
+    TermCons_x = np.zeros((n, 2*(N + 1) * n + N * d))
+    TermCons_x[:, (N + 1) * n + N * d + N * n: 2 * (N + 1) * n + N * d] = np.eye(n) # Constrain the terminal point for x
+
+    G_enlarged = np.vstack((G, TermCons_z, np.zeros((1,2*(N + 1) * n + N * d)), TermCons_x, np.zeros((1,2*(N + 1) * n + N * d)) ))
+
+    # np.savetxt('G_enlarged.csv', G_enlarged, delimiter=',', fmt='%f')
+
+    G_lambda_z = np.zeros(( n+1, 2*xSS_Points.shape[1] + 2*n))
+    G_lambda_z[0:n, 0:zSS_Points.shape[1]] = -zSS_Points
+    G_lambda_z[ -1, 0:zSS_Points.shape[1]] = np.ones((1,zSS_Points.shape[1]))
+    G_lambda_z[0:n, 2*zSS_Points.shape[1]:2*zSS_Points.shape[1]+n] = np.eye(6)
+
+    G_lambda_x = np.zeros((n + 1, 2 * xSS_Points.shape[1] + 2 * n))
+    G_lambda_x[0:n, xSS_Points.shape[1]:2 * xSS_Points.shape[1]] = -xSS_Points
+    G_lambda_x[-1, xSS_Points.shape[1]:2 * xSS_Points.shape[1]] = np.ones((1, xSS_Points.shape[1]))
+    G_lambda_x[0:n, 2 * xSS_Points.shape[1] + n:2 * xSS_Points.shape[1] + 2 * n] = np.eye(6)
 
-    G_enlarged = np.vstack((G, TermCons))
+    G_lambda = np.vstack(( np.zeros((G.shape[0], G_lambda_z.shape[1])), G_lambda_z, G_lambda_x ))
 
-    G_lambda = np.zeros(( G_enlarged.shape[0], SS_Points.shape[1] + n))
-    G_lambda[G_enlarged.shape[0] - n:G_enlarged.shape[0], :] = np.hstack((-SS_Points, np.eye(n)))
+    # np.savetxt('G_lambda.csv', G_lambda, delimiter=',', fmt='%f')
 
-    G_LMPC0 = np.hstack((G_enlarged, G_lambda))
-    G_ConHull = np.zeros((1, G_LMPC0.shape[1]))
-    G_ConHull[-1, G_ConHull.shape[1]-SS_Points.shape[1]-n:G_ConHull.shape[1]-n] = np.ones((1,SS_Points.shape[1]))
 
-    G_LMPC = np.vstack((G_LMPC0, G_ConHull))
+    G_LMPC = np.hstack((G_enlarged, G_lambda))
 
-    E_LMPC = np.vstack((E, np.zeros((n + 1, n))))
+    # print "Before term constr: ", E.shape
 
-    # np.savetxt('G.csv', G_LMPC, delimiter=',', fmt='%f')
-    # np.savetxt('E.csv', E_LMPC, delimiter=',', fmt='%f')
+    E_LMPC = E
+
+    # np.savetxt('Gtot.csv', G_LMPC, delimiter=',', fmt='%f')
+    # np.savetxt('E_LMPC.csv', E_LMPC, delimiter=',', fmt='%f')
 
     G_LMPC_sparse = spmatrix(G_LMPC[np.nonzero(G_LMPC)], np.nonzero(G_LMPC)[0], np.nonzero(G_LMPC)[1], G_LMPC.shape)
     E_LMPC_sparse = spmatrix(E_LMPC[np.nonzero(E_LMPC)], np.nonzero(E_LMPC)[0], np.nonzero(E_LMPC)[1], E_LMPC.shape)
@@ -100,29 +123,32 @@ def LMPC_BuildMatCost(Sel_Qfun, numSS_Points, N, np, spmatrix, Qslack, Q, R):
     c = [R] * (N)
     Mu = linalg.block_diag(*c)
 
-    M00 = linalg.block_diag(Mx, P, Mu)
-    M0  = linalg.block_diag(M00, np.zeros((numSS_Points, numSS_Points)), Qslack)
+    M00 = linalg.block_diag(Mx, P, Mu, Mx, P)
+    M0  = linalg.block_diag(M00, np.zeros((numSS_Points, numSS_Points)), np.zeros((numSS_Points, numSS_Points)), Qslack, Qslack)
     xtrack = np.array([vt, 0, 0, 0, 0, 0])
-    q0 = - 2 * np.dot(np.append(np.tile(xtrack, N+1), np.zeros(R.shape[0]*N)), M00)
+    # print np.append(np.zeros(Q.shape[0]*(N+1) + R.shape[0]*N), np.tile(xtrack, N+1)).shape, M00.shape
+    q0 = - 2 * np.dot(np.append(np.zeros(Q.shape[0]*(N+1) + R.shape[0]*N), np.tile(xtrack, N+1)), M00)
     # print q0.shape, Sel_Qfun.shape, Q.shape[0], np.zeros(Q.shape[0]).shape
-    q  = np.append(np.append(q0, Sel_Qfun), np.zeros(Q.shape[0]))
 
-    # np.savetxt('q.csv', q, delimiter=',', fmt='%f')
+    q  = np.append(np.append(np.append(q0, 0*Sel_Qfun), Sel_Qfun), np.zeros(2*Q.shape[0]) )
 
     M = 2 * M0  # Need to multiply by two because CVX considers 1/2 in front of quadratic cost
 
+    # np.savetxt('q.csv', q, delimiter=',', fmt='%f')
+    # np.savetxt('M.csv', M, delimiter=',', fmt='%f')
+
     M_sparse = spmatrix(M[np.nonzero(M)], np.nonzero(M)[0], np.nonzero(M)[1], M.shape)
     return M_sparse, q
 
-def LMPC_FTOCP(M, q, G, L, E, F, b, x0, np, qp, matrix):
+def LMPC_FTOCP(M, q, G, L, E, E_LMPC, F, b, x0, np, qp, matrix):
     from numpy.linalg import matrix_rank
     G_cvx = F
     A_cvx = G
 
     # print A_cvx.size, G_cvx.size
-    # print M.size,  matrix(q).size, F.size, matrix(b).size, G.size, E.size, L.size
-
-    res_cons = qp(M, matrix(q), F, matrix(b), G, E * matrix(x0) + L)
+    # print M.size,  matrix(q).size, F.size, matrix(b).size, np.dot(E_LMPC, x0).shape, G.size, L.size
+#    print G.size, E.size, np.dot(E, x0).size
+    res_cons = qp(M, matrix(q),         F, matrix(b + np.dot(E_LMPC, x0)),           G, L + E * matrix(x0))
     if res_cons['status'] == 'optimal':
         feasible = 1
     else:
@@ -131,36 +157,75 @@ def LMPC_FTOCP(M, q, G, L, E, F, b, x0, np, qp, matrix):
     return np.squeeze(res_cons['x']), feasible
 
 
-def LMPC_BuildMatEqConst(A, B, C, N, n, d, np, spmatrix, TimeVarying):
+def LMPC_BuildMatEqConst(Ax, Bx, A, B, C, N, n, d, np, spmatrix, Ke, linalg):
+    from numpy import linalg as LA
     # Buil matrices for optimization (Convention from Chapter 15.2 Borrelli, Bemporad and Morari MPC book)
     # We are going to build our optimization vector z \in \mathbb{R}^((N+1) \dot n \dot N \dot d), note that this vector
     # stucks the predicted trajectory x_{k|t} \forall k = t, \ldots, t+N+1 over the horizon and
     # the predicte input u_{k|t} \forall k = t, \ldots, t+N over the horizon
     Gx = np.eye(n * (N + 1))
-    Gu = np.zeros((n * (N + 1), d * (N)))
+    Gxu = np.zeros((n * (N + 1), d * (N)))
+
+    Gz  = np.eye(n * (N + 1))
+    Gze = np.zeros((n * (N + 1),n * (N + 1)))
+    Gzu = np.zeros((n * (N + 1), d * (N)))
 
-    E = np.zeros((n * (N + 1), n))
-    E[np.arange(n)] = np.eye(n)
 
-    L = np.zeros((n * (N + 1) + n + 1, 1)) # n+1 for the terminal constraint
-    L[-1] = 1 # Summmation of lamba must add up to 1
+    Lold      = np.zeros((n * (N + 1), 1))
+    ErrorProp = np.zeros((n * (N + 1), n))
 
     for i in range(0, N):
         ind1 = n + i * n + np.arange(n)
         ind2x = i * n + np.arange(n)
         ind2u = i * d + np.arange(d)
 
-        if TimeVarying == 0:
-            Gx[np.ix_(ind1, ind2x)] = -A
-            Gu[np.ix_(ind1, ind2u)] = -B
-            L[ind1, :]              =  C
+        Gx[np.ix_(ind1, ind2x)]  = -Ax
+        Gxu[np.ix_(ind1, ind2u)] = -Bx
+
+        Gz[np.ix_(ind1, ind2x)]             = -A[i]
+        if i == 0:
+            Gze[np.ix_(ind1, ind2x)]        =  np.dot(B[i], Ke) - np.dot(np.dot(B[i], Ke), LA.matrix_power(Ax, i))
         else:
-            Gx[np.ix_(ind1, ind2x)] = -A[i]
-            Gu[np.ix_(ind1, ind2u)] = -B[i]
-            L[ind1, :]              =  C[i]
+            Gze[np.ix_(ind1, ind2x)]        =  np.dot(B[i], Ke)
+            Gze[np.ix_(ind1, np.arange(n))] = -np.dot(np.dot(B[i], Ke), LA.matrix_power(Ax, i))
+        ErrorProp[ind1, :]                  = -np.dot(np.dot(B[i], Ke), LA.matrix_power(Ax, i))
+        Gzu[np.ix_(ind1, ind2u)]            = -B[i]
+        Lold[ind1, :]                       =  C[i]
 
-    G = np.hstack((Gx, Gu))
+    L = np.vstack(( np.zeros((n*N,1)), Lold[n:n * (N + 1) + 2*(n + 1),:], np.zeros((n,1)),np.zeros((2*(n+1),1)) ))# 2*(n+1) for the terminal constraints
+    sizeL = L.shape[0]
+    L[sizeL -(n + 1) - 1] = 1  # Summmation of lamba for x must add up to 1
+    L[sizeL - 1] = 1  # Summmation of lamba for z must add up to 1
 
+    E = np.vstack(( np.zeros((n*N,n)), ErrorProp[n:n * (N + 1) + 2*(n + 1),:], np.zeros((n,n)),np.zeros((2*(n+1),n)) ))# 2*(n+1) for the terminal constraints
+
+    # print "Shape L :", L.shape
+    # np.savetxt('L.csv', L, delimiter=',', fmt='%f')
+
+    Gxtot = np.hstack((Gx, Gxu))
+    Gztot = np.hstack((Gzu, Gz)) # Note that for z is need to put the input first as these are the same which are applied to x
+
+    Zeros = np.zeros((n * N, n*(N+1)))
+
+    InitialCond = np.zeros((n, 2*n * (N + 1) + d * (N)))
+    InitialCond[:, 0:n]                                           =  np.eye(n)
+    InitialCond[:, n * (N + 1) + d * (N):n * (N + 1) + d * (N)+n] = -np.eye(n)
+
+    # print InitialCond.shape
+    # print np.hstack((Gxtot[n:n * (N + 1), :],                              Zeros)).shape
+    # print np.hstack((                  Zeros, Gztot[n:n * (N + 1), :])).shape
+
+    FeedbackTerm = Gze[n:n * (N + 1), :]
+    # np.savetxt('Gze.csv', Gze, delimiter=',', fmt='%f')
+    # np.savetxt('Gz.csv', Gz, delimiter=',', fmt='%f')
+    # print np.hstack((           FeedbackTerm, Gztot[n:n * (N + 1), :])).shape
+    G = np.vstack((np.hstack((Gxtot[n:n * (N + 1), :],                   Zeros)),
+                   np.hstack((           FeedbackTerm, Gztot[n:n * (N + 1), :])),
+                   InitialCond))
+
+    # np.savetxt('G_LMPC.csv', G, delimiter=',', fmt='%f')
+    # np.savetxt('Eprop_LMPC.csv', E, delimiter=',', fmt='%f')
+    # np.savetxt('L.csv', L, delimiter=',', fmt='%f')
 
     G_sparse = spmatrix(G[np.nonzero(G)], np.nonzero(G)[0], np.nonzero(G)[1], G.shape)
     E_sparse = spmatrix(E[np.nonzero(E)], np.nonzero(E)[0], np.nonzero(E)[1], E.shape)
@@ -169,15 +234,15 @@ def LMPC_BuildMatEqConst(A, B, C, N, n, d, np, spmatrix, TimeVarying):
     return G_sparse, E_sparse, L_sparse, G, E
 
 
-def LMPC_BuildMatIneqConst(N, n, np, linalg, spmatrix, numSS_Points):
+def LMPC_BuildMatIneqConst(N, n, np, linalg, spmatrix, numSS_Points, Error_Bounds, Ke):
     # Buil the matrices for the state constraint in each region. In the region i we want Fx[i]x <= bx[b]
     Fx = np.array([[ 1., 0., 0., 0., 0., 0.],
                    [ 0., 0., 0., 0., 0., 1.],
                    [ 0., 0., 0., 0., 0.,-1.]])
 
     bx = np.array([[ 3.], # vx max
-                   [ 0.8], # max ey
-                   [ 0.8]])# max ey
+                   [ 1.8], # max ey
+                   [ 1.8]])# max ey
 
     # Buil the matrices for the input constraint in each region. In the region i we want Fx[i]x <= bx[b]
     Fu = np.array([[ 1., 0.],
@@ -187,8 +252,14 @@ def LMPC_BuildMatIneqConst(N, n, np, linalg, spmatrix, numSS_Points):
 
     bu = np.array([[ 0.5],  # Max Steering
                    [ 0.5],  # Max Steering
-                   [ 1.],  # Max Acceleration
-                   [ 1.]]) # Max Acceleration
+                   [ 2.],  # Max Acceleration
+                   [ 2.]]) # Max Acceleration
+
+    # Buil the matrices for the input constraint in each region. In the region i we want Fx[i]x <= bx[b]
+    Fux = np.array([-Ke[0, :],  # Need to take into account  u_tot = -Kx + u
+                     Ke[0, :],  # Need to take into account -u_tot =  Kx - u
+                    -Ke[1, :],  # Need to take into account  u_tot = -Kx + u
+                     Ke[1, :]]) # Need to take into account -u_tot =  Kx - u
 
     # Now stuck the constraint matrices to express them in the form Fz<=b. Note that z collects states and inputs
     # Let's start by computing the submatrix of F relates with the state
@@ -203,31 +274,53 @@ def LMPC_BuildMatIneqConst(N, n, np, linalg, spmatrix, numSS_Points):
     Futot = linalg.block_diag(*rep_b)
     butot = np.tile(np.squeeze(bu), N)
 
+    rep_c = [np.squeeze(Fux)] * (N)       # This parts considers that u_tot = -Kx + u
+    Mat1  = linalg.block_diag(*rep_c)
+    NoTerminalConstr_x_N = np.zeros((np.shape(Mat1)[0],n)) # No need to consider x_N as there is not u_N
+    Fxutot = np.hstack((Mat1, NoTerminalConstr_x_N))
+
+
     # Let's stack all together
     rFxtot, cFxtot = np.shape(Fxtot)
     rFutot, cFutot = np.shape(Futot)
-    Dummy1 = np.hstack( (Fxtot                    , np.zeros((rFxtot,cFutot))))
-    Dummy2 = np.hstack( (np.zeros((rFutot,cFxtot)), Futot))
+    Dummy1 = np.hstack( (Fxtot  , np.zeros((rFxtot,cFutot))))
+    Dummy2 = np.hstack( (Fxutot , Futot))
 
-    FDummy = np.vstack( ( Dummy1, Dummy2) )
+    FDummy = np.hstack((np.vstack( ( Dummy1, Dummy2)), np.zeros( (rFxtot + rFutot, cFxtot) ) ))
     I = -np.eye(numSS_Points)
 
-    FDummy2 = linalg.block_diag( FDummy, I )
+    FDummy2 = linalg.block_diag( FDummy, I, I ) # Make sure the lambda are => 0
+
+    Fslack = np.zeros((FDummy2.shape[0], 2*n)) # Adding terms related with the slack variable associated with the terminal constraint
+
+    F_horizon = np.hstack((FDummy2, Fslack))
+    b_horizon = np.hstack((bxtot, butot, np.zeros(2*numSS_Points)))
 
-    Fslack = np.zeros((FDummy2.shape[0], n))
+    # Now constraint x(t) - x_0 \in O_e, basically -x(t) + Lower_bound <= -x_0 <= -x(t) + Upper_bound
+    # --> -x_0 <= -x(t) + Upper_bound, x_0 <= x(t) - Lower_bound)
+    F_0 = np.zeros((2 * n, F_horizon.shape[1]))
+    F_0[0:n, 0:n] = -np.eye(n)
+    F_0[n:2 * n, 0:n] = np.eye(n)
 
-    F = np.hstack((FDummy2, Fslack))
+    F = np.vstack((F_0, F_horizon))
+    Lower_bound = Error_Bounds[0]
+    Upper_bound = Error_Bounds[1]
+    b = np.hstack((Upper_bound, -Lower_bound, b_horizon))
 
     # np.savetxt('F.csv', F, delimiter=',', fmt='%f')
+    # np.savetxt('b.csv', b, delimiter=',', fmt='%f')
 
-    b = np.hstack((bxtot, butot, np.zeros(numSS_Points)))
+    E = np.zeros((F.shape[0], n))
+    E[0:n,0:n]   = -np.eye(n)
+    E[n:2*n,0:n] =  np.eye(n)
 
     F_sparse = spmatrix(F[np.nonzero(F)], np.nonzero(F)[0], np.nonzero(F)[1], F.shape)
-    return F_sparse, b
+    return F_sparse, b, E
 
 def LMPC_GetPred(Solution,n,d,N, np):
-    xPred = np.squeeze(np.transpose(np.reshape((Solution[np.arange(n*(N+1))]),(N+1,n))))
+    zPred = np.squeeze(np.transpose(np.reshape((Solution[np.arange(n*(N+1))]),(N+1,n))))
     uPred = np.squeeze(np.transpose(np.reshape((Solution[n*(N+1)+np.arange(d*N)]),(N, d))))
-    lambd = Solution[n*(N+1)+d*N:Solution.shape[0]-n]
-    slack = Solution[Solution.shape[0]-n:]
-    return xPred, uPred, lambd, slack
\ No newline at end of file
+    xPred = np.squeeze(np.transpose(np.reshape((Solution[n*(N+1)+d*N + np.arange(n * (N + 1))]), (N + 1, n))))
+    lambd = Solution[2*n*(N+1)+d*N:Solution.shape[0]-2*n]
+    slack = Solution[Solution.shape[0]-2*n:]
+    return zPred, uPred, xPred, lambd, slack
\ No newline at end of file
diff --git a/src/fnc/LMPC.pyc b/src/fnc/LMPC.pyc
index e7cba06..db438ef 100644
Binary files a/src/fnc/LMPC.pyc and b/src/fnc/LMPC.pyc differ
diff --git a/src/fnc/SysID.py b/src/fnc/SysID.py
index c484397..e7c2edc 100644
--- a/src/fnc/SysID.py
+++ b/src/fnc/SysID.py
@@ -8,7 +8,7 @@ def LMPC_EstimateABC(LinPoints, LinInput, N, n, d, SS, uSS, TimeSS, qp, matrix,
     usedIt = range(it-2,it)
 
     for i in range(0, N):
-        MaxNumPoint = 40 # Need to reason on how these points are selected
+        MaxNumPoint = 80 # Need to reason on how these points are selected
         x0 = LinPoints[i, :]
 
         Ai = np.zeros((n, n))
@@ -16,7 +16,7 @@ def LMPC_EstimateABC(LinPoints, LinInput, N, n, d, SS, uSS, TimeSS, qp, matrix,
         Ci = np.zeros((n, 1))
 
         # Compute Index to use
-        h = 5
+        h = 7
         lamb = 0.0
         stateFeatures = [0, 1, 2]
         ConsiderInput = 1
@@ -71,6 +71,7 @@ def LMPC_EstimateABC(LinPoints, LinInput, N, n, d, SS, uSS, TimeSS, qp, matrix,
 
         if s<0:
             print "s is negative, here the state: \n", LinPoints
+            s=0
 
         startTimer = datetime.datetime.now()  # Start timer for LMPC iteration
         cur = Curvature(s, PointAndTangent)
@@ -226,7 +227,7 @@ def ComputeIndex(h, SS, uSS, TimeSS, it, x0, stateFeatures, scaling, MaxNumPoint
 
     return index, K
 
-def EstimateABC(LinPoints, N, n, d, x, u, qp, matrix, PointAndTangent, dt):
+def EstimateABC(LinPoints, N, n, d, x, u, qp, matrix, PointAndTangent, dt, Ke):
     import numpy as np
     from SysModel import Curvature
 
@@ -294,6 +295,7 @@ def EstimateABC(LinPoints, N, n, d, x, u, qp, matrix, PointAndTangent, dt):
 
         if s<0:
             print "s is negative, here the state: \n", LinPoints
+            s = 0
 
         cur = Curvature(s, PointAndTangent)
         den = 1 - cur *ey
@@ -305,7 +307,7 @@ def EstimateABC(LinPoints, N, n, d, x, u, qp, matrix, PointAndTangent, dt):
         depsi_wz   =      dt
         depsi_epsi =  1 - dt * ( -vx * np.sin(epsi) - vy * np.cos(epsi) ) / den * cur
         depsi_s    =      0                                                                      # Because cur = constant
-        depsi_ey   =    - dt * (vx * np.cos(epsi) - vy * np.sin(epsi)) / (den**2) * cur * (-cur)
+        depsi_ey   =      dt * (vx * np.cos(epsi) - vy * np.sin(epsi)) / (den**2) * cur * (-cur)
 
         Ai[3, :]   = [depsi_vx, depsi_vy, depsi_wz, depsi_epsi, depsi_s, depsi_ey]
 
@@ -317,7 +319,7 @@ def EstimateABC(LinPoints, N, n, d, x, u, qp, matrix, PointAndTangent, dt):
         ds_wz    =  0
         ds_epsi  =  dt * (-vx * np.sin(epsi) - vy * np.cos(epsi)) / den
         ds_s     = 1 #+ Ts * (Vx * cos(epsi) - Vy * sin(epsi)) / (1 - ey * rho) ^ 2 * (-ey * drho);
-        ds_ey    =  dt * ( vx * np.cos(epsi) - vy * np.sin(epsi)) / (( den )**2)* (-cur)
+        ds_ey    = -dt * ( vx * np.cos(epsi) - vy * np.sin(epsi)) / ( den*2)* (-cur)
 
         Ai[4, :] = [ds_vx, ds_vy, ds_wz, ds_epsi, ds_s, ds_ey]
 
@@ -333,7 +335,7 @@ def EstimateABC(LinPoints, N, n, d, x, u, qp, matrix, PointAndTangent, dt):
 
         Ai[5, :] = [dey_vx, dey_vy, dey_wz, dey_epsi, dey_s, dey_ey]
 
-        Atv.append(Ai)
+        Atv.append(Ai-Bi*Ke)
         Btv.append(Bi)
         Ctv.append(Ci)
 
diff --git a/src/fnc/SysID.pyc b/src/fnc/SysID.pyc
index 9d0bd35..8317055 100644
Binary files a/src/fnc/SysID.pyc and b/src/fnc/SysID.pyc differ
diff --git a/src/fnc/SysModel.pyc b/src/fnc/SysModel.pyc
index f64cd82..f76b4e4 100644
Binary files a/src/fnc/SysModel.pyc and b/src/fnc/SysModel.pyc differ
diff --git a/src/fnc/Track.pyc b/src/fnc/Track.pyc
index ccc1f73..ad14e8e 100644
Binary files a/src/fnc/Track.pyc and b/src/fnc/Track.pyc differ
diff --git a/src/main.py b/src/main.py
index 44e9351..10107f9 100644
--- a/src/main.py
+++ b/src/main.py
@@ -4,7 +4,7 @@
 from FTOCP import BuildMatEqConst, BuildMatCost, BuildMatIneqConst, FTOCP, GetPred
 from Track import CreateTrack, Evaluate_e_ey
 from SysID import LocLinReg, Regression, EstimateABC, LMPC_EstimateABC
-from LMPC import LMPC, ComputeCost, LMPC_BuildMatEqConst, LMPC_BuildMatIneqConst
+from LMPC import LMPC, ComputeCost, LMPC_BuildMatEqConst, LMPC_BuildMatIneqConst, LMPC_GetPred
 from InvariantSets import PropagatePoly, GenerateW, Invariance
 import numpy as np
 import matplotlib.pyplot as plt
@@ -26,15 +26,41 @@
 solvers.options['show_progress'] = False
 # CHOOSE WHAT TO RUN
 RunPID     = 0; plotFlag       = 0
-RunMPC     = 0; plotFlagMPC    = 1
+RunMPC     = 0; plotFlagMPC    = 0
 RunMPC_tv  = 0; plotFlagMPC_tv = 0
 RunLMPC    = 1; plotFlagLMPC   = 1
 
+Lower_d = np.array([-0.0793, -0.0230, -0.2260, -0.0306, 0.0000, 0.0000])
+Upper_d = np.array([ 0.1178,  0.0142,  0.1748,  0.0385, 0.2493, 0.0414])
+Error_Bounds = [Lower_d, Upper_d]
+print Error_Bounds[0]
+print Error_Bounds[1]
+
+def dlqr(A, B, Q, R):
+    """Solve the discrete time lqr controller. From MWM website
+
+
+    x[k+1] = A x[k] + B u[k]
+
+    cost = sum x[k].T*Q*x[k] + u[k].T*R*u[k]
+    """
+    # ref Bertsekas, p.151
+
+    # first, try to solve the ricatti equation
+    X = np.matrix(scipy.linalg.solve_discrete_are(A, B, Q, R))
+
+    # compute the LQR gain
+    K = np.matrix(scipy.linalg.inv(B.T * X * B + R) * (B.T * X * A))
+
+    eigVals, eigVecs = scipy.linalg.eig(A - B * K)
+
+    return K, X, eigVals
+
 # ======================================================================================================================
 # ====================================== INITIALIZE PARAMETERS =========================================================
 # ======================================================================================================================
 dt = 1.0/10.0                      # Controller discretization time
-Time = 100                          # Simulation time
+Time = 100                         # Simulation time
 Points = int(Time/dt)              # Number of points in the simulation
 u = np.zeros((Points, 2))          # Initialize the input vector
 x      = np.zeros((Points+1, 6))   # Initialize state vector (In curvilinear abscissas)
@@ -42,7 +68,7 @@
 vt = 0.8
 
 x[0,0] = 0.5; x_glob[0,0] = 0.5
-x[0,4] = 0.5; x_glob[0,4] = 0.5
+x[0,4] = 0.0; x_glob[0,4] = 0.0
 # Create the track. The vector PointAndTangent = [xf yf]
 PointAndTangent, TrackLength = CreateTrack()
 # ======================================================================================================================
@@ -74,6 +100,11 @@
 # np.savetxt('B.csv', B, delimiter=',', fmt='%f')
 #
 # W = GenerateW(Error*SafetyFactor)
+Q = np.eye(6)
+R = 100*np.eye(2)
+Ke, _, _ = dlqr(A,B,Q,R)
+
+Acl = A-B*Ke
 
 #rho = 0.1
 #max_r = 10
@@ -85,21 +116,24 @@
 d = 2
 N = 12
 
-Q = np.diag([1.0, 1.0, 1, 1, 0.0, 100.0]) # vx, vy, wz, epsi, s, ey
-R = np.diag([1.0, 10.0]) # delta, a
+Q = np.diag([500.0, 1.0, 1, 1, 0.0, 100.0]) # vx, vy, wz, epsi, s, ey
+R = np.diag([1.0, 0.1]) # delta, a
 
 M, q    = BuildMatCost(Q, R, Q, N, linalg, np, spmatrix, vt)
-F, b    = BuildMatIneqConst(N, n, np, linalg, spmatrix)
-G, E, L = BuildMatEqConst(A, B, np.zeros((n,1)), N, n, d, np, spmatrix, 0)
+F, b, E = BuildMatIneqConst(N, n, np, linalg, spmatrix, Ke, Error_Bounds)
+G, L    = BuildMatEqConst(Acl, B, np.zeros((n,1)), N, n, d, np, spmatrix, 0)
 
 # Initialize
-TimeMPC = 100                             # Simulation time
+TimeMPC = 100                            # Simulation time
 PointsMPC = int(TimeMPC / dt)            # Number of points in the simulation
 uMPC = np.zeros((PointsMPC, 2))          # Initialize the input vector
 xMPC      = np.zeros((PointsMPC+1, 6))   # Initialize state vector (In curvilinear abscissas)
+zMPC      = np.zeros((PointsMPC+1, 6))   # Initialize state vector (In curvilinear abscissas)
 x_globMPC = np.zeros((PointsMPC+1, 6))   # Initialize the state vector in absolute reference frame
 
 xMPC[0,:] = x[0,:]
+zMPC[0,:] = x[0,:]
+
 x_globMPC[0,:] = x_glob[0,:]
 # Time loop
 if RunMPC == 1:
@@ -110,8 +144,10 @@
         endTimer = datetime.datetime.now(); deltaTimer = endTimer - startTimer
 
         xPred, uPred = GetPred(Sol, n, d, N, np)
-        uMPC[i, :] = uPred[:, 0]
+
+        uMPC[i, :] = uPred[:, 0] - np.dot(Ke,xMPC[i, :])
         xMPC[i+1, :], x_globMPC[i+1, :] = DynModel(xMPC[i, :], x_globMPC[i, :], uMPC[i, :], np, dt, PointAndTangent)
+        zMPC[i+1, :] = xPred[:, 0]
 
         if i <= 5:
             print("Solver time: %.4fs" % (deltaTimer.total_seconds()))
@@ -124,10 +160,11 @@
 
             break
 
-    np.savez('MPC_PathFollowing', x=xMPC, u=uMPC, x_glob=x_globMPC)
+    np.savez('MPC_PathFollowing', x=xMPC, z=zMPC, u=uMPC, x_glob=x_globMPC)
 else:
     data = np.load('MPC_PathFollowing.npz')
     xMPC      = data['x']
+    zMPC      = data['z']
     uMPC      = data['u']
     x_globMPC = data['x_glob']
 
@@ -137,13 +174,16 @@
 # ===================================  LOCAL LINEAR REGRESSION =========================================================
 # ======================================================================================================================
 # Initialize
-TimeMPC_tv = 100                             # Simulation time
+TimeMPC_tv = 50                             # Simulation time
 PointsMPC_tv = int(TimeMPC_tv / dt)            # Number of points in the simulation
 uMPC_tv = np.zeros((PointsMPC_tv, 2))          # Initialize the input vector
 xMPC_tv      = np.zeros((PointsMPC_tv+1, 6))   # Initialize state vector (In curvilinear abscissas)
+zMPC_tv      = np.zeros((PointsMPC_tv+1, 6))   # Initialize state vector (In curvilinear abscissas)
 x_globMPC_tv = np.zeros((PointsMPC_tv+1, 6))   # Initialize the state vector in absolute reference frame
 
 xMPC_tv[0,:] = x[0,:]
+zMPC_tv[0,:] = x[0,:]
+
 x_globMPC_tv[0,:] = x_glob[0,:]
 # Time loop
 LinPoints = x[0:N+1,:]
@@ -154,11 +194,11 @@
 
         startTimer = datetime.datetime.now() # Start timer for LMPC iteration
         if i == 0:
-            F, b = BuildMatIneqConst(N, n, np, linalg, spmatrix)
-            G, E, L = BuildMatEqConst(A, B, np.zeros((n, 1)), N, n, d, np, spmatrix, 0)
+            F, b, E = BuildMatIneqConst(N, n, np, linalg, spmatrix, Ke, Error_Bounds)
+            G, L = BuildMatEqConst(Acl, B, np.zeros((n, 1)), N, n, d, np, spmatrix, 0)
         else:
-            Atv, Btv, Ctv = EstimateABC(LinPoints, N, n, d, x, u, qp, matrix, PointAndTangent, dt)
-            G, E, L = BuildMatEqConst(Atv, Btv, Ctv, N, n, d, np, spmatrix, 1)
+            Atv_cl, Btv, Ctv = EstimateABC(LinPoints, N, n, d, x, u, qp, matrix, PointAndTangent, dt, Ke)
+            G, L = BuildMatEqConst(Atv_cl, Btv, Ctv, N, n, d, np, spmatrix, 1)
         endTimer = datetime.datetime.now(); deltaTimer_tv = endTimer - startTimer
 
         startTimer = datetime.datetime.now() # Start timer for LMPC iteration
@@ -167,8 +207,9 @@
 
         xPred, uPred = GetPred(Sol, n, d, N, np)
         LinPoints = xPred.T
-        uMPC_tv[i, :] = uPred[:, 0]
+        uMPC_tv[i, :] = uPred[:, 0] - np.dot(Ke,xMPC_tv[i, :])
         xMPC_tv[i+1, :], x_globMPC_tv[i+1, :] = DynModel(xMPC_tv[i, :], x_globMPC_tv[i, :], uMPC_tv[i, :], np, dt, PointAndTangent)
+        zMPC_tv[i+1, :] = xPred[:, 0]
 
         if i <= 5:
             print("Linearization time: %.4fs Solver time: %.4fs" % (deltaTimer_tv.total_seconds(), deltaTimer.total_seconds()))
@@ -179,10 +220,11 @@
             print "Unfeasible at time ", i*dt
             break
 
-    np.savez('MPC_tv_PathFollowing', x=xMPC_tv, u=uMPC_tv, x_glob=x_globMPC_tv)
+    np.savez('MPC_tv_PathFollowing', x=xMPC_tv, z=zMPC_tv, u=uMPC_tv, x_glob=x_globMPC_tv)
 else:
     data = np.load('MPC_tv_PathFollowing.npz')
     xMPC_tv      = data['x']
+    zMPC_tv      = data['z']
     uMPC_tv      = data['u']
     x_globMPC_tv = data['x_glob']
 
@@ -195,45 +237,59 @@
 # Initialize
 PlotIndex  = 0
 PlotPred   = 0
-TimeLMPC   = 400                             # Simulation time
+TimeLMPC   = 800                             # Simulation time
 PointsLMPC = int(TimeLMPC / dt)            # Number of points in the simulation
 uLMPC = np.zeros((PointsLMPC, 2))          # Initialize the input vector
 xLMPC      = np.zeros((PointsLMPC+1, 6))   # Initialize state vector (In curvilinear abscissas)
+zLMPC      = np.zeros((PointsLMPC+1, 6))   # Initialize state vector (In curvilinear abscissas)
 x_globLMPC = np.zeros((PointsLMPC+1, 6))   # Initialize the state vector in absolute reference frame
-Laps       = 5
+Laps       = 10
 
 xLMPC[0,:] = x[0,:]
+zLMPC[0,:] = x[0,:]
+z0 = x[0,:]
 x_globLMPC[0,:] = x_glob[0,:]
 # Time loop
-LinPoints = xMPC_tv[0:N+1,:]
+LinPoints = xMPC_tv[0:N+1, :]
+LinInput  = uMPC_tv[0:N, :]
 
-numSS_Points = 30
+numSS_Points = 40
 swifth = N-1
 
 TimeSS = 10000*np.ones(Laps+2)
-SS     = 10000*np.ones((2*xMPC_tv.shape[0], 6, Laps+2))
+xSS    = 10000*np.ones((2*xMPC_tv.shape[0], 6, Laps+2))
+zSS    = 10000*np.ones((2*xMPC_tv.shape[0], 6, Laps+2))
 uSS    = 10000*np.ones((2*xMPC_tv.shape[0], 2, Laps+2))
 Qfun   = 0*np.ones((2*xMPC_tv.shape[0], Laps+2)) # Need to initialize at zero as adding point on the fly
 
 # Adding Trajectory to safe set iteration 0
 TimeSS[0] = x.shape[0]
-SS[0:TimeSS[0],:, 0]  = x
-uSS[0:TimeSS[0]-1,:, 0]  = u
-Qfun[0:TimeSS[0], 0] = ComputeCost(x, u, np, TrackLength)
+xSS[0:TimeSS[0],:, 0]  = xMPC
+zSS[0:TimeSS[0],:, 0]  = zMPC
+uSS[0:TimeSS[0]-1,:, 0]  = uMPC
+Qfun[0:TimeSS[0], 0] = ComputeCost(xMPC, uMPC, np, TrackLength)
+for i in np.arange(0, Qfun.shape[0]):
+    if Qfun[i, 0] == 0:
+        Qfun[i, 0] = Qfun[i-1, 0] - 1
 
 # Adding Trajectory to safe set iteration 1
 TimeSS[1] = xMPC_tv.shape[0]
-SS[0:TimeSS[1],:, 1]  = xMPC_tv
+xSS[0:TimeSS[1],:, 1]  = xMPC_tv
+zSS[0:TimeSS[1],:, 1]  = zMPC_tv
 uSS[0:TimeSS[1]-1,:, 1]  = uMPC_tv
 Qfun[0:TimeSS[1], 1] = ComputeCost(xMPC_tv, uMPC_tv, np, TrackLength)
+for i in np.arange(0, Qfun.shape[0]):
+    if Qfun[i, 1] == 0:
+        Qfun[i, 1] = Qfun[i-1, 1] - 1
 
 print Qfun[0:TimeSS[0], 0], Qfun[0:TimeSS[1], 1]
 
-F_LMPC, b_LMPC = LMPC_BuildMatIneqConst(N, n, np, linalg, spmatrix, numSS_Points)
+F_LMPC, b_LMPC, E_LMPC = LMPC_BuildMatIneqConst(N, n, np, linalg, spmatrix, numSS_Points, Error_Bounds, Ke)
+
+Qslack = 50 * np.diag([30, 10, 10, 10, 10, 10])
+Q_LMPC =  0 * np.diag([0.0, 0.0, 0.0, 0.0, 0.0, 0.0])  # vx, vy, wz, epsi, s, ey
+R_LMPC =  5 * np.diag([1.0, 0.1])  # delta, a
 
-Qslack = 50*np.diag([1, 10, 10, 10, 10, 10])
-Q_LMPC = 0 * np.diag([0.0, 0.0, 0.0, 0.0, 0.0, 0.0])  # vx, vy, wz, epsi, s, ey
-R_LMPC = 5 * np.diag([1.0, 1.0])  # delta, a
 
 if PlotIndex == 1:
     plt.figure(105)
@@ -284,12 +340,6 @@
     ax5.plot(xMPC_tv[0:PointsLMPC + 100, 5], '-o')
     line5, = ax5.plot(xdata, ydata, 'or-')
 
-print uSS[0:TimeSS[1]-1,:, 1].shape, uMPC_tv.shape
-print SS[0:TimeSS[1],:, 1].shape, xMPC_tv.shape
-
-print (uSS[0:TimeSS[1]-1,:, 1]== uMPC_tv).all()
-print (SS[0:TimeSS[1],:, 1]== xMPC_tv).all()
-print SS[0:TimeSS[1],:, 1],"\n", xMPC_tv
 
 absTime = 0
 if RunLMPC == 1:
@@ -299,16 +349,19 @@
             u_ID = uMPC_tv
         else:
             print xLMPC[i-2:i+2, :], xLMPC[i, :]
-            SS[0:i, :, it-1]  = xLMPC[0:i, :]
+            zSS[0:i, :, it-1]  = zLMPC[0:i, :]
+            xSS[0:i, :, it-1]  = xLMPC[0:i, :]
             uSS[0:i-1, :, it-1] = uLMPC[0:i-1, :]
             TimeSS[it-1] = i
 
-            x_ID = SS[0:i, :, it-1]
-            u_ID = uSS[0:i-1, :, it-1]
 
             Qfun[0:i, it-1] = ComputeCost(xLMPC[0:i, :], xLMPC[0:i-1, :], np, TrackLength)
 
             print Qfun[:, it-1], Qfun[:, it-2], it
+            zLMPC[0, :] = zLMPC[i, :]
+            zLMPC[0, 4] = zLMPC[i, 4] - TrackLength
+            zLMPC[1:,:] = 0*zLMPC[1:,:]
+
             xLMPC[0, :] = xLMPC[i, :]
             xLMPC[0, 4] = xLMPC[i, 4] - TrackLength
             xLMPC[1:,:] = 0*xLMPC[1:,:]
@@ -319,45 +372,45 @@
         while (xLMPC[i, 4] < TrackLength):
             x0 = xLMPC[i, :]
 
-            if i == 0:
-                startTimer = datetime.datetime.now()  # Start timer for LMPC iteration
-                G, E, L, npG, npE = LMPC_BuildMatEqConst(A, B, np.zeros((n, 1)), N, n, d, np, spmatrix, 0)
-                endTimer = datetime.datetime.now(); deltaTimer_tv = endTimer - startTimer
-
-            else:
-                startTimer = datetime.datetime.now()  # Start timer for LMPC iteration
-
-                Atv, Btv, Ctv, indexUsed_list = LMPC_EstimateABC(LinPoints, LinInput, N, n, d, SS, uSS, TimeSS, qp, matrix,
-                                                                 PointAndTangent, dt, it)
-                endTimer = datetime.datetime.now(); deltaTimer_tv = endTimer - startTimer
-                # Atv0, Btv0, Ctv0 = EstimateABC(LinPoints, N, n, d, x_ID, u_ID, qp, matrix, PointAndTangent, dt)
-                # print (Atv0[0]==Atv[0]).all()
-                #
-                G, E, L, npG, npE = LMPC_BuildMatEqConst(Atv, Btv, Ctv, N, n, d, np, spmatrix, 1)
-                # G, E, L, npG, npE = LMPC_BuildMatEqConst(A, B, np.zeros((n, 1)), N, n, d, np, spmatrix, 0)
-
-                if PlotIndex == 1:
-                    line.set_xdata(x_globMPC_tv[indexUsed_list[0], 4])
-                    line.set_ydata(x_globMPC_tv[indexUsed_list[0], 5])
-                    line0.set_xdata(x_globLMPC[i,4])
-                    line0.set_ydata(x_globLMPC[i,5])
-                    plt.draw()
-                    plt.pause(1e-17)
+            startTimer = datetime.datetime.now()  # Start timer for LMPC iteration
+
+            Atv, Btv, Ctv, indexUsed_list = LMPC_EstimateABC(LinPoints, LinInput, N, n, d, xSS, uSS, TimeSS, qp, matrix,
+                                                             PointAndTangent, dt, it)
+            endTimer = datetime.datetime.now(); deltaTimer_tv = endTimer - startTimer
+            # Atv0, Btv0, Ctv0 = EstimateABC(LinPoints, N, n, d, x_ID, u_ID, qp, matrix, PointAndTangent, dt)
+            # print (Atv0[0]==Atv[0]).all()
+            #
+            G, E, L, npG, npE = LMPC_BuildMatEqConst(Acl, B, Atv, Btv, Ctv, N, n, d, np, spmatrix, Ke, linalg)
+
+            if PlotIndex == 1:
+                line.set_xdata(x_globMPC_tv[indexUsed_list[0], 4])
+                line.set_ydata(x_globMPC_tv[indexUsed_list[0], 5])
+                line0.set_xdata(x_globLMPC[i,4])
+                line0.set_ydata(x_globLMPC[i,5])
+                plt.draw()
+                plt.pause(1e-17)
 
 
 
-            Sol, feasible, deltaTimer, slack = LMPC(npG, L, npE, F_LMPC, b_LMPC, x0, np, qp, matrix, datetime, la, SS,
+            Sol, feasible, deltaTimer, slack = LMPC(npG, L, npE, E_LMPC, F_LMPC, b_LMPC, z0, x0, np, qp, matrix, datetime, la, zSS, xSS,
                                                     Qfun,  N, n, d, spmatrix, numSS_Points, Qslack, Q_LMPC, R_LMPC, it, swifth)
 
-            xPred, uPred = GetPred(Sol, n, d, N, np)
+            zPred, uPred, xPred, lamb, slack = LMPC_GetPred(Sol, n, d, N, np)
+
+            # print "zPred: \n",zPred.T
+            # print "uPred: \n",uPred.T
+            # print "xPred: \n",xPred.T
+            # print "slack: \n", slack
 
             LinPoints = np.vstack((xPred.T[1:,:], xPred.T[-1,:]))
             LinInput = uPred.T
 
-            uLMPC[i, :] = uPred[:, 0]
+            uLMPC[i, :] = uPred[:, 0] - np.dot(Ke, xLMPC[i, :])
             xLMPC[i + 1, :], x_globLMPC[absTime + 1, :] = DynModel(xLMPC[i, :], x_globLMPC[absTime, :], uLMPC[i, :], np, dt,
                                                              PointAndTangent)
-
+            zLMPC[i, :] =zPred[:, 0]
+            print "Previois: ", xLMPC[i, :], "Next: ", xLMPC[i+1, :], "Input: ", uLMPC[i, :], "Nom Input: ", uPred[:, 0]
+            z0 = zLMPC[i, :]
             print xLMPC[i + 1, 4], TrackLength, it, xLMPC[i + 1, 0], np.dot(slack, slack), slack
             if PlotPred == 1:
                 line1.set_xdata(np.arange(i, i+N+1))
@@ -385,30 +438,37 @@
                 break
 
             if it > 2:
-                SS[Counter + i + 1, :, it - 1]  = xLMPC[i + 1, :] + np.array([0, 0, 0, 0, TrackLength, 0])
-                uSS[Counter + i + 1, :, it - 1] = uLMPC[i, :]
+                zSS[Counter + i + 1, :, it - 1]  = zLMPC[i + 1, :] + np.array([0, 0, 0, 0, TrackLength, 0])
+                xSS[Counter + i + 1, :, it - 1]  = xLMPC[i + 1, :] + np.array([0, 0, 0, 0, TrackLength, 0])
+                uSS[Counter + i + 1, :, it - 1]  = uLMPC[i, :]
+                if  Qfun[Counter + i + 1, it - 1] == 0:
+                    Qfun[Counter + i + 1, it - 1] = Qfun[Counter + i, it - 1] - 1
+
             i = i + 1
             absTime = absTime + 1
 
 
 
-    np.savez('LMPC_PathFollowing', x=xLMPC, u=uLMPC, x_glob=x_globLMPC, ss=SS, uss=uSS)
+    np.savez('LMPC_PathFollowing', x=xLMPC, u=uLMPC, x_glob=x_globLMPC, xss=xSS, uss=uSS)
 else:
     data = np.load('LMPC_PathFollowing.npz')
     xLMPC      = data['x']
     uLMPC      = data['u']
     x_globLMPC = data['x_glob']
-    SS         = data['ss']
+    xSS         = data['xss']
     uSS        = data['uss']
 
 if RunLMPC == 1:
     it = 2 + Laps
-    SS[0:i, :, it-1]  = xLMPC[0:i, :]
+    zSS[0:i, :, it-1]  = zLMPC[0:i, :]
+    xSS[0:i, :, it-1]  = xLMPC[0:i, :]
     uSS[0:i-1, :, it-1] = uLMPC[0:i-1, :]
     TimeSS[it-1] = i
     Qfun[0:i, it-1] = ComputeCost(xLMPC[0:i, :], xLMPC[0:i-1, :], np, TrackLength)
 
 print "===== LMPC terminated"
+np.savetxt('Qfun.csv', Qfun, delimiter=',', fmt='%f')
+
 # ======================================================================================================================
 # ========================================= PLOT TRACK =================================================================
 # ======================================================================================================================
@@ -475,18 +535,23 @@
 
     plt.figure(4)
     plt.subplot(711)
+    plt.plot(zMPC[:, 0], '-rs')
     plt.plot(xMPC[:, 0], '-o')
     plt.ylabel('vx')
     plt.subplot(712)
+    plt.plot(zMPC[:, 1], '-rs')
     plt.plot(xMPC[:, 1], '-o')
     plt.ylabel('vy')
     plt.subplot(713)
+    plt.plot(zMPC[:, 2], '-rs')
     plt.plot(xMPC[:, 2],'-o')
     plt.ylabel('wz')
     plt.subplot(714)
+    plt.plot(zMPC[:, 3], '-rs')
     plt.plot(xMPC[:, 3],'-o')
     plt.ylabel('epsi')
     plt.subplot(715)
+    plt.plot(zMPC[:, 5], '-rs')
     plt.plot(xMPC[:, 5], '-o')
     plt.ylabel('ey')
     plt.subplot(716)
@@ -517,18 +582,23 @@
     plt.figure(6)
     plt.subplot(711)
     plt.plot(xMPC_tv[:, 0], '-o')
+    plt.plot(zMPC_tv[:, 0], '-rs')
     plt.ylabel('vx')
     plt.subplot(712)
     plt.plot(xMPC_tv[:, 1], '-o')
+    plt.plot(zMPC_tv[:, 1], '-rs')
     plt.ylabel('vy')
     plt.subplot(713)
     plt.plot(xMPC_tv[:, 2],'-o')
+    plt.plot(zMPC_tv[:, 2], '-rs')
     plt.ylabel('wz')
     plt.subplot(714)
     plt.plot(xMPC_tv[:, 3],'-o')
+    plt.plot(zMPC_tv[:, 3], '-rs')
     plt.ylabel('epsi')
     plt.subplot(715)
     plt.plot(xMPC_tv[:, 5], '-o')
+    plt.plot(zMPC_tv[:, 5], '-rs')
     plt.ylabel('ey')
     plt.subplot(716)
     plt.plot(uMPC_tv[:, 0], '-o')
@@ -557,23 +627,28 @@
     plt.figure(8)
     plt.subplot(711)
     for i in range(2, Laps + 2):
-        plt.plot(SS[0:TimeSS[i], 4, i], SS[0:TimeSS[i], 0, i], '-o')
+        plt.plot(xSS[0:TimeSS[i], 4, i], zSS[0:TimeSS[i], 0, i], '-rs')
+        plt.plot(xSS[0:TimeSS[i], 4, i], xSS[0:TimeSS[i], 0, i], '-o')
     plt.ylabel('vx')
     plt.subplot(712)
     for i in range(2, Laps + 2):
-        plt.plot(SS[0:TimeSS[i], 4, i], SS[0:TimeSS[i], 1, i], '-o')
+        plt.plot(xSS[0:TimeSS[i], 4, i], zSS[0:TimeSS[i], 1, i], '-rs')
+        plt.plot(xSS[0:TimeSS[i], 4, i], xSS[0:TimeSS[i], 1, i], '-o')
     plt.ylabel('vy')
     plt.subplot(713)
     for i in range(2, Laps + 2):
-        plt.plot(SS[0:TimeSS[i], 4, i], SS[0:TimeSS[i], 2, i], '-o')
+        plt.plot(xSS[0:TimeSS[i], 4, i], zSS[0:TimeSS[i], 2, i], '-rs')
+        plt.plot(xSS[0:TimeSS[i], 4, i], xSS[0:TimeSS[i], 2, i], '-o')
     plt.ylabel('wz')
     plt.subplot(714)
     for i in range(2, Laps + 2):
-        plt.plot(SS[0:TimeSS[i], 4, i], SS[0:TimeSS[i], 3, i], '-o')
+        plt.plot(xSS[0:TimeSS[i], 4, i], zSS[0:TimeSS[i], 3, i], '-rs')
+        plt.plot(xSS[0:TimeSS[i], 4, i], xSS[0:TimeSS[i], 3, i], '-o')
     plt.ylabel('epsi')
     plt.subplot(715)
     for i in range(2, Laps + 2):
-        plt.plot(SS[0:TimeSS[i], 4, i], SS[0:TimeSS[i], 5, i], '-o')
+        plt.plot(xSS[0:TimeSS[i], 4, i], zSS[0:TimeSS[i], 5, i], '-rs')
+        plt.plot(xSS[0:TimeSS[i], 4, i], xSS[0:TimeSS[i], 5, i], '-o')
     plt.ylabel('ey')
     plt.subplot(716)
     for i in range(2, Laps + 2):
@@ -584,4 +659,4 @@
         plt.plot(uSS[0:TimeSS[i]-1, 1, i], '-o')
     plt.ylabel('Acc')
 
-plt.show()
+plt.show()
\ No newline at end of file
diff --git a/src/xPred.csv b/src/xPred.csv
new file mode 100644
index 0000000..9544604
--- /dev/null
+++ b/src/xPred.csv
@@ -0,0 +1,6 @@
+0.054255,0.086224,0.112618,0.126203,0.120036,0.107069,0.088325,0.076310,0.080536,0.092445,0.094525,0.108027,0.127415
+-0.022652,0.046905,0.005836,-0.022051,-0.020856,-0.023248,-0.026365,0.067887,0.034594,-0.035630,-0.033329,-0.020397,0.006329
+0.379638,1.113162,0.683664,-0.055337,-0.294691,-0.455707,-0.580960,0.677956,0.863061,-0.066496,-0.433825,-0.252667,-0.056963
+0.015741,0.053704,0.165021,0.233387,0.227853,0.198384,0.152813,0.094718,0.162513,0.248819,0.242170,0.198787,0.173520
+19.044921,19.050448,19.058956,19.069942,19.081619,19.092483,19.101994,19.109832,19.115202,19.122033,19.130213,19.141190,19.151458
+-0.223344,-0.225300,-0.219950,-0.217732,-0.217300,-0.215688,-0.213582,-0.211569,-0.200714,-0.192589,-0.190617,-0.188965,-0.186333
diff --git a/src/xSS_Points.csv b/src/xSS_Points.csv
new file mode 100644
index 0000000..e0b9f7f
--- /dev/null
+++ b/src/xSS_Points.csv
@@ -0,0 +1,6 @@
+1.552311,1.698620,1.810744,1.836830,1.985335,1.939047,2.128565,2.256235,2.229485,2.300060,2.404275,2.421009,2.350626,2.321660,2.397440,2.469556,2.454810,2.274469,2.136148,1.949590,0.984038,1.024837,1.163152,1.320128,1.383967,1.476317,1.573417,1.663223,1.803841,1.851748,1.929234,1.995625,1.843837,1.877565,2.020482,2.225975,2.395080,2.273715,2.000675,1.831317
+0.006011,-0.056040,0.010592,0.078746,-0.027371,-0.157909,0.066675,0.170136,0.236041,0.399014,0.348595,0.023248,0.192732,0.400668,0.405784,0.293013,0.165858,0.213646,0.378936,0.072749,-0.015806,0.023549,0.040403,0.003577,0.045304,-0.043222,0.000138,0.035014,-0.032961,-0.054940,0.062502,0.011052,-0.023052,0.086922,0.208430,0.218197,0.136888,0.005563,0.149403,0.194051
+0.684136,-0.486752,-0.168785,1.541019,1.092818,-2.212898,-2.077747,-1.937895,-3.154599,-1.786315,1.224138,-1.862378,-3.219971,-2.361979,-1.253140,-0.237361,-1.565976,-2.998667,1.585892,2.940478,-0.152972,0.247503,0.641383,0.049796,0.839526,-0.378375,0.134067,0.732233,-0.195341,-1.552583,-0.145644,-0.836660,-2.758227,-3.108908,-1.782087,-0.338680,0.448971,-2.279873,-3.172158,-3.234237
+0.133879,0.130098,0.100956,0.186293,0.312469,0.229571,0.141548,0.093865,-0.017952,-0.100882,0.049093,0.154371,0.038090,-0.089631,-0.117254,-0.036599,-0.035685,-0.275306,-0.314782,0.013321,-0.018813,-0.006804,0.043637,0.067908,0.122751,0.129292,0.123752,0.173674,0.190251,0.114867,0.175998,0.251086,0.178714,0.002261,-0.100888,-0.056817,0.103156,0.138213,-0.014212,-0.219450
+20.014570,20.175417,20.349580,20.529280,20.714246,20.904628,21.120876,21.351071,21.582464,21.814692,22.051419,22.284727,22.511575,22.732744,22.954150,23.179459,23.410876,23.646814,23.866550,24.063800,19.694286,19.795905,19.905102,20.029378,20.164209,20.305226,20.456693,20.616504,20.786377,20.970926,21.171729,21.371620,21.562125,21.746046,21.939718,22.148414,22.374305,22.595710,22.796106,22.976381
+-0.297563,-0.279005,-0.260947,-0.230981,-0.182986,-0.139256,-0.106805,-0.068066,-0.039357,-0.021154,0.009555,0.051507,0.086574,0.111378,0.127278,0.143519,0.160591,0.144317,0.109066,0.095322,-0.263827,-0.264430,-0.258645,-0.250561,-0.234653,-0.217429,-0.199249,-0.173829,-0.143199,-0.121265,-0.091855,-0.047062,-0.005820,0.014912,0.020862,0.025228,0.046968,0.081746,0.104825,0.101698