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ref_hybrid.bib
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@book{abrialFormalMethodsIndustrial1996,
title = {Formal {{Methods}} for {{Industrial Applications}}: {{Specifying}} and {{Programming}} the {{Steam Boiler Control}}},
shorttitle = {Formal {{Methods}} for {{Industrial Applications}}},
author = {Abrial, Jean-Raymond and B{\"o}rger, Egon and Langmaack, Hans},
year = {1996},
month = oct,
publisher = {Springer Science \& Business Media},
abstract = {This book, with the CD-ROM included, is the documentation of a unique collaborative effort in evaluating formal methods for usage under industrial constraints: the major techniques for formally supported specification, design, and verification of large programs and complex systems are applied to a non-trivial and non-academic problem which is typical for industrial informal requirements specifications.The 21 papers included in the book, together with an introduction and competition report, were selected from 33 candidate solutions. This book comes with a CD-ROM containing, besides the printed papers, executable code, full definitions of all parts of the specifications, and detailed descriptions of foundational matters where appropriate.},
googlebooks = {rBluUemThUEC},
isbn = {978-3-540-61929-1},
langid = {english}
}
@book{acaryNonsmoothModelingSimulation2011,
title = {Nonsmooth {{Modeling}} and {{Simulation}} for {{Switched Circuits}}},
author = {Acary, Vincent and Bonnefon, Olivier and Brogliato, Bernard},
year = {2011},
series = {Lecture {{Notes}} in {{Electrical Engineering}}},
number = {69},
publisher = {Springer},
address = {Dordrecht ; New York},
url = {https://doi.org/10.1007/978-90-481-9681-4},
isbn = {978-90-481-9680-7},
langid = {english}
}
@book{acaryNumericalMethodsNonsmooth2008,
title = {Numerical {{Methods}} for {{Nonsmooth Dynamical Systems}}: {{Applications}} in {{Mechanics}} and {{Electronics}}},
shorttitle = {Numerical {{Methods}} for {{Nonsmooth Dynamical Systems}}},
author = {Acary, Vincent and Brogliato, Bernard},
year = {2008},
month = feb,
series = {Lecture {{Notes}} in {{Applied}} and {{Computational Mechanics}}},
number = {35},
publisher = {Springer},
address = {Berlin Heidelberg},
url = {https://doi.org/10.1007/978-3-540-75392-6},
isbn = {978-3-540-75391-9},
langid = {english}
}
@inproceedings{alurModularSpecificationHybrid2000,
title = {Modular {{Specification}} of {{Hybrid Systems}} in {{Charon}}},
booktitle = {Hybrid {{Systems}}: {{Computation}} and {{Control}}},
author = {Alur, Rajeev and Grosu, Radu and Hur, Yerang and Kumar, Vijay and Lee, Insup},
editor = {Lynch, Nancy and Krogh, Bruce H.},
year = {2000},
series = {Lecture {{Notes}} in {{Computer Science}}},
pages = {6--19},
publisher = {Springer},
address = {Berlin, Heidelberg},
doi = {10.1007/3-540-46430-1_5},
abstract = {We propose a language, called Charon, for modular specification of interacting hybrid systems. For hierarchical description of the system architecture, Charon supports building complex agents via the operations of instantiation, hiding, and parallel composition. For hierarchical description of the behavior of atomic components, Charon supports building complex modes via the operations of instantiation, scoping, and encapsulation. Features such as weak preemption, history retention, and externally defined Java functions, facilitate the description of complex discrete behavior. Continuous behavior can be specified using differential as well as algebraic constraints, and invariants restricting the flow spaces, all of which can be declared at various levels of the hierarchy. The modular structure of the language is not merely syntactic, but can be exploited during analysis. We illustrate this aspect by presenting a scheme for modular simulation in which each mode can be compiled solely based on the locally declared information to execute its discrete and continuous updates, and furthermore, submodes can integrate at a finer time scale than the enclosing modes.},
isbn = {978-3-540-46430-3},
langid = {english}
}
@book{alurPrinciplesCyberPhysicalSystems2015,
title = {Principles of {{Cyber-Physical Systems}}},
author = {Alur, Rajeev},
year = {2015},
month = apr,
publisher = {MIT Press},
address = {Cambridge, MA, USA},
url = {https://mitpress.mit.edu/9780262029117/principles-of-cyber-physical-systems/},
abstract = {A foundational text that offers a rigorous introduction to the principles of design, specification, modeling, and analysis of cyber-physical systems.},
isbn = {978-0-262-02911-7},
langid = {english}
}
@article{anconaPatchyVectorFields1999,
title = {Patchy {{Vector Fields}} and {{Asymptotic Stabilization}}},
author = {Ancona, Fabio and Bressan, Alberto},
year = {1999/ed},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
volume = {4},
pages = {445--471},
publisher = {EDP Sciences},
issn = {1292-8119, 1262-3377},
doi = {10.1051/cocv:1999117},
url = {https://www.cambridge.org/core/journals/esaim-control-optimisation-and-calculus-of-variations/article/abs/patchy-vector-fields-and-asymptotic-stabilization/749A15B83380FB80A12C6764D7904410},
urldate = {2022-06-21},
abstract = {This paper is concerned with the structure of asymptotically stabilizing feedbacks for a nonlinear control system on . We first introduce a family of discontinuous, piecewise smooth vector fields and derive a number of properties enjoyed by solutions of the corresponding O.D.E's. We then define a class of ``patchy feedbacks'' which are obtained by patching together a locally finite family of smooth controls. Our main result shows that, if a system is asymptotically controllable at the origin, then it can be stabilized by a piecewise constant patchy feedback control.},
langid = {english}
}
@inproceedings{antoniottiSHIFTSMARTAHSLanguage1997,
title = {{{SHIFT}} and {{SMART-AHS}}: {{A Language For Hybrid System Engineering Modeling}} and {{Simulation}}},
booktitle = {Proceedings of the {{Conference}} on {{Domain-Specific Languages}}},
author = {Antoniotti, Marco and G{\"o}ll{\"u}, A},
year = {1997-10-15/1997-10-17},
pages = {12},
address = {Santa Barbara, CA},
url = {https://www.usenix.org/conference/dsl-97/shift-and-smart-ahs-language-hybrid-system-engineering-modeling-and-simulation},
abstract = {shift is a new programming language, whose aim is to facilitate the implementation of reusable simulation frameworks by teams of engineers. shift incorporates system theoretic concepts emerging from the eld of Hybrid Systems analysis and modeling. The SMART AHS framework is a col lection of shift libraries devoted to the construction of Hybrid System based simulation of Automated Highways Systems. In this paper we describe how the shift simulation environment and language have impacted on the development of the SMART AHS framework. Our claim is that shift provides the proper level of abstraction for engineers who face complex modeling and simulation tasks, where phase changes and continuous variables interact in subtle ways.},
langid = {english}
}
@inproceedings{astromHybridControlInverted1999,
title = {Hybrid Control of Inverted Pendulums},
booktitle = {Learning, Control and Hybrid Systems},
author = {{\AA}str{\"o}m, K. J.},
editor = {Yamamoto, Yutaka and Hara, Shinji},
year = {1999},
series = {Lecture {{Notes}} in {{Control}} and {{Information Sciences}}},
pages = {150--163},
publisher = {Springer},
address = {London},
doi = {10.1007/BFb0109727},
abstract = {Several control tasks for inverted pendulums have been discussed. It has been demonstrated that they are natural tasks for applications of hybrid control and that energy control is a control principle that can be used to structure the system.},
isbn = {978-1-84628-533-2},
langid = {english}
}
@article{astromSwingingPendulumEnergy2000,
title = {Swinging up a Pendulum by Energy Control},
author = {{\AA}str{\"o}m, K. J. and Furuta, K.},
year = {2000},
month = feb,
journal = {Automatica},
volume = {36},
number = {2},
pages = {287--295},
issn = {0005-1098},
doi = {10.1016/S0005-1098(99)00140-5},
url = {https://www.sciencedirect.com/science/article/pii/S0005109899001405},
urldate = {2022-10-16},
abstract = {Properties of simple strategies for swinging up an inverted pendulum are discussed. It is shown that the behavior critically depends on the ratio of the maximum acceleration of the pivot to the acceleration of gravity. A comparison of energy-based strategies with minimum time strategy gives interesting insights into the robustness of minimum time solutions.},
langid = {english}
}
@article{bemporadBoundederrorApproachPiecewise2005,
title = {A Bounded-Error Approach to Piecewise Affine System Identification},
author = {Bemporad, A. and Garulli, A. and Paoletti, S. and Vicino, A.},
year = {2005},
journal = {IEEE Transactions on Automatic Control},
volume = {50},
number = {10},
pages = {1567--1580},
issn = {1558-2523},
doi = {10.1109/TAC.2005.856667},
abstract = {This paper proposes a three-stage procedure for parametric identification of piecewise affine autoregressive exogenous (PWARX) models. The first stage simultaneously classifies the data points and estimates the number of submodels and the corresponding parameters by solving the partition into a minimum number of feasible subsystems (MIN PFS) problem for a suitable set of linear complementary inequalities derived from data. Second, a refinement procedure reduces misclassifications and improves parameter estimates. The third stage determines a polyhedral partition of the regressor set via two-class or multiclass linear separation techniques. As a main feature, the algorithm imposes that the identification error is bounded by a quantity /spl delta/. Such a bound is a useful tuning parameter to trade off between quality of fit and model complexity. The performance of the proposed PWA system identification procedure is demonstrated via numerical examples and on experimental data from an electronic component placement process in a pick-and-place machine.}
}
@article{bemporadControlSystemsIntegrating1999,
title = {Control of Systems Integrating Logic, Dynamics, and Constraints},
author = {Bemporad, Alberto and Morari, Manfred},
year = {1999},
month = mar,
journal = {Automatica},
volume = {35},
number = {3},
pages = {407--427},
issn = {0005-1098},
doi = {10.1016/S0005-1098(98)00178-2},
url = {https://www.sciencedirect.com/science/article/pii/S0005109898001782},
urldate = {2021-10-11},
abstract = {This paper proposes a framework for modeling and controlling systems described by interdependent physical laws, logic rules, and operating constraints, denoted as mixed logical dynamical (MLD) systems. These are described by linear dynamic equations subject to linear inequalities involving real and integer variables. MLD systems include linear hybrid systems, finite state machines, some classes of discrete event systems, constrained linear systems, and nonlinear systems which can be approximated by piecewise linear functions. A predictive control scheme is proposed which is able to stabilize MLD systems on desired reference trajectories while fulfilling operating constraints, and possibly take into account previous qualitative knowledge in the form of heuristic rules. Due to the presence of integer variables, the resulting on-line optimization procedures are solved through mixed integer quadratic programming (MIQP), for which efficient solvers have been recently developed. Some examples and a simulation case study on a complex gas supply system are reported.},
langid = {english}
}
@article{bemporadDiscretetimeHybridModeling2001,
title = {Discrete-Time {{Hybrid Modeling}} and {{Verification}} of the {{Batch Evaporator Process Benchmark}}},
author = {Bemporad, A. and Torrisi, F. D. and Morari, M.},
year = {2001},
month = jan,
journal = {European Journal of Control},
volume = {7},
number = {4},
pages = {382--399},
issn = {0947-3580},
doi = {10.3166/ejc.7.382-399},
url = {https://www.sciencedirect.com/science/article/pii/S0947358001701793},
urldate = {2022-12-06},
abstract = {For hybrid systems described by interconnections of linear discrete-time dynamical systems, automata, and propositional logic rules, we recently proposed the Mixed Logical Dynamical (MLD) systems formalism and the language HYSDEL (Hybrid System Descrip- tion Language) as a modeling tool. For MLD models, we developed a reachability analysis algorithm which combines forward reach set computation and feasibility analysis of trajectories by linear and mixed-integer linear programming. In this paper the versatility of the overall analysis tool is illustrated on the batch evaporator benchmark process.},
langid = {english}
}
@inproceedings{bemporadGreedyApproachIdentification2003,
title = {A {{Greedy Approach}} to {{Identification}} of {{Piecewise Affine Models}}},
booktitle = {Hybrid {{Systems}}: {{Computation}} and {{Control}}},
author = {Bemporad, Alberto and Garulli, Andrea and Paoletti, Simone and Vicino, Antonio},
editor = {Maler, Oded and Pnueli, Amir},
year = {2003},
series = {Lecture {{Notes}} in {{Computer Science}}},
pages = {97--112},
publisher = {Springer},
address = {Berlin, Heidelberg},
doi = {10.1007/3-540-36580-X_10},
url = {https://link.springer.com/chapter/10.1007/3-540-36580-X_10},
abstract = {This paper addresses the problem of identification of piecewise affine (PWA) models. This problem involves the estimation from data of both the parameters of the affine submodels and the partition of the PWA map. The procedure that we propose for PWA identification exploits a greedy strategy for partitioning an infeasible system of linear inequalities into a minimum number of feasible subsystems: this provides an initial clustering of the datapoints. Then a refinement procedure is applied repeatedly to the estimated clusters in order to improve both the data classification and the parameter estimation. The partition of the PWA map is finally estimated by considering pairwise the clusters of regression vectors, and by finding a separating hyperplane for each of such pairs. We show that our procedure does not require to fix a priori the number of affine submodels, which is instead automatically estimated from the data.},
isbn = {978-3-540-36580-8},
langid = {english}
}
@misc{bemporadHybridToolboxMatlab,
title = {Hybrid {{Toolbox}} for {{Matlab}}},
author = {Bemporad, Alberto},
url = {http://cse.lab.imtlucca.it/~bemporad/hybrid/toolbox/hybrid_presentation.pdf}
}
@misc{bemporadHybridToolboxUser2022,
title = {Hybrid {{Toolbox User}}'s {{Guide}}},
author = {Bemporad, Alberto},
year = {2022},
month = dec
}
@inproceedings{bemporadIdentificationHybridSystems2001,
title = {Identification of Hybrid Systems via Mixed-Integer Programming},
booktitle = {Proceedings of the 40th {{IEEE Conference}} on {{Decision}} and {{Control}} ({{Cat}}. {{No}}.{{01CH37228}})},
author = {Bemporad, A. and Roll, J. and Ljung, L.},
year = {2001},
month = dec,
volume = {1},
pages = {786-792 vol.1},
doi = {10.1109/CDC.2001.980202},
abstract = {Addresses the problem of identification of hybrid dynamical systems, by focusing the attention on hinging hyperplanes and Wiener piecewise affine autoregressive exogenous models. In particular, we provide algorithms based on mixed-integer linear or quadratic programming which are guaranteed to converge to a global optimum.}
}
@article{bemporadPiecewiseLinearRegression2023,
title = {A {{Piecewise Linear Regression}} and {{Classification Algorithm With Application}} to {{Learning}} and {{Model Predictive Control}} of {{Hybrid Systems}}},
author = {Bemporad, Alberto},
year = {2023},
month = jun,
journal = {IEEE Transactions on Automatic Control},
volume = {68},
number = {6},
pages = {3194--3209},
issn = {1558-2523},
doi = {10.1109/TAC.2022.3183036},
url = {https://ieeexplore.ieee.org/document/9796616},
urldate = {2023-11-16},
abstract = {This article proposes an algorithm for solving multivariate regression and classification problems using piecewise linear predictors over a polyhedral partition of the feature space. The resulting algorithm that we call piecewise affine regression and classification (PARC) alternates between first, solving ridge regression problems for numeric targets, softmax regression problems for categorical targets, and either softmax regression or cluster centroid computation for piecewise linear separation, and second, assigning the training points to different clusters on the basis of a criterion that balances prediction accuracy and piecewise-linear separability. We prove that PARC is a block-coordinate descent algorithm that minimizes a suitably constructed objective function and that it converges in a finite number of steps. The algorithm is used to learn hybrid numerical/categorical dynamical models from data that contain real and discrete labeled values. The resulting model has a piecewise linear structure that is particularly useful to formulate model predictive control problems and solve them by mixed-integer programming.}
}
@article{benczeSeparationPrincipleHybrid1995,
title = {A Separation Principle for Hybrid Control System Design},
author = {Bencze, W.J. and Franklin, G.F.},
year = {1995},
month = apr,
journal = {IEEE Control Systems Magazine},
volume = {15},
number = {2},
pages = {80--84},
issn = {1941-000X},
doi = {10.1109/37.375289},
abstract = {Presented here is a method, based on automatic control system design practice, for the synthesis of hybrid control systems, controllers that contain both real-time feedback loops and logical decision-making components. In the proposed framework, the overall design task is separated into three component parts: (1) design of the real-time control loops, (2) synthesis of the decision-making logic, and (3) construction of appropriate Boolean/real-time translation routines. This is an effective partitioning of the control system design task, as shown through two examples: (1) control of a highly flexible structure and (2) a robotic manipulator control task. This framework was found to be compatible with expert system-based intelligent control systems and can employ expert system techniques when necessary or effective.{$<>$}}
}
@book{bogdanManufacturingSystemsControl2006,
title = {Manufacturing {{Systems Control Design}}: {{A Matrix-based Approach}}},
shorttitle = {Manufacturing {{Systems Control Design}}},
author = {Bogdan, Stjepan and Lewis, Frank L. and Kovacic, Zdenko and Mireles, Jose},
year = {2006},
month = may,
series = {Advances in {{Industrial Control}}},
publisher = {Springer},
address = {London},
url = {https://doi.org/10.1007/1-84628-334-5},
isbn = {978-1-85233-982-1},
langid = {english}
}
@inproceedings{bogomolovJuliaReachToolboxSetbased2019,
title = {{{JuliaReach}}: A Toolbox for Set-Based Reachability},
shorttitle = {{{JuliaReach}}},
booktitle = {Proceedings of the 22nd {{ACM International Conference}} on {{Hybrid Systems}}: {{Computation}} and {{Control}}},
author = {Bogomolov, Sergiy and Forets, Marcelo and Frehse, Goran and Potomkin, Kostiantyn and Schilling, Christian},
year = {2019},
month = apr,
series = {{{HSCC}} '19},
pages = {39--44},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
doi = {10.1145/3302504.3311804},
url = {https://doi.org/10.1145/3302504.3311804},
urldate = {2022-06-03},
abstract = {We present JuliaReach, a toolbox for set-based reachability analysis of dynamical systems. JuliaReach consists of two main packages: Reachability, containing implementations of reachability algorithms for continuous and hybrid systems, and LazySets, a standalone library that implements state-of-the-art algorithms for calculus with convex sets. The library offers both concrete and lazy set representations, where the latter stands for the ability to delay set computations until they are needed. The choice of the programming language Julia and the accompanying documentation of our toolbox allow researchers to easily translate set-based algorithms from mathematics to software in a platform-independent way, while achieving runtime performance that is comparable to statically compiled languages. Combining lazy operations in high dimensions and explicit computations in low dimensions, JuliaReach can be applied to solve complex, large-scale problems.},
isbn = {978-1-4503-6282-5}
}
@book{bohmeHybridSystemsOptimal2017,
title = {Hybrid {{Systems}}, {{Optimal Control}} and {{Hybrid Vehicles}}: {{Theory}}, {{Methods}} and {{Applications}}},
shorttitle = {Hybrid {{Systems}}, {{Optimal Control}} and {{Hybrid Vehicles}}},
author = {B{\"o}hme, Thomas J. and Frank, Benjamin},
year = {2017},
month = feb,
series = {Advances in {{Industrial Control}}},
publisher = {Springer},
address = {New York, NY},
url = {https://doi.org/10.1007/978-3-319-51317-1},
isbn = {978-3-319-51315-7},
langid = {english}
}
@book{borrelliPredictiveControlLinear2017,
title = {Predictive {{Control}} for {{Linear}} and {{Hybrid Systems}}},
author = {Borrelli, Francesco and Bemporad, Alberto and Morari, Manfred},
year = {2017},
month = jul,
publisher = {Cambridge University Press},
address = {Cambridge, New York},
url = {http://cse.lab.imtlucca.it/~bemporad/publications/papers/BBMbook.pdf},
abstract = {Model Predictive Control (MPC), the dominant advanced control approach in industry over the past twenty-five years, is presented comprehensively in this unique book. With a simple, unified approach, and with attention to real-time implementation, it covers predictive control theory including the stability, feasibility, and robustness of MPC controllers. The theory of explicit MPC, where the nonlinear optimal feedback controller can be calculated efficiently, is presented in the context of linear systems with linear constraints, switched linear systems, and, more generally, linear hybrid systems. Drawing upon years of practical experience and using numerous examples and illustrative applications, the authors discuss the techniques required to design predictive control laws, including algorithms for polyhedral manipulations, mathematical and multiparametric programming and how to validate the theoretical properties and to implement predictive control policies. The most important algorithms feature in an accompanying free online MATLAB toolbox, which allows easy access to sample solutions. Predictive Control for Linear and Hybrid Systems is an ideal reference for graduate, postgraduate and advanced control practitioners interested in theory and/or implementation aspects of predictive control.},
isbn = {978-1-107-01688-0},
langid = {english}
}
@inproceedings{branickyGeneralHybridDynamical1996,
title = {General Hybrid Dynamical Systems: {{Modeling}}, Analysis, and Control},
shorttitle = {General Hybrid Dynamical Systems},
booktitle = {Hybrid {{Systems III}}},
author = {Branicky, Michael S.},
editor = {Alur, Rajeev and Henzinger, Thomas A. and Sontag, Eduardo D.},
year = {1996},
series = {Lecture {{Notes}} in {{Computer Science}}},
pages = {186--200},
publisher = {Springer},
address = {Berlin, Heidelberg},
doi = {10.1007/BFb0020945},
abstract = {Complex systems typically possess a hierarchical structure, characterized by continuous-variable dynamics at the lowest level and logical decision-making at the highest. Virtually all control systems today perform computer-coded checks and issue logical as well as continuous-variable control commands. Such are ``hybrid'' systems. In this paper, we introduce a formal notion of such systems: ``general hybrid dynamical systems''; they are interacting collections of dynamical systems, evolving on continuous-variable state spaces, and subject to continuous controls and discrete phenomena. We discuss modeling issues, giving definitions and conditions for hybrid trajectories and providing a taxonomy for hybrid systems models. We review our hybrid systems analysis results, including topological issues, complexity and computation, stability tools, and analyzed examples. We summarize our hybrid control results, including optimal control theory, control algorithms, and solved examples.},
isbn = {978-3-540-68334-6},
langid = {english}
}
@incollection{branickyIntroductionHybridSystems2005,
title = {Introduction to {{Hybrid Systems}}},
booktitle = {Handbook of {{Networked}} and {{Embedded Control Systems}}},
author = {Branicky, Michael S.},
editor = {{Hristu-Varsakelis}, Dimitrios and Levine, William S.},
year = {2005},
series = {Control {{Engineering}}},
pages = {91--116},
publisher = {Birkh{\"a}user},
address = {Boston, MA},
doi = {10.1007/0-8176-4404-0_5},
url = {https://doi.org/10.1007/0-8176-4404-0_5},
urldate = {2023-11-15},
abstract = {Hybrid systems arise when the continuous and the discrete meet. Combine continuous and discrete inputs, outputs, states, or dynamics, and you have a hybrid system. Particularly, hybrid systems arise from the use of finite-state logic to govern continuous physical processes (as in embedded control systems) or from topological and network constraints interacting with continuous control (as in networked control systems). This chapter provides an introduction to hybrid systems, building them up first from the completely continuous side and then from the completely discrete side. It should be accessible to control theorists and computer scientists alike.},
isbn = {978-0-8176-4404-8},
langid = {english}
}
@article{branickyMultipleLyapunovFunctions1998,
title = {Multiple {{Lyapunov}} Functions and Other Analysis Tools for Switched and Hybrid Systems},
author = {Branicky, M.S.},
year = {1998},
month = apr,
journal = {IEEE Transactions on Automatic Control},
volume = {43},
number = {4},
pages = {475--482},
issn = {1558-2523},
doi = {10.1109/9.664150},
abstract = {We introduce some analysis tools for switched and hybrid systems. We first present work on stability analysis. We introduce multiple Lyapunov functions as a tool for analyzing Lyapunov stability and use iterated function systems theory as a tool for Lagrange stability. We also discuss the case where the switched systems are indexed by an arbitrary compact set. Finally, we extend Bendixson's theorem to the case of Lipschitz continuous vector fields, allowing limit cycle analysis of a class of "continuous switched" systems.}
}
@article{branickyStabilityHybridSystems,
title = {Stability of Hybrid Systems},
author = {Branicky, Michael S.},
editor = {Unbehauen, Heinz},
journal = {Encyclopedia of life support systems},
series = {Control {{Systems}}, {{Robotics}}, and {{Automation}}},
volume = {XV},
publisher = {UNESCO-EOLSS}
}
@inproceedings{branickyStabilityHybridSystems1997,
title = {Stability of Hybrid Systems: State of the Art},
shorttitle = {Stability of Hybrid Systems},
booktitle = {Proceedings of the 36th {{IEEE Conference}} on {{Decision}} and {{Control}}},
author = {Branicky, M.S.},
year = {1997},
month = dec,
volume = {1},
pages = {120-125 vol.1},
issn = {0191-2216},
doi = {10.1109/CDC.1997.650600},
url = {https://ieeexplore.ieee.org/abstract/document/650600?casa_token=E6mKoFbNDrYAAAAA:X1ZCs1xwNhLDEYxYURDPytCc9hT5Fif4wazWYjXXAgM8vAiKHt7LxWUZB8FXtYD8bpjWIak5Xw},
urldate = {2023-11-15},
abstract = {This paper collects work on the stability analysis of hybrid systems. The hybrid systems considered are those that combine continuous dynamics (represented by differential or difference equations) with finite dynamics, usually thought of as being a finite automaton. We review multiple Lyapunov functions as a tool for analyzing Lyapunov stability of general hybrid systems. Background results, the author's introductory work, and subsequent extensions are covered. Specializing to hybrid systems with linear dynamics in each constituent mode and linear jump operators, we review some key theorems of Barabanov-Staroshilov (1988), and give corollaries encompassing several recently-derived "stability by first approximation" theorems in the literature. We also comment on the use of computational tests for stability of hybrid systems, and the general complexity. The result is a tutorial on the state of the art in theory and computation of hybrid systems stability.}
}
@inproceedings{branickyStabilitySwitchedHybrid1994,
title = {Stability of Switched and Hybrid Systems},
booktitle = {Proceedings of 1994 33rd {{IEEE Conference}} on {{Decision}} and {{Control}}},
author = {Branicky, M.S.},
year = {1994},
month = dec,
volume = {4},
pages = {3498-3503 vol.4},
doi = {10.1109/CDC.1994.411688},
url = {https://ieeexplore.ieee.org/abstract/document/411688?casa_token=3B1J5SOYqREAAAAA:4uWWDxHQfl53SQVIEtaN1xxUva_-pRRfZzr5vhWSkdIlO98iC2VDRqABb9l4D-wfxexUvGtJOw},
urldate = {2023-11-15},
abstract = {This paper outlines some preliminary work on the stability analysis of switched and hybrid systems. The hybrid systems considered are those that combine continuous dynamics, represented by differential or difference equations, with finite dynamics usually thought of as being a finite automaton. Here, we concentrate on the continuous dynamics and model the finite dynamics as switching among finitely many continuous systems. We introduce multiple Lyapunov functions as a tool for analyzing Lyapunov stability of such "switched systems". We use iterated function systems theory as a tool for Lagrange stability. We also discuss the case where the switched systems are indexed by an arbitrary compact set.{$<>$}}
}
@phdthesis{branickyStudiesHybridSystems1995,
title = {Studies in {{Hybrid Systems}}: {{Modeling}}, {{Analysis}}, and {{Control}}},
author = {Branicky, Michael Stephen},
year = {1995},
month = jun,
address = {Cambridge, MA},
school = {MIT}
}
@article{bressanUniqueSolutionsClass1988,
title = {Unique Solutions for a Class of Discontinuous Differential Equations},
author = {Bressan, Alberto},
year = {1988},
journal = {Proceedings of the American Mathematical Society},
volume = {104},
number = {3},
pages = {772--778},
issn = {0002-9939, 1088-6826},
doi = {10.1090/S0002-9939-1988-0964856-0},
url = {https://www.ams.org/proc/1988-104-03/S0002-9939-1988-0964856-0/},
urldate = {2023-11-04},
abstract = {Advancing research. Creating connections.},
langid = {english}
}
@book{brogliatoNonsmoothMechanicsModels2016,
title = {Nonsmooth {{Mechanics}}: {{Models}}, {{Dynamics}} and {{Control}}},
shorttitle = {Nonsmooth {{Mechanics}}},
author = {Brogliato, Bernard},
year = {2016},
month = mar,
series = {Communications and {{Control Engineering}}},
edition = {3},
publisher = {Springer},
address = {New York, NY},
abstract = {Now in its third edition, this standard reference is a comprehensive treatment of nonsmooth mechanical systems refocused to give more prominence to issues connected with control and modelling. It covers Lagrangian and Newton--Euler systems, detailing mathematical tools such as convex analysis and complementarity theory. The ways in which nonsmooth mechanics influence and are influenced by well-posedness analysis, numerical analysis and simulation, modelling and control are explained. Contact/impact laws, stability theory and trajectory-tracking control are given detailed exposition connected by a mathematical framework formed from complementarity systems and measure-differential inclusions. Links are established with electrical circuits with set-valued nonsmooth elements as well as with other nonsmooth dynamical systems like impulsive and piecewise linear systems.Nonsmooth Mechanics (third edition) retains the topical structure familiar from its predecessors but has been substantially rewritten, edited and updated to account for the significant body of results that have emerged in the twenty-first century{\texthorizontalbar}including developments in:the existence and uniqueness of solutions;impact models;extension of the~Lagrange--Dirichlet theorem and trajectory tracking; andwell-posedness of contact complementarity problems with and without friction.Many figures (both new and redrawn to improve the clarity of the presentation) and examples are used to illustrate the theoretical developments. Material introducing the mathematics of nonsmooth mechanics has been improved to reflect the broad range of applications interest that has developed since publication of the second edition. The detail of some mathematical essentials is provided in four appendices.With its improved bibliography of over 1,300 references and wide-ranging coverage, Nonsmooth Mechanics~(third edition) is sure to be an invaluable resource for researchers and postgraduates studying the control of mechanical systems, robotics, granular matter and relevant fields of applied mathematics.``The book's two best features, in my view are its detailed survey of the literature{\dots} and its detailed presentation of many examples illustrating both the techniques and their limitations{\dots} For readers interested in the field, this book will serve as an excellent introductory survey.'' Andrew Lewis in~Automatica``It is written with clarity, contains the latest research results in the area of impact problems for rigid bodies and is recommended for both applied mathematicians and engineers.'' Panagiotis D. Panagiotopoulos in~Mathematical Reviews``The presentation is excellent in combining rigorous mathematics with a great number of examples{\dots} allowing the reader to understand the basic concepts.'' Hans Troger in~Mathematical Abstracts{$<$}},
isbn = {978-3-319-28662-4},
langid = {english}
}
@article{bylMetastableWalkingMachines2009,
title = {Metastable {{Walking Machines}}},
author = {Byl, Katie and Tedrake, Russ},
year = {2009},
month = aug,
journal = {The International Journal of Robotics Research},
volume = {28},
number = {8},
pages = {1040--1064},
publisher = {SAGE Publications Ltd STM},
issn = {0278-3649},
doi = {10.1177/0278364909340446},
url = {https://doi.org/10.1177/0278364909340446},
urldate = {2022-08-22},
abstract = {Legged robots that operate in the real world are inherently subject to stochasticity in their dynamics and uncertainty about the terrain. Owing to limited energy budgets and limited control authority, these ``disturbances'' cannot always be canceled out with high-gain feedback. Minimally actuated walking machines subject to stochastic disturbances no longer satisfy strict conditions for limit-cycle stability; however, they can still demonstrate impressively long-living periods of continuous walking. Here, we employ tools from stochastic processes to examine the ``stochastic stability'' of idealized rimless-wheel and compass-gait walking on randomly generated uneven terrain. Furthermore, we employ tools from numerical stochastic optimal control to design a controller for an actuated compass gait model which maximizes a measure of stochastic stability---the mean first-passage time---and compare its performance with a deterministic counterpart. Our results demonstrate that walking is well characterized as a metastable process, and that the stochastic dynamics of walking should be accounted for during control design in order to improve the stability of our machines.},
langid = {english}
}
@phdthesis{camlibelComplementarityMethodsAnalysis2001,
type = {Doctoral {{Thesis}}},
title = {Complementarity Methods in the Analysis of Piecewise Linear Dynamical Systems},
author = {Camlibel, M.K.},
year = {2001},
address = {Tilburg},
abstract = {The main object of this thesis is a class of piecewise linear dynamical systems that are related both to system theory and to mathematical programming. The dynamical systems in this class are known as complementarity systems. With regard to these nonlinear and nonsmooth dynamical systems, the research in the thesis concentrates on two themes: well-posedness and approximations. The well-posedness issue, in the sense of existence and uniqueness of solutions, is of considerable importance from a model validation point of view. In the thesis, sufficient conditions are established for the well-posedness of complementarity systems. Furthermore, an investigation is made of the convergence of approximations of these systems with an eye towards simulation.},
isbn = {9789056680794},
school = {CentER, Center for Economic Research}
}
@article{camlibelLinearPassiveComplementarity2002,
title = {On {{Linear Passive Complementarity Systems}}},
author = {{\c C}aml{\i}bel, M. K. and Heemels, W. P. M. H. and Schumacher, J. M.},
year = {2002},
month = jan,
journal = {European Journal of Control},
volume = {8},
number = {3},
pages = {220--237},
issn = {0947-3580},
doi = {10.3166/ejc.8.220-237},
url = {https://www.sciencedirect.com/science/article/pii/S0947358002710832},
urldate = {2022-11-28},
abstract = {We study the notion of passivity in the context of complementarity systems, which form a class of nonsmooth dynamical systems that is obtained from the coupling of a standard input/output system to complementarity conditions as used in mathematical programming. In terms of electrical circuits, the systems that we study may be viewed as passive networks with ideal diodes. Extending results from earlier work, we consider here complementarity systems with external inputs. It is shown that the assumption of passivity of the underlying input/output dynamical system plays an important role in establishing existence and uniqueness of solutions. We prove that solutions may contain delta functions but no higher-order impulses. Several characterizations are provided for the state jumps that may occur due to inconsistent initialization or to input discontinuities. Many of the results still hold when the assumption of passivity is replaced by the assumption of ``passifiability by pole shifting''. The paper ends with some remarks on stability.},
langid = {english}
}
@article{carloniLanguagesToolsHybrid2006,
title = {Languages and {{Tools}} for {{Hybrid Systems Design}}},
author = {Carloni, Luca P. and Passerone, Roberto and Pinto, Alessandro and {Sangiovanni-Vincentelli}, Alberto L.},
year = {2006},
month = jun,
journal = {Foundations and Trends{\textregistered} in Electronic Design Automation},
volume = {1},
number = {1--2},
pages = {1--193},
publisher = {Now Publishers, Inc.},
issn = {1551-3939, 1551-3947},
doi = {10.1561/1000000001},
url = {https://www.nowpublishers.com/article/Details/EDA-001},
urldate = {2022-10-12},
abstract = {Languages and Tools for Hybrid Systems Design},
langid = {english}
}
@book{cassandrasStochasticHybridSystems2006,
title = {Stochastic {{Hybrid Systems}}},
editor = {Cassandras, Christos G. and Lygeros, John},
year = {7 listopadu 2006},
series = {Control {{Engineering Series}}},
publisher = {CRC Press},
address = {Boca Raton},
abstract = {Because they incorporate both time- and event-driven dynamics, stochastic hybrid systems (SHS) have become ubiquitous in a variety of fields, from mathematical finance to biological processes to communication networks to engineering. Comprehensively integrating numerous cutting-edge studies, Stochastic Hybrid Systems presents a captivating treatment of some of the most ambitious types of dynamic systems. Cohesively edited by leading experts in the field, the book introduces the theoretical basics, computational methods, and applications of SHS. It first discusses the underlying principles behind SHS and the main design limitations of SHS. Building on these fundamentals, the authoritative contributors present methods for computer calculations that apply SHS analysis and synthesis techniques in practice. The book concludes with examples of systems encountered in a wide range of application areas, including molecular biology, communication networks, and air traffic management. It also explains how to resolve practical problems associated with these systems. Stochastic Hybrid Systems achieves an ideal balance between a theoretical treatment of SHS and practical considerations. The book skillfully explores the interaction of physical processes with computerized equipment in an uncertain environment, enabling a better understanding of sophisticated as well as everyday devices and processes.},
isbn = {978-0-8493-9083-8}
}
@misc{cleachFastContactImplicitModelPredictive2021,
title = {Fast {{Contact-Implicit Model-Predictive Control}}},
author = {Cleac'h, Simon Le and Howell, Taylor and Schwager, Mac and Manchester, Zachary},
year = {2021},
month = sep,
number = {arXiv:2107.05616},
eprint = {2107.05616},
primaryclass = {cs, eess},
publisher = {arXiv},
doi = {10.48550/arXiv.2107.05616},
url = {http://arxiv.org/abs/2107.05616},
urldate = {2022-12-20},
abstract = {We present a general approach for controlling robotic systems that make and break contact with their environments. Contact-implicit model-predictive control (CI-MPC) generalizes linear MPC to contact-rich settings by relying on linear complementarity problems (LCP) computed using strategic Taylor approximations about a reference trajectory and retaining non-smooth impact and friction dynamics, allowing the policy to not only reason about contact forces and timing, but also generate entirely new contact mode sequences online. To achieve reliable and fast numerical convergence, we devise a structure-exploiting, path-following solver for the LCP contact dynamics and a custom trajectory optimizer for trajectory-tracking MPC problems. We demonstrate CI-MPC at real-time rates in simulation, and show that it is robust to model mismatch and can respond to disturbances by discovering and exploiting new contact modes across a variety of robotic systems, including a pushbot, hopper, and planar quadruped and biped.},
archiveprefix = {arxiv}
}
@article{cortesDiscontinuousDynamicalSystems2008,
title = {Discontinuous Dynamical Systems: {{A}} Tutorial on Solutions, Nonsmooth Analysis, and Stability},
author = {Cortes, Jorge},
year = {2008},
month = jun,
journal = {IEEE Control Systems Magazine},
volume = {28},
number = {3},
pages = {36--73},
issn = {1941-000X},
doi = {10.1109/MCS.2008.919306},
abstract = {This article has presented an introductory tutorial on discontinuous dynamical systems. Various examples illustrate the pertinence of the continuity and Lipschitzness properties that guarantee the existence and uniqueness of classical solutions to ordinary differential equations. The lack of these properties in examples drawn from various disciplines motivates the need for more general notions than the classical one. First, we introduced notions of solution for discontinuous systems. Second, we reviewed the available tools from non- smooth analysis to study the gradient information of candidate Lyapunov functions. And, third, we presented nonsmooth stability tools to characterize the asymptotic behavior of solutions.}
}
@article{decarloPerspectivesResultsStability2000,
title = {Perspectives and Results on the Stability and Stabilizability of Hybrid Systems},
author = {Decarlo, R.A. and Branicky, M.S. and Pettersson, S. and Lennartson, B.},
year = {2000},
month = jul,
journal = {Proceedings of the IEEE},
volume = {88},
number = {7},
pages = {1069--1082},
issn = {1558-2256},
doi = {10.1109/5.871309},
abstract = {This paper introduces the concept of a hybrid system and some of the challenges associated with the stability of such systems, including the issues of guaranteeing stability of switched stable systems and finding conditions for the existence of switched controllers for stabilizing switched unstable systems. In this endeavour, this paper surveys the major results in the (Lyapunov) stability of finite-dimensional hybrid systems and then discusses the stronger, more specialized results of switched linear (stable and unstable) systems. A section detailing how some of the results can be formulated as linear matrix inequalities is given. Stability analyses on the regulation of the angle of attack of an aircraft and on the PI control of a vehicle with an automatic transmission are given. Other examples are included to illustrate various results in this paper.}
}
@incollection{deshpandeSHIFTProgrammingLanguage2000,
title = {The {{SHIFT Programming Language}} and {{Run-time System}} for {{Dynamic Networks}} of {{Hybrid Automata}}},
booktitle = {Verification of {{Digital}} and {{Hybrid Systems}}},
author = {Deshpande, Akash and G{\"o}ll{\"u}, Aleks and Semenzato, Luigi},
editor = {Inan, M. Kemal and Kurshan, Robert P.},
year = {2000},
series = {{{NATO ASI Series}}},
pages = {355--371},
publisher = {Springer},
address = {Berlin, Heidelberg},
doi = {10.1007/978-3-642-59615-5_17},
url = {https://doi.org/10.1007/978-3-642-59615-5_17},
urldate = {2022-07-09},
abstract = {SHIFT is a programming language for describing and simulating dynamic networks of hybrid automata. Such Systems consist of components that can be created, interconnected and destroyed as the system evolves. Components exhibit hybrid behavior, consisting of continuous-time phases separated by discrete-event transitions. Components may evolve independently, or they may interact through selected state variables and events. The interaction network itself may evolve.SHIFT is currently used in two applications: automated highway Systems and coordinated submarine Systems. The SHIFT model offers the proper level of abstraction for describing these and other applications such as air traffic control Systems and robotic shop-floors whose dynamic reconfigurations cannot be captured easily by conventional models. We have implemented a Compiler and a run-time system for SHIFT. The Compiler translates a SHIFT program into a C program, which, when run, simulates the design specified in the SHIFT source program.More Information about SHIFT can be found at www.path.berkeley.edu/ shift.},
isbn = {978-3-642-59615-5},
langid = {english}
}
@inproceedings{deschutterExtendedLinearComplementarity1999,
title = {The {{Extended Linear Complementarity Problem}} and the {{Modeling}} and {{Analysis}} of {{Hybrid Systems}}},
booktitle = {Hybrid {{Systems V}}},
author = {De Schutter, Bart and De Moor, Bart},
editor = {Antsaklis, Panos and Lemmon, Michael and Kohn, Wolf and Nerode, Anil and Sastry, Shankar},
year = {1999},
series = {Lecture {{Notes}} in {{Computer Science}}},
pages = {70--85},
publisher = {Springer},
address = {Berlin, Heidelberg},
doi = {10.1007/3-540-49163-5_4},
url = {https://doi.org/10.1007/3-540-49163-5_4},
abstract = {First we give a short description of the Extended Linear Complementarity Problem (ELCP), which is a mathematical programming problem. We briefly discuss how this problem can be used in the analysis of discrete event systems and continuous variable systems. Next we show that the ELCP can also be used to model and to analyze hybrid systems. More specifically, we consider a traffic-light-controlled intersection, which can be considered as a hybrid system. We construct a model that describes the evolution of the queue lengths in the various lanes (as continuous variables) as a function of time and we show that this leads to an ELCP. Furthermore, it can be shown that some problems in the analysis of another class of hybrid systems, the ``complementary-slackness systems'', also lead to an ELCP.},
isbn = {978-3-540-49163-7},
langid = {english}
}
@article{deschutterLinearDynamicComplementarity1998,
title = {The {{Linear Dynamic Complementarity Problem}} Is a Special Case of the {{Extended Linear Complementarity Problem}}},
author = {De Schutter, Bart and De Moor, Bart},
year = {1998},
month = may,
journal = {Systems \& Control Letters},
volume = {34},
number = {1},
pages = {63--75},
issn = {0167-6911},
doi = {10.1016/S0167-6911(97)00136-9},
url = {https://www.sciencedirect.com/science/article/pii/S0167691197001369},
urldate = {2022-07-31},
abstract = {In this paper we consider some extensions of the Linear Complementarity Problem, which is one of the fundamental problems in mathematical programming. More specifically we consider the Linear Dynamic Complementarity Problem (LDCP), the Generalized Linear Complementarity Problem (GLCP) and the Extended Linear Complementarity Problem (ELCP). In this note we show that the LDCP is a special case of the ELCP and the GLCP.},
langid = {english}
}
@incollection{deschutterSurveyModelingAnalysis2009,
title = {Survey of Modeling, Analysis, and Control of Hybrid Systems},
booktitle = {Handbook of {{Hybrid Systems Control}}: {{Theory}}, {{Tools}}, {{Applications}}},
author = {De Schutter, B. and Heemels, W. P. M. H. and Lunze, J. and Prieur, C.},
editor = {{Lamnabhi-Lagarrigue}, Fran{\c c}oise and Lunze, Jan},
year = {2009},
pages = {31--56},
publisher = {Cambridge University Press},
address = {Cambridge},
doi = {10.1017/CBO9780511807930.003},
url = {https://www.cambridge.org/core/books/handbook-of-hybrid-systems-control/survey-of-modeling-analysis-and-control-of-hybrid-systems/DFEC4B1DB428CD8F14863C1645660B95},
urldate = {2022-09-12},
abstract = {An overview of various modeling frameworks for hybrid systems is given followed by a comparison of the modeling power and the model complexity, which can serve as a guideline for choosing the right model for a given analysis or control problem with hybrid dynamics. Then, the main analysis and design tasks for hybrid systems are surveyed together with the methods for their solution, which will be discussed in more detail in subsequent chapters.Models for hybrid systemsOverviewAs models are the ultimate tools for obtaining and dealing with knowledge, not only in engineering, but also in philosophy, biology, sociology, and economics, a search has been undertaken for appropriate mathematical models for hybrid systems. This section gives an overview of the modeling formalisms that have been elaborated in hybrid systems theory in the past.Structure of hybrid systems Many different models have been proposed in literature, as will be seen in following chapters. These models can be distinguished with respect to the phenomena that they are able to represent in an explicit form. Consequently, these models have different fields of applications. The main idea of these models is described by the block diagram shown in Fig. 2.1, which is often used in literature as a starting point of hybrid systems modeling and analysis, although not all models use this structure in a direct way.},
isbn = {978-0-521-76505-3}
}
@book{DiscreteContinuousHybrid,
title = {Discrete, {{Continuous}}, and {{Hybrid Petri Nets}}},
author = {David, Ren{\'e} and Alla, Hassane},
year = {2010},
edition = {2},
publisher = {Springer},
address = {Berlin, Heidelberg},
url = {https://doi.org/10.1007/978-3-642-10669-9},
urldate = {2024-05-06},
abstract = {Petri Nets were introduced and still successfully used to analyze and model discrete event systems especially in engineering and computer sciences such as in automatic control. Recently this discrete Petri Nets formalism was successfully extended to continuous and hybrid systems. This monograph presents a well written and clearly organized introduction in the standard methods of Petri Nets with the aim to reach an accurate understanding of continuous and hybrid Petri Nets, while preserving the consistency of basic concepts throughout the book. The book is a monograph as well as a didactic tool which is easy to understand due to many simple solved examples and detailed figures. In its second completely reworked edition various sections, concepts and recently developed algorithms are added as well as additional examples/exercises.},
isbn = {978-3-642-10668-2},
langid = {english}
}
@article{ekerDesignImplementationHybrid1999,
title = {Design and Implementation of a Hybrid Control Strategy},
author = {Eker, J. and Malmborg, J.},
year = {1999},
month = aug,
journal = {IEEE Control Systems Magazine},
volume = {19},
number = {4},
pages = {12--21},
issn = {1941-000X},
doi = {10.1109/37.777785},
url = {https://ieeexplore.ieee.org/abstract/document/777785?casa_token=zIXSUymXM5MAAAAA:6V5UA0x8z0xj2HaYyPy4ZBT5l0EL-6XRJFSQrqZdt9rXKFmum8-KOc8cWADuSd4M9NPvSNXyKg},
urldate = {2023-11-15},
abstract = {Hybrid controllers for a double-tank system and a heating/ventilation process have been designed and implemented. Both simulations and real experiments are presented. It is shown that a hybrid controller consisting of a time-optimal controller combined with a PID controller gives very good performance. The controller is easy to implement. It gives, in one of its forms, guaranteed closed loop stability.}
}
@article{elhamifarAdaptivePiecewiseAffine2014,
title = {Adaptive {{Piecewise}}--{{Affine Inverse Modeling}} of {{Hybrid Dynamical Systems}}},
author = {Elhamifar, Ehsan and Burden, Samuel A. and Sastry, S. Shankar},
year = {2014},
month = jan,
journal = {IFAC Proceedings Volumes},
series = {19th {{IFAC World Congress}}},
volume = {47},
number = {3},
pages = {10844--10849},
issn = {1474-6670},
doi = {10.3182/20140824-6-ZA-1003.02610},
url = {https://www.sciencedirect.com/science/article/pii/S1474667016433380},
urldate = {2022-07-15},
abstract = {Motivated by the study of complex motor control systems, we consider the identification and control of PieceWise Affine (PWA) systems and propose a novel data-driven framework that adaptively inverts the dynamics of such systems using noisy sampled data. First, we propose a novel PWA identification algorithm based on convex optimization applicable to both state--space and input/output models. Given a PWA model of the dynamics obtained from the identification algorithm, we consider the control of the resulting hybrid system where our goal is to find an input that reproduces a given reference trajectory or that extremizes a performance criterion. We demonstrate our proposed framework on a model of a jumping robot.},
langid = {english}
}
@article{elmqvistObjectOrientedHybridModeling2001,
title = {Object-{{Oriented}} and {{Hybrid Modeling}} in {{Modelica}}},
author = {Elmqvist, Hilding and Mattsson, Sven Erik and Otter, Martin},
year = {2001},
journal = {Journal Europ{\'e}en des syst{\`e}mes automatis{\'e}s},
volume = {35},
number = {4},
pages = {395--404},
url = {https://elib.dlr.de/11522/},
abstract = {Modelica is an object-oriented language for modeling of large and heterogeneous physical systems. Typical applications include mechatronic models in robotics, automotive and aerospace applications involving mechanical, electrical, hydraulic and control subsystems, process oriented applications and generation and distribution of electric power. The unique features of Modelica to model combined continuous time and discrete event systems are discussed. A hybrid Modelica model is described by a set of synchronous differential, algebraic and discrete equations leading to deterministic behaviour and automatic synchronization of the continuous time and discrete event parts of a model.},
langid = {english}
}
@book{engellModellingAnalysisDesign2014,
title = {Modelling, {{Analysis}} and {{Design}} of {{Hybrid Systems}}},
editor = {Engell, S. and Frehse, G. and Schnieder, E.},
year = {2014},
month = mar,
series = {Lecture {{Notes}} in {{Control}} and {{Information Sciences}}},
publisher = {Springer},
address = {Berlin; New York},
url = {https://doi.org/10.1007/3-540-45426-8},
isbn = {978-3-662-21024-6},
langid = {english}
}
@article{ferrari-trecateClusteringTechniqueIdentification2003,
title = {A Clustering Technique for the Identification of Piecewise Affine Systems},
author = {{Ferrari-Trecate}, Giancarlo and Muselli, Marco and Liberati, Diego and Morari, Manfred},
year = {2003},
month = feb,
journal = {Automatica},
volume = {39},
number = {2},
pages = {205--217},
issn = {0005-1098},
doi = {10.1016/S0005-1098(02)00224-8},
url = {https://www.sciencedirect.com/science/article/pii/S0005109802002248},
urldate = {2022-07-15},
abstract = {We propose a new technique for the identification of discrete-time hybrid systems in the piecewise affine (PWA) form. This problem can be formulated as the reconstruction of a possibly discontinuous PWA map with a multi-dimensional domain. In order to achieve our goal, we provide an algorithm that exploits the combined use of clustering, linear identification, and pattern recognition techniques. This allows to identify both the affine submodels and the polyhedral partition of the domain on which each submodel is valid avoiding gridding procedures. Moreover, the clustering step (used for classifying the datapoints) is performed in a suitably defined feature space which allows also to reconstruct different submodels that share the same coefficients but are defined on different regions. Measures of confidence on the samples are introduced and exploited in order to improve the performance of both the clustering and the final linear regression procedure.},
langid = {english}
}
@inproceedings{ferrari-trecateIdentificationPiecewiseAffine2001,
title = {Identification of Piecewise Affine and Hybrid Systems},
booktitle = {Proceedings of the 2001 {{American Control Conference}}. ({{Cat}}. {{No}}.{{01CH37148}})},
author = {{Ferrari-Trecate}, G. and Muselli, M. and Liberati, D. and Morari, M.},
year = {2001},
month = jun,
volume = {5},
pages = {3521-3526 vol.5},
issn = {0743-1619},
doi = {10.1109/ACC.2001.946178},
abstract = {We focus on the identification of discrete time hybrid systems in the piecewise affine (PWA) form. This problem can be formulated as the reconstruction of a possibly discontinuous PWA map with a multidimensional domain. In order to achieve our goal, we propose an algorithm that exploits the combined use of clustering, linear identification, and classification techniques. This allows one to identify both the affine sub-models and the polyhedral partition of the domain on which each submodel is valid.}
}
@book{filippovDifferentialEquationsDiscontinuous1988,
title = {Differential {{Equations}} with {{Discontinuous Righthand Sides}}},
author = {Filippov, A. F.},
year = {1988},
series = {Mathematics and Its {{Applications}}},
publisher = {Springer},
address = {Dordrecht},
url = {https://link.springer.com/book/10.1007/978-94-015-7793-9},
urldate = {2022-06-08},
isbn = {978-90-277-2699-5},
langid = {english}
}
@inproceedings{frehseSpaceExScalableVerification2011,
title = {{{SpaceEx}}: {{Scalable Verification}} of {{Hybrid Systems}}},
shorttitle = {{{SpaceEx}}},
booktitle = {Proc. of 23rd {{International Conference}} on {{Computer Aided Verification}}, {{CAV}} 2011},
author = {Frehse, Goran and Le Guernic, Colas and Donz{\'e}, Alexandre and Cotton, Scott and Ray, Rajarshi and Lebeltel, Olivier and Ripado, Rodolfo and Girard, Antoine and Dang, Thao and Maler, Oded},
editor = {Gopalakrishnan, Ganesh and Qadeer, Shaz},
year = {2011},
series = {Lecture {{Notes}} in {{Computer Science}}},
pages = {379--395},
publisher = {Springer},
address = {Snowbird, UT},
doi = {10.1007/978-3-642-22110-1_30},
abstract = {We present a scalable reachability algorithm for hybrid systems with piecewise affine, non-deterministic dynamics. It combines polyhedra and support function representations of continuous sets to compute an over-approximation of the reachable states. The algorithm improves over previous work by using variable time steps to guarantee a given local error bound. In addition, we propose an improved approximation model, which drastically improves the accuracy of the algorithm. The algorithm is implemented as part of SpaceEx, a new verification platform for hybrid systems, available at spaceex.imag.fr. Experimental results of full fixed-point computations with hybrid systems with more than 100 variables illustrate the scalability of the approach.},
isbn = {978-3-642-22110-1},
langid = {english}
}
@article{frickLowcomplexityMethodHybrid2019,
title = {Low-Complexity Method for Hybrid {{MPC}} with Local Guarantees},
author = {Frick, Damian and Georghiou, Angelos and Jerez, Juan L. and Domahidi, Alexander and Morari, Manfred},
year = {2019},
month = jan,
journal = {SIAM Journal on Control and Optimization},
volume = {57},
number = {4},
eprint = {1609.02819},
primaryclass = {math},
pages = {2328--2361},
issn = {0363-0129, 1095-7138},
doi = {10.1137/17M114251X},
url = {http://arxiv.org/abs/1609.02819},
urldate = {2022-12-03},
abstract = {Model predictive control problems for constrained hybrid systems are usually cast as mixed-integer optimization problems (MIP). However, commercial MIP solvers are designed to run on desktop computing platforms and are not suited for embedded applications which are typically restricted by limited computational power and memory. To alleviate these restrictions, we develop a novel low-complexity, iterative method for a class of non-convex, non-smooth optimization problems. This class of problems encompasses hybrid model predictive control problems where the dynamics are piece-wise affine (PWA). We give conditions such that the proposed algorithm has fixed points and show that, under practical assumptions, our method is guaranteed to converge locally to local minima. This is in contrast to other low-complexity methods in the literature, such as the non-convex alternating directions method of multipliers (ADMM), for which no such guarantees are known for this class of problems. By interpreting the PWA dynamics as a union of polyhedra we can exploit the problem structure and develop an algorithm based on operator splitting procedures. Our algorithm departs from the traditional MIP formulation, and leads to a simple, embeddable method that only requires matrix-vector multiplications and small-scale projections onto polyhedra. We illustrate the efficacy of the method on two numerical examples, achieving good closed-loop performance with computational times several orders of magnitude smaller compared to state-of-the-art MIP solvers. Moreover, it is competitive with ADMM in terms of suboptimality and computation time, but additionally provides local optimality and local convergence guarantees.},
archiveprefix = {arxiv}
}
@phdthesis{frickNumericalMethodsDecisionMaking2018,
type = {Doctoral {{Thesis}}},
title = {Numerical {{Methods}} for {{Decision-Making}} in {{Control}} from {{Hybrid Systems}} to {{Formal Specifications}}},
author = {Frick, Damian},
year = {2018},
month = jun,
address = {Zurich, Switzerland},
doi = {10.3929/ethz-b-000259120},
url = {https://www.research-collection.ethz.ch/handle/20.500.11850/259120},
urldate = {2022-06-29},
copyright = {http://rightsstatements.org/page/InC-NC/1.0/},
isbn = {9783906916194},
langid = {english},
school = {ETH},
annotation = {Accepted: 2018-09-03T12:50:18Z}
}
@misc{fridmanEquationsDiscontinuousRight2019,
type = {Lecture},
title = {Equations with {{Discontinuous Right Hand Side}}},
author = {Fridman, L},
year = {2019},
address = {State University of Rio de Janeiro, Rio de Janeiro, Brazil},
url = {http://www.lee.uerj.br/~vss2020/Homepage-Summer-School/lectures.html},
langid = {english}
}
@article{garulliSurveySwitchedPiecewise2012,
title = {A Survey on Switched and Piecewise Affine System Identification},
author = {Garulli, Andrea and Paoletti, Simone and Vicino, Antonio},
year = {2012},
month = jul,
journal = {IFAC Proceedings Volumes},
series = {16th {{IFAC Symposium}} on {{System Identification}}},
volume = {45},
number = {16},
pages = {344--355},
issn = {1474-6670},
doi = {10.3182/20120711-3-BE-2027.00332},
url = {https://www.sciencedirect.com/science/article/pii/S1474667015379751},
urldate = {2022-07-15},
abstract = {Recent years have witnessed a growing interest on system identification techniques for switched and piecewise affine models. These model classes have become popular not only due to the universal approximation properties of piecewise affine functions, but also because the proposed identification procedures have proven to be effective in problems involving complex nonlinear systems with large data sets. This paper presents a review of recent advances in this research field, including theoretical results, algorithms and applications.},
langid = {english}
}
@article{goebelHybridDynamicalSystems2009,
title = {Hybrid Dynamical Systems},
author = {Goebel, Rafal and Sanfelice, Ricardo G. and Teel, Andrew R.},
year = {2009},
month = apr,
journal = {IEEE Control Systems Magazine},
volume = {29},
number = {2},
pages = {28--93},
issn = {1066-033X},
doi = {10.1109/MCS.2008.931718},
abstract = {Robust stability and control for systems that combine continuous-time and discrete-time dynamics. This article is a tutorial on modeling the dynamics of hybrid systems, on the elements of stability theory for hybrid systems, and on the basics of hybrid control. The presentation and selection of material is oriented toward the analysis of asymptotic stability in hybrid systems and the design of stabilizing hybrid controllers. Our emphasis on the robustness of asymptotic stability to data perturbation, external disturbances, and measurement error distinguishes the approach taken here from other approaches to hybrid systems. While we make some connections to alternative approaches, this article does not aspire to be a survey of the hybrid system literature, which is vast and multifaceted.}
}
@book{goebelHybridDynamicalSystems2012,
title = {Hybrid {{Dynamical Systems}}: {{Modeling}}, {{Stability}}, and {{Robustness}}},
shorttitle = {Hybrid {{Dynamical Systems}}},
author = {Goebel, Rafal and Sanfelice, Ricardo G. and Teel, Andrew R.},
year = {2012},
month = mar,
publisher = {Princeton University Press},
url = {https://press.princeton.edu/books/hardcover/9780691153896/hybrid-dynamical-systems},
isbn = {0-691-15389-2}
}
@misc{GPROMSProducts,
title = {{{gPROMS}}},
url = {https://www.psenterprise.com/products/gproms},
urldate = {2022-06-03},
abstract = {Siemens PSE's next-generation tools are specifically designed for digital R\&D, design and operations applications, enabling users across all process industry sectors to create value through accelerated R\&D, enhanced process designs and better operations.},
howpublished = {Siemens}
}
@article{grizzleAsymptoticallyStableWalking2001,
title = {Asymptotically Stable Walking for Biped Robots: Analysis via Systems with Impulse Effects},
shorttitle = {Asymptotically Stable Walking for Biped Robots},
author = {Grizzle, J.W. and Abba, G. and Plestan, F.},
year = {2001},
month = jan,
journal = {IEEE Transactions on Automatic Control},
volume = {46},
number = {1},
pages = {51--64},
issn = {1558-2523},
doi = {10.1109/9.898695},
abstract = {Biped robots form a subclass of legged or walking robots. The study of mechanical legged motion has been motivated by its potential use as a means of locomotion in rough terrain, as well as its potential benefits to prothesis development and testing. The paper concentrates on issues related to the automatic control of biped robots. More precisely, its primary goal is to contribute a means to prove asymptotically-stable walking in planar, underactuated biped robot models. Since normal walking can be viewed as a periodic solution of the robot model, the method of Poincare sections is the natural means to study asymptotic stability of a walking cycle. However, due to the complexity of the associated dynamic models, this approach has had limited success. The principal contribution of the present work is to show that the control strategy can be designed in a way that greatly simplifies the application of the method of Poincare to a class of biped models, and, in fact, to reduce the stability assessment problem to the calculation of a continuous map from a subinterval of R to itself. The mapping in question is directly computable from a simulation model. The stability analysis is based on a careful formulation of the robot model as a system with impulse effects and the extension of the method of Poincare sections to this class of models.}
}
@article{gruneHigherOrderNumerical2006,
title = {Higher Order Numerical Approximation of Switching Systems},
author = {Gr{\"u}ne, L. and Kloeden, P. E.},
year = {2006},
month = sep,
journal = {Systems \& Control Letters},
volume = {55},
number = {9},
pages = {746--754},
issn = {0167-6911},
doi = {10.1016/j.sysconle.2006.03.002},
url = {https://www.sciencedirect.com/science/article/pii/S0167691106000442},
urldate = {2022-12-04},
abstract = {Higher order numerical schemes for affine nonlinear control systems developed elsewhere by the authors are adapted to switching systems with prescribed switching times. In addition the calculation of the required multiple switching control integrals is discussed. These schemes are particularly useful in situations involving very rapid switching.},
langid = {english}
}
@article{heemelsEquivalenceHybridDynamical2001,
title = {Equivalence of Hybrid Dynamical Models},
author = {Heemels, W. P. M. H. and De Schutter, B. and Bemporad, A.},
year = {2001},
month = jul,
journal = {Automatica},
volume = {37},
number = {7},
pages = {1085--1091},
issn = {0005-1098},
doi = {10.1016/S0005-1098(01)00059-0},
url = {https://www.sciencedirect.com/science/article/pii/S0005109801000590},
urldate = {2022-07-09},
abstract = {This paper establishes equivalences among five classes of hybrid systems: mixed logical dynamical (MLD) systems, linear complementarity (LC) systems, extended linear complementarity (ELC) systems, piecewise affine (PWA) systems, and max-min-plus-scaling (MMPS) systems. Some of the equivalences are established under (rather mild) additional assumptions. These results are of paramount importance for transferring theoretical properties and tools from one class to another, with the consequence that for the study of a particular hybrid system that belongs to any of these classes, one can choose the most convenient hybrid modeling framework.},
langid = {english}
}
@incollection{heemelsIntroductionHybridSystems2009,
title = {Introduction to Hybrid Systems},
booktitle = {Handbook of {{Hybrid Systems Control}}: {{Theory}}, {{Tools}}, {{Applications}}},
author = {Heemels, W. P. M. H. and Lehmann, D. and Lunze, J. and De Schutter, B.},
editor = {Lunze, Jan and {Lamnabhi-Lagarrigue}, Fran{\c c}oise},
year = {2009},
month = oct,
pages = {3--30},
publisher = {Cambridge University Press},
doi = {10.1017/CBO9780511807930.002},
url = {https://heemels.tue.nl/content/papers/HeeLeh_BOOK_CONTRIB09a.pdf},
urldate = {2020-09-23},
abstract = {This chapter gives an informal introduction to hybrid dynamical systems and illustrates by simple examples the main phenomena that are encountered due to the interaction of continuous and discrete dynamics. References to numerous applications show the practical importance of hybrid systems theory.{$<$}/p{$><$}p{$>$}What is a hybrid system?{$<$}/p{$><$}p{$>$}Wherever continuous and discrete dynamics interact, hybrid systems arise. This is especially profound in many technological systems, in which logic decision making and embedded control actions are combined with continuous physical processes. To capture the evolution of these systems, mathematical models are needed that combine in one way or another the dynamics of the continuous parts of the system with the dynamics of the logic and discrete parts. These mathematical models come in all kinds of variations, but basically consist of some form of differential or difference equations on the one hand and automata or other discrete-event models on the other hand. The collection of analysis and synthesis techniques based on these models forms the research area of hybrid systems theory, which plays an important role in the multi-disciplinary design of many technological systems that surround us.{$<$}/p{$><$}p{$>$}Three reasons to study hybrid systems{$<$}/p{$><$}p{$>$}The reasons to study hybrid systems can be quite diverse. Here we will provide three sources of motivation, which are related to (i) the design of technological systems, (ii) networked control systems, and (iii) physical processes exhibiting non-smooth behavior.},
langid = {english}
}
@phdthesis{heemelsLinearComplementaritySystems1999,
title = {{Linear complementarity systems: a study in hybrid dynamics}},
shorttitle = {{Linear complementarity systems}},
author = {Heemels, Maurice},
year = {1999},
address = {Eindhoven, NL},
url = {https://heemels.tue.nl/content/papers/Hee_TUE99a.pdf},
langid = {dutch},
school = {Technische Universiteit Eindhoven}
}
@article{heemelsLinearComplementaritySystems2000,
title = {Linear {{Complementarity Systems}}},
author = {Heemels, W. P. M. H. and Schumacher, J. M. and Weiland, S.},
year = {2000},
month = jan,
journal = {SIAM Journal on Applied Mathematics},
volume = {60},
number = {4},
pages = {1234--1269},
publisher = {{Society for Industrial and Applied Mathematics}},
issn = {0036-1399},
doi = {10.1137/S0036139997325199},
url = {https://epubs.siam.org/doi/abs/10.1137/S0036139997325199},
urldate = {2022-07-09},
abstract = {We introduce a new class of dynamical systems called "linear complementarity systems." The time evolution of these systems consists of a series of continuous phases separated by "events" which cause a change in dynamics and possibly a jump in the state vector. The occurrence of events is governed by certain inequalities similar to those appearing in the linear complementarity problem of mathematical programming. The framework we describe is suitable for certain situations in which both differential equations and inequalities play a role; for instance, in mechanics, electrical networks, piecewise linear systems, and dynamic optimization. We present a precise definition of the solution concept of linear complementarity systems and give sufficient conditions for existence and uniqueness of solutions.}
}
@inproceedings{henzingerTheoryHybridAutomata1996,
title = {The Theory of Hybrid Automata},
booktitle = {Proceedings 11th {{Annual IEEE Symposium}} on {{Logic}} in {{Computer Science}}},
author = {Henzinger, T.A.},
year = {1996},
month = jul,
pages = {278--292},
issn = {1043-6871},
doi = {10.1109/LICS.1996.561342},
url = {https://ieeexplore.ieee.org/document/561342},
urldate = {2023-10-18},
abstract = {We summarize several recent results about hybrid automata. Our goal is to demonstrate that concepts from the theory of discrete concurrent systems can give insights into partly continuous systems, and that methods for the verification of finite-state systems can be used to analyze certain systems with uncountable state spaces.}
}
@article{henzingerWhatDecidableHybrid1998,
title = {What's {{Decidable}} about {{Hybrid Automata}}?},
author = {Henzinger, Thomas A. and Kopke, Peter W. and Puri, Anuj and Varaiya, Pravin},
year = {1998},
month = aug,
journal = {Journal of Computer and System Sciences},
volume = {57},
number = {1},
pages = {94--124},
issn = {0022-0000},
doi = {10.1006/jcss.1998.1581},
url = {https://www.sciencedirect.com/science/article/pii/S0022000098915811},
urldate = {2022-09-01},
abstract = {Hybrid automata model systems with both digital and analog components, such as embedded control programs. Many verification tasks for such programs can be expressed as reachability problems for hybrid automata. By improving on previous decidability and undecidability results, we identify a boundary between decidability and undecidability for the reachability problem of hybrid automata. On the positive side, we give an (optimal) PSPACE reachability algorithm for the case of initialized rectangular automata, where all analog variables follow independent trajectories within piecewise-linear envelopes and are reinitialized whenever the envelope changes. Our algorithm is based on the construction of a timed automaton that contains all reachability information about a given initialized rectangular automaton. The translation has practical significance for verification, because it guarantees the termination of symbolic procedures for the reachability analysis of initialized rectangular automata. The translation also preserves the{$\omega$}-languages of initialized rectangular automata with bounded nondeterminism. On the negative side, we show that several slight generalizations of initialized rectangular automata lead to an undecidable reachability problem. In particular, we prove that the reachability problem is undecidable for timed automata augmented with a single stopwatch.},
langid = {english}
}
@misc{hercegHYSDELManual,
title = {{{HYSDEL}} 3.0 -- Manual},
author = {Herceg, Martin and Kvasnica, Michal and Morari, Manfred and Gaulocher, Sebastian and Poland, Jan},
url = {http://people.ee.ethz.ch/~cohysys/hysdel/download/HYSDEL3_manual.pdf},
howpublished = {STU, ETH, ABB}
}
@incollection{herzingerTheoryHybridAutomata2000,
title = {The {{Theory}} of {{Hybrid Automata}}},
booktitle = {Verification of {{Digital}} and {{Hybrid Systems}}},
author = {Herzinger, Thomas A.},
editor = {Inan, M.K. and Kurshan, R.P.},
year = {2000},
series = {{{NATO ASI Series}}},
number = {170},
pages = {265--292},
publisher = {Springer},
address = {Berlin; Heidelberg},
url = {https://doi.org/10.1007/978-3-642-59615-5_13},
isbn = {978-3-642-64052-0}