Return Interpolated Value Functions

[pulsipher]

We should build in some interpolation functionality to automatically construct start value functions and optionally return infinite variable solutions as functions.

[pulsipher]

This should probably just use Interpolations.jl. To avoid adding too many dependencies, it might be better to do this in a separate package.

[shobhitvoleti]

Hey, I've been using InfiniteOpt.jl for a race car track minimum time optimal control problem and it does really well! I'm pleased with the results and the interface is very intuitive! However, my next task is to extract the optimal control trajectory from InfiniteOpt and pass it through an MTK model to validate that the control will indeed predictably keep the lap time to a minimum in an external model. I'm using OpenMDAO's example as a benchmark to test against. They use a GaussLobatto orthogonal collocation scheme of degree 3. In my Julia code, I use this in the @infinite_parameter like this:

@infinite_parameter(m, τ in [0, chosen_track_length], num_supports = 51, derivative_method = OrthogonalCollocation(4))

My question is, when I extract the optimal control using
opt_thrust = value.(u[1], label = InfiniteOpt.All)
The trajectory I get looks physically infeasible. Is there a specific way to extract the control at the intermediate collocation points that I'm missing?

[pulsipher]

Hi @shobhitvoleti. Using the label = all keyword will extract all the intermediate collocation points. If you want to further interpolate, I suggest using Interpolations.jl on the provided discretized solutions.

The unexpected behavior you are seeing is likely because the collocation introduces additional degrees of freedom to the control variables. To resolve this, you can use constant_over_collcation to keep the control variables constant over the internal collocation nodes. Note that this has not been released quite yet and is available on the current release candidate of InfiniteOpt which you can install via:

import Pkg
Pkg.add(url = "https://github.com/infiniteopt/InfiniteOpt.jl", rev = "master")