`ControlSystem` without defined loss function

[cadojo]

I typically use many different loss functions for the same control system / model. Defining the loss function once for each ControlSystem is a bit limiting, because I can't define one common System (model) for a bunch of analysis cases.

For reference, I've extended ModelingToolkit to PolynomialGTM. Right now, I'm representing the model aircraft dynamics as an ODESystem. It would be great to instead represent this model as a ControlSystem because I could then separate states and controls. But I have no common loss function I'd want to use as a default. I'd prefer not to make a factory function, since lots of controls analysis is not optimal control analysis.

Would changing ControlSystem to OptimalControlSystem, and then introducing a new struct ControlSystem <: AbstractControlSystem be appropriate here? The new ControlSystem type would have all of the same fields, except for the loss function. The generate_jacobian and calculate_jacobian functions would essentially produce the symbolic "A" matrix (the homogeneous dynamics), and we could add functions to generate the full symbolic state space model pretty easily.

This is a breaking change, obviously feel free to throw this out. I do think that non-optimal control problem modeling would be a valuable addition to ModelingToolkit.jl, and I'm definitely interested in helping out with that.

[ChrisRackauckas]

You're on the right track. I was going to talk to @YingboMa about modifying every every system to allow a control variable. I don't think control needs to be separate from ODESystem, but instead should be a part of it. And then we need to think about how to do optimal control as just a loss function on top of that, instead of duplicating system code.

[ChrisRackauckas]

ControlSystem was removed. OptimziationSystem as it grows should just cover this.