Control parameter specification for AbstractODESystem, DiscreteSystem

[cadojo]

Adds control parameter specification, related to #1041. Also adds a control Jacobian cached reference and an associated function. If the calculate_jacobian function generates a state space model A matrix, then the new calculate_control_jacobian function calculates the B matrix.

@ChrisRackauckas @YingboMa what do you think about this design? Thoughts before I proceed? Should I proceed? The rules are...

1. Control parameters are specified with a kwarg to ODESystem, and are empty by default
2. Control parameters must be some subset of the parameters of a system (I think this makes sense, since we don't want the control parameters to have their own dynamics)
3. Users can call calculate_control_jacobian to calculate the Jacobian of the system's dynamics with respect to the control parameters, not with respect to the state variables as is the case in calculate_jacobian

It would be nice to add a generate_statespace function to produce expressions for calculating the tuple A,B. That way, users can easily linearize an ODESystem about any operating point.

[ChrisRackauckas]

Analogues of this same functionality should be added to SDESystem and DiscreteSystem.

[cadojo]

Added a simple spring-mass-damper test for the control Jacobian, which should pass. Is there anything else y'all would recommend for this PR? I'm thinking a future PR could add the capability of replacing the control parameters with functions in ODEFunction so you can simulate control laws, but I won't be able to help with that until August or so.

[ChrisRackauckas]

I think this looks good, though note CI is failing. @YingboMa what do you think of the design?

[cadojo]

I don't think the DataDrivenDiffEq integration test failure is related to this PR. Could someone confirm?

[ChrisRackauckas]

Yes, unrelated. That's the Symbolic arrays stuff.

[cadojo]

I've added the control input to the DiscreteSystem test, hopefully that meets the code coverage requirements.

Edit: Is this code coverage failure an issue with merging this PR? I can try to add more tests, but adding the new control = ... keyword argument to DiscreteSystem tests did not increase (or change at all) the codecov/patch statistic.

[ChrisRackauckas]

What happens with the controls when the ODEProblem is built? Looks like nothing?

[ChrisRackauckas]

I guess let's move one step at a time. The ODEProblem step needs a solution to #1088 .

[ChrisRackauckas]

Now if we do this, we should put a deprecation warning on ControlSystem and remove it.

[cadojo]

Now if we do this, we should put a deprecation warning on ControlSystem and remove it.

Should this be done in this PR?

[ChrisRackauckas]

Do it in the next.