Understanding controls

Dear package authors! I have much fun playing with this tool (and diffeqflux), this will be a game changer in my field also (ecology). I was wondering if I could get some advice on how to deal with controls, or independent (or external) variables. My concrete example is data from a lake, measuring nutrients, algae and zooplankton. I also have measurements of temperature and influx of nutrients. The later two are external to the system. I think I have managed to set up a system to make the data driven problem identification. I am not sure though, How to use the resulting system and plugging the external variables back in. I did a MWE to generate similar but simpler data:

function T(t)
		10*(1+sin(t/200)*0.4+0.4)
	end
	function Inp(t)
		0.05+0.1*(sin(t/100)*0.4+0.4)
	end
	function system(u,p,t)
		N=u[1]
		A=u[2]
		Z=u[3]
		inp=Inp(t)

		TA=exp(-(T(t)-10.0).^2/200)
		TZ=exp(-(T(t)-15.0).^2/200)
		dN=inp-N*0.05-0.4*N/(0.2+N)*A*TA
		dA=0.4*N/(0.2+N)*A*TA-0.1*A/(0.2+A)*Z*TZ-0.05*A
		dZ=0.1*A/(0.2+A)*Z*TZ-0.05*Z
		return [dN;dA;dZ]
	end
	z0 = [0.1; 0.1;0.1]
	ztspan = (0.0, 500.0) # this gets really slow for endtime>50....
	zprob = ODEProblem(system, z0, ztspan)
	zsol = solve(zprob, Tsit5(), saveat = 0.1);

	X = zsol[:, :]  .* (1.0.+ 0.02.*randn(rng, size(zsol)));
	ts = zsol.t;
	controls=vcat(Inp.(ts)',T.(ts)')

	prob = ContinuousDataDrivenProblem(X, ts, GaussianKernel(),U = controls)

	#Three variables: N,A,Z and two controls: Inp and T
	@variables u[1:3] c[1:2]
	u = collect(u)
	c = collect(c)

	# just a start for basis exploration
	h = Num[polynomial_basis(u, 3); polynomial_basis(c, 3);exp(c[2])]
	
	basis = Basis(h, u, controls = c);
	println(basis) # hide
	
	sampler = DataProcessing(split = 0.8, shuffle = true, batchsize = 30, rng = rng)
	λs = exp10.(-10:0.1:0)
	opt = STLSQ(λs)
	res = solve(prob, basis, opt,
	            options = DataDrivenCommonOptions(data_processing = sampler, digits = 1))
       sys = get_basis(res)

This gives me a system of equations. I am not entirely sure what the best way to get the parameters as an array is but I use:

P=ModelingToolkit.varmap_to_vars(get_parameter_map(get_basis(res)),parameters(get_basis(res)))

If I do eqns=sys(z0,P,0) I get

My Question: How would I be able to get the controls, c1 and c2 into the equations as external variables so that I can run it as an ODE directly, assuming the controls are measured variables, controls and not the functions T(t) and Inc(t) at the top of the MWE.

I would want to run:

ODEProblem(eqns,z0,ztspan,P)

but driven by the variables in the matrix controls.

I hope this is reasonably clear as a question? Any recommendations for improvements are greatly appreciated!

Cheers, J

The issue names no repository files or tests; begin by reproducing the Julia MWE and tracing the controls-related API calls it uses. Done would be a documented, verifiable path for using measured controls with the generated ODE system, including an example based on the supplied matrix.