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ControlSystem with parameters #594

@AlCap23

Description

@AlCap23

I have problems implementing a ControlSystem conversion in DataDrivenDiffEq ( SciML/DataDrivenDiffEq.jl#158 ).

I think it boils down to adding parameters to the problem. Is this a known limitation right now?

A MWE would be

using ModelingToolkit

@variables t x(t) v(t) u(t)
@parameters p
@derivatives D'~t

loss = (4-x)^2 + 2v^2 + u^2
eqs = [
    D(x) ~ v
    D(v) ~ p*u^3
]

sys = ControlSystem(loss,eqs,t,[x,v],[u],[p])
runge_kutta_discretize(sys, 0.1, (0.0, 1.0))

Which gives

ERROR: LoadError: MethodError: no method matching *(::Variable{ModelingToolkit.Parameter{Number}}, ::Operation)
Closest candidates are:
  *(::Any, ::Any, ::Any, ::Any...) at operators.jl:538
  *(::LightGraphs.LinAlg.Noop, ::Any) at /home/alcapitan/.julia/packages/LightGraphs/HsNig/src/linalg/graphmatrices.jl:226
  *(::Missing, ::Number) at missing.jl:115
  ...
Stacktrace:
 [1] (::ModelingToolkit.var"#561#562")(::Array{Operation,1}, ::Array{Operation,1}, ::Array{Variable,1}, ::Operation) at ./none:0
 [2] #invokelatest#1 at ./essentials.jl:710 [inlined]
 [3] invokelatest at ./essentials.jl:709 [inlined]
 [4] (::ModelingToolkit.var"#279#301"{Int64,Float64,ModelingToolkit.var"#561#562",Array{Array{Array{Operation,1},1},1},Array{Variable,1},Operation,Array{Array{Array{Operation,1},1},1}})(::Int64) at ./none:0
 [5] iterate at ./generator.jl:47 [inlined]
 [6] collect(::Base.Generator{UnitRange{Int64},ModelingToolkit.var"#279#301"{Int64,Float64,ModelingToolkit.var"#561#562",Array{Array{Array{Operation,1},1},1},Array{Variable,1},Operation,Array{Array{Array{Operation,1},1},1}}}) at ./array.jl:686
 [7] #278 at ./none:0 [inlined]
 [8] iterate at ./generator.jl:47 [inlined]
 [9] collect(::Base.Generator{UnitRange{Int64},ModelingToolkit.var"#278#300"{Float64,Int64,ModelingToolkit.var"#561#562",Array{Array{Array{Operation,1},1},1},Array{Variable,1},Operation,Array{Array{Array{Operation,1},1},1}}}) at ./array.jl:686
 [10] runge_kutta_discretize(::ControlSystem, ::Float64, ::Tuple{Float64,Float64}; tab::DiffEqBase.ImplicitRKTableau{Array{Float64,2},Array{Float64,1}}) at /home/alcapitan/.julia/packages/ModelingToolkit/CEB9b/src/systems/control/controlsystem.jl:153
 [11] runge_kutta_discretize(::ControlSystem, ::Float64, ::Tuple{Float64,Float64}) at /home/alcapitan/.julia/packages/ModelingToolkit/CEB9b/src/systems/control/controlsystem.jl:131
 [12] top-level scope at /home/alcapitan/Documents/code/DataDrivenDiffEq.jl/examples/ISInDy_Examples2.jl:87
 [13] include_string(::Function, ::Module, ::String, ::String) at ./loading.jl:1088
 [14] include_string(::Module, ::String, ::String) at ./loading.jl:1096

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