Differentiable control design

[baggepinnen]

A number of functions in this package and in RobustAndOptimalControl.jl fail when trying to compute gradients through them using ForwardDiff or Zygote. This issue tries to summarize the current status

Problematic functions

Function	AD package	Comment
c2d	ForwardDiff	:zoh requires exp!(::Matrix{Dual}). ForwardDiffChainRules buggy, but manual implementation possible. #844
feedback	Zygote	try/catch and @warn
are	All	Handled through ImplicitDiff #844
hinfnorm	ForwardDiff	Non-smooth. Works for Zygote. See tests for comments and comment. ForwardDiff in #844 but not for MIMO
svd/qr/schur	ForwardDiff	DifferentiableFactorizations.jl may be helpful
hessenberg	ForwardDiff, ReverseDiff	GenericLinearAlgebra.Hessenberg has different fieldnames from LinearAlgebra.Hessenberg

---

c2d example failing

foo(x) = sum(exp(reshape(x, 2, 2)))
v = randn(4)
using ForwardDiff
ForwardDiff.gradient(foo, v)

ERROR: MethodError: no method matching exp(::Matrix{ForwardDiff.Dual...

Related issues:

• make feedback differentiable by avoiding try-catch #596
• Differentiable control design RobustAndOptimalControl.jl#57

[baggepinnen]

With in-place exp!

using ForwardDiff
using ForwardDiffChainRules
@ForwardDiff_frule LinearAlgebra.exp!(x1::AbstractMatrix{<:ForwardDiff.Dual})
foo(x) = sum(LinearAlgebra.exp!(reshape(x, 2, 2)))
v = randn(4)
ForwardDiff.gradient(foo, v)

julia> ForwardDiff.gradient(foo, v)
4-element Vector{Float64}:
 1.1002741981700268
 1.0554893997879182
 0.7951393746830535
 0.7605002893053368