Support state and input arrays of different types in linearize

[baggepinnen]

Summary

linearize(f, x, u, args...) computed the Jacobian with respect to the input as

B = ForwardDiff.jacobian(u -> f(convert(typeof(u), xi), u, args...), ui)

convert(typeof(u), xi) converts the state to the array type of the input. This causes two failures:

• If the state and the input are static arrays of different lengths, it throws a DimensionMismatch, e.g., x::SVector{4} and u::SVector{2}. This occurs, for example, in ControlSystemsBase.observability(filter, x, u, p, t) for nonlinear filters of LowLevelParticleFilters.jl with static arrays.
• It discards the array type of the state. With a ComponentArray state and a Vector input, the components are lost, and x.v in f throws a FieldError.

The state is now converted element-wise, convert.(eltype(u), xi), which keeps the container type of the state and gives its elements the dual-number type of the input.

Tests

• Two cases were added to lib/ControlSystemsBase/test/test_hammerstein_wiener.jl: an SVector{3} state with an SVector{2} input, and a ComponentArray state with a Vector input. Both fail with the previous implementation (DimensionMismatch and FieldError) and pass with the new one.
• The rest of test_hammerstein_wiener.jl passes. The full test suite was not run.

The ControlSystemsBase version is bumped to 1.22.1.

---

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 91.64%. Comparing base (7e1ac64) to head (aebbfb9).

Additional details and impacted files

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##           master    #1072   +/-   ##
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  Coverage   91.64%   91.64%           
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  Files          42       42           
  Lines        5795     5795           
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  Hits         5311     5311           
  Misses        484      484           

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