JuliaControl / JuliaControl/ControlSystems.jl
dare validation unsuitable for H-inf synthesis
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Description
The command dare(A, B, Q, R) has validation on R > 0, this is unsuitable for H-infinity synthesis.
finding the stationary H-inf controller amounts to finding a fixpoint to the dare:
P = Q + A'(P^(-1) + BR^(-1)B -I/gamma^2)A.
This is equivalent to solving the lqr problem with augmented B* = [B I] and R* = [R 0;0 -gamma^2]. The algorithm which is already implemented works well, however R* is indefinite so calling dare(A, B, Q, R) throws an error.
Minimal test case:
gamma = 2
A = ones((1,1))
B = ones((1,2))
Q = ones((1,1))
R = [1. 0;0 -gamma^2]
P = dare(A,B,Q,R)
@test P[1,1] \approx 1/2 + sqrt(4/3 + 1/4)
Contributor guide
First steps
- Read the whole issue, then the project's contributing guide.
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Research direction
Start at the dare(A, B, Q, R) entry point and reproduce the minimal test case from the issue with the indefinite R matrix. Check how validation handles R > 0 and confirm the existing algorithm's behavior for the H-infinity formulation. Done means the example no longer fails validation and the stated P[1,1] approximation is satisfied by a regression test.
Written by the indexing model from the issue text.
Assessment
- Tech stack
- julia
- Domain
- backend
- Issue type
- Bug
- Difficulty
- 4/5
- Estimated time
- 3-5 days
- Activity status
- Stale
- Clarity
- Mostly clear
- Newbie friendliness
- 38/100