JuliaControl / JuliaControl/ControlSystems.jl

dare validation unsuitable for H-inf synthesis

Open
#440 4 comments 0 reactions 0 assignees View on GitHub

Nobody has claimed this yet.

Dominant language
Julia
Stars
582
Forks
92
Avg merge
1h 12m
Merged PRs (30d)
2

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

Open the contributing guide

First steps

  1. Read the whole issue, then the project's contributing guide.
  2. Comment on the issue to say you are picking it up — it saves two people doing the same work.
  3. Fork the repository and make your change on a branch.
  4. Open a pull request that references the issue number.

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

Get new issues in your inbox

A short digest of beginner-friendly GitHub issues.