On moment relaxations for linear state feedback controller synthesis with non-convex quadratic costs and constraints

2024/03/22 by Dennis Gramlich, Gramlich, Dennis, Sheng Gao +7 · 1 citation
Engineering · #Advanced Control Systems Optimization #Control and Stability of Dynamical Systems #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2403.15228

openalex publication_date 2024/03/22 · openalex created_date 2024/03/26 · openalex updated_date 2026/07/28

Abstract

We present a simple and effective way to account for non-convex costs and constraints~in~state feedback synthesis, and an interpretation for the variables in which state feedback synthesis is typically convex. We achieve this by deriving the controller design using moment matrices of state and input. It turns out that this approach allows the consideration of non-convex constraints by relaxing them as expectation constraints, and that the variables in which state feedback synthesis is typically convexified can be identified with blocks of these moment matrices.

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