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

arXiv (Cornell University)

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.

Authors 5

1. Dennis Gramlich Aachen Intelligent Control Systems

   RWTH Aachen University

   Affiliation as printed

   Intelligent Control Systems , RWTH Aachen University , 52074 Aachen , Germany

2. Sheng Gao
3. Hao Zhang Aachen Intelligent Control Systems

   RWTH Aachen University

   Affiliation as printed

   Intelligent Control Systems , RWTH Aachen University , 52074 Aachen , Germany

4. Carsten W. Scherer Aachen Intelligent Control Systems

   RWTH Aachen University

   Affiliation as printed

   Intelligent Control Systems , RWTH Aachen University , 52074 Aachen , Germany

5. Christian Ebenbauer Aachen Intelligent Control Systems

   RWTH Aachen University

   Affiliation as printed

   Intelligent Control Systems , RWTH Aachen University , 52074 Aachen , Germany