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

Proceedings of the IEEE Conference on Decision & Control, including the Symposium on Adaptive Processes, pp. 1010–1016

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 constraints on the expected value of quadratic functions, and that the variables in which state feedback synthesis is typically convexified can be identified with blocks of these moment matrices. The employed relaxation can lead to constraint violation along sample paths.

Authors 5

1. Dennis Gramlich Aachen Chair of Intelligent Control Systems

   RWTH Aachen University

   Affiliation as printed

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

2. Sheng Gao

   Tongji University

   Affiliation as printed

   Tongji University,College of Electronic and Information Engineering,Department of Control Science and Engineering,Shanghai,P. R. China,200092

3. Hao Zhang

   Tongji University

   Affiliation as printed

   Tongji University,College of Electronic and Information Engineering,Department of Control Science and Engineering,Shanghai,P. R. China,200092

4. Carsten W. Scherer

   University of Stuttgart

   Affiliation as printed

   University of Stuttgart,Chair of Mathematical Systems Theory,Stuttgart,Germany,70569

5. Christian Ebenbauer Aachen Chair of Intelligent Control Systems

   RWTH Aachen University

   Affiliation as printed

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