On efficient computation of low-complexity controlled invariant sets for uncertain linear systems

Abstract

A method is presented for determining invariant low-complexity polytopic sets and associated linear feedback laws for linear systems with polytopic uncertainty. Conditions based on the relationship between 2- and ∞-norms are used to define an initial invariant low-complexity polytope as the solution of a semi-definite program. The problem of computing a maximal controlled invariant low-complexity polytopic set is then formulated as a bilinearly constrained problem, and a relaxation of this problem is derived as an iterative sequence of convex programs. The proposed method scales linearly with the state dimension, which allows the possibility of determining low-complexity robust controlled invariant sets for high-order systems.

Keywords:

• polytopic invariant sets
• optimisation
• constrained control

Acknowledgements

This research was supported by Research Council KUL: GOA AMBioRICS, CoE EF/05/006 OPTEC, IOF-SCORES4CHEM, several PhD/postdoc and fellow grants; Flemish Government: FWO (PhD/postdoc grants, G.0452.04, G.0499.04, G.0211.05, G.0226.06, G.0321.06, G.0302.07, G.0320.08, G.0558.08, G.0557.08, research communities (ICCoS, ANMMM, MLDM)); IWT (PhD Grants, McKnow-E, Eureka-Flite+); Helmholtz: viCERP; Belgian Federal Science Policy Office: IUAP P6/04 (DYSCO, Dynamical systems, control and optimisation, 2007-2011); EU: ERNSI; Contract Research: AMINAL.