Robust steady state optimization for polytopic systems

Florian David Brunner, Florian A. Bayer, Frank Allgöwer

Abstract: We propose a novel method of jointly computing feedback controllers and associated robust invariant sets for discrete-time uncertain time-varying affine systems. The sets are parameterized as Minkowski sums of scaled and translated base sets and the control inputs as interpolations between control values at the vertices of the base sets. Robust invariance is enforced by a set of linear constraints. Various objectives can be approximated with the proposed method by specifying suitable convex cost functions, such as maximization and minimization of the resulting invariant sets, and optimization of the worst-case closed-loop performance.