Parameter Dependent Robust Control Invariant Sets for LPV Systems with Bounded Parameter Variation Rate

TL;DR

This paper introduces a novel method for synthesizing parameter-dependent robust control invariant sets for LPV systems with bounded parameter variation, using a single SDP to improve efficiency and reduce conservativeness.

Contribution

The paper presents a new approach to synthesize PD-RCI sets for LPV systems with bounded parameter variation using a joint parameterization and a single SDP.

Findings

Outperforms existing methods in conservativeness

Reduces computational load compared to state-of-the-art

Demonstrates effectiveness through numerical examples

Abstract

Real-time measurements of the scheduling parameter of linear parameter-varying (LPV) systems enables the synthesis of robust control invariant (RCI) sets and parameter dependent controllers inducing invariance. We present a method to synthesize parameter-dependent robust control invariant (PD-RCI) sets for LPV systems with bounded parameter variation, in which invariance is induced using PD-vertex control laws. The PD-RCI sets are parameterized as configuration-constrained polytopes that admit a joint parameterization of their facets and vertices. The proposed sets and associated control laws are computed by solving a single semidefinite programing (SDP) problem. Through numerical examples, we demonstrate that the proposed method outperforms state-of-the-art methods for synthesizing PD-RCI sets, both with respect to conservativeness and computational load.