Computation of Parameter Dependent Robust Invariant Sets for LPV Models with Guaranteed Performance

TL;DR

This paper introduces an iterative method to compute larger, parameter-dependent robust invariant sets for LPV systems, guaranteeing invariance and performance using LMIs and SDP, with demonstrated improvements over non-parameter-dependent approaches.

Contribution

The paper develops a novel iterative algorithm that computes parameter-dependent RCI sets for LPV systems, incorporating a volume maximization and performance guarantees within an SDP framework.

Findings

Generated larger invariant sets than non-parameter-dependent methods.

Ensured invariance and performance within the RCI set.

Validated approach with a numerical example showing improved results.

Abstract

This paper presents an iterative algorithm to compute a Robust Control Invariant (RCI) set, along with an invariance-inducing control law, for Linear Parameter-Varying (LPV) systems. As the real-time measurements of the scheduling parameters are typically available, in the presented formulation, we allow the RCI set description along with the invariance-inducing controller to be scheduling parameter dependent. The considered formulation thus leads to parameter-dependent conditions for the set invariance, which are replaced by sufficient Linear Matrix Inequality (LMI) conditions via Polya's relaxation. These LMI conditions are then combined with a novel volume maximization approach in a Semidefinite Programming (SDP) problem, which aims at computing the desirably large RCI set. In addition to ensuring invariance, it is also possible to guarantee performance within the RCI set by imposing a chosen quadratic performance level as an additional constraint in the SDP problem. The reported numerical example shows that the presented iterative algorithm can generate invariant sets which are larger than the maximal RCI sets computed without exploiting scheduling parameter information.