Computation of parameter dependent robust invariant sets for LPV models with guaranteed performance?

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 real-time measurements of the scheduling parameters are typically available, we allow the RCI set description and the invariance-inducing controller to be scheduling parameter dependent. Thus, the considered formulation leads to parameter-dependent conditions for the set invariance, which are replaced by sufficient Linear Matrix Inequalities (LMIs) 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. Besides 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. Using numerical examples, we show that the presented iterative algorithm can generate RCI sets for large parameter variations where commonly used robust approaches fail. (c) 2023 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Automated summary

This paper proposes an iterative algorithm to compute the Robust Control Invariant (RCI) set and the corresponding control law for Linear Parameter-Varying (LPV) systems. The algorithm considers the dependence of RCI set description and control law on scheduling parameters. By replacing parameter-dependent conditions for set invariance with Linear Matrix Inequalities (LMIs) using Polya's relaxation, a Semidefinite Programming (SDP) problem is formulated to maximize the volume of the RCI set. The presented algorithm outperforms commonly used robust approaches in handling large parameter variations.