Switched Data-Driven Model Predictive Control for a Class of Unknown Hybrid Fuzzy Systems

Abstract

This paper studies the issue of switched data driven model predictive control (MPC) for a class of hybrid nonlinear systems with modal dwell time (MDT) restriction, where each subsystem is approximated by a T-S fuzzy system with bounded uncertainties. The unknown system matrices are characterized by a quadratic-matrix-inequality representation using the input-state-membership data. On this basis, a numerically tractable semi-definite programming (SDP) problem is formulated to design fuzzy-dependent feedback control law in a receding horizon manner for each switched mode, resulting in the optimization of worst-case infinite-horizon performance cost. Utilizing a set of feasible solutions of the constructed SDP problem, a feasible region and the corresponding approximated reachable set are deduced for each subsystem, based on which an algorithm is proposed to determine an admissible MDT ensuring the persistent feasibility of the switched data-driven MPC and the robust stability of the closed-loop system. The validity and potential of the theoretical results are illustrated through numerical applications to a single-link robot arm and a class of tail-sitter vertical take-off and landing unmanned air vehicles.