Polytopic inclusion-based model predictive control for quasi-LPV systems using vertex system models and gain scheduling

Abstract

This paper proposes a Model Predictive Control (MPC) strategy for a class of Quasi-Linear Parameter-Varying (quasi-LPV) systems characterized by a measurable time-varying parameter. The core of the proposed quasi-LPV-MPC controller lies in the utilization of a polytopic representation along with a gain-scheduled controller. A terminal cost that depends explicitly on the scheduling parameter is used. However, for the implementation, a complementary cost function is used to frame the optimization problem at each vertex level so that the requirement of updating the varying parameters over the prediction horizon is relaxed. Though the resulting suboptimal controller involves more computational burden, the proposed method demonstrates improvement in control performance over traditional MPC schemes. Experimental validation on a cascaded coupled tank system underscores the practical efficacy of the proposed quasi-LPV-MPC controller, while simulation studies on a twin rotor multi-input multi-output system serve as an additional demonstration example case. Comparative performance evaluations against both linear and nonlinear MPCs clearly illustrate that the quasi-LPV-MPC offers better control precision, adaptability, and the overall system responsiveness, thus positioning it as an effective solution for quasi-LPV systems.