Semi-Explicit Model Predictive Control of Quasi Linear Parameter Varying Systems

Abstract

Explicit linear model predictive control (MPC) is a proven method for constrained optimal control of fast, linear time invariant (LTI) dynamic systems. However, an extension to quasi-linear parameter varying (Q-LPV) systems requires overcoming significant challenges, since neither the explicit MPC law is piecewise linear in state nor are the critical regions polytopic. In this work, we propose a semi-explicit solution to a sub-optimal MPC solution for a class of Q-LPV systems, which are obtained as multiple linear model approximations to nonlinear systems. The sub-optimal MPC for Q-LPV systems, which has been shown to be stabilizing in an earlier work, requires an online solution of a quadratic program (QP). Casting the QP into a multiparametric form leads to a new class of multiparametric QP (mpQP), termed herein as generalized mpQP (GmpQP). Information about the critical regions and the MPC law are obtained offline using a semi-explicit solution of the GmpQP based on an implicit enumeration of the active sets. Three algorithms are compared for the online evaluation of the control law. Offline and online complexity of the proposed method are presented for an example, including comparison of computational speeds with well-known implicit QP solvers.