Multiparametric Nonlinear MPC: A region free approach

Abstract

Determination of active constraints forms an essential part of the multiparametric MPC approach for linear systems. An analysis of KKT conditions to identify active constraints provides piecewise affine control laws and their corresponding critical regions (CRs). However, an extension of multiparametric MPC for nonlinear systems requires overcoming significant challenges: predictions are nonlinear and so are constraints, in which case the MPC problems takes the form of a nonlinear program (NLP). Application of KKT conditions show that, in general, the MPC control law for nonlinear systems is piecewise, implicit, nonlinear function of the state. Moreover, the CRs have nonlinear boundaries. In this work, we propose an offline combinatorial approach to identify all active sets of constraints for the nonlinear MPC problem a priori. The offline approach uses implicit enumeration of the constraints based on feasibility of KKT conditions and a primal criteria. Thus, the offline step provides all the admissible CRs as well as the corresponding nonlinear system of KKT equations corresponding to each CR. The online MPC implementation uses a region-free approach, wherein the CR corresponding to the current state as well as the control action is determined by solving the nonlinear system of KKT equations online. The method is demonstrated using a numerical example from literature.