A Semi-Continuous PWA Model Based Optimal Control Method for Nonlinear Systems

Abstract

To alleviate the mode mismatch of multiple model methods for nonlinear systems when completely discrete dynamical equations are adopted, a semi-continuous piecewise affine (SCPWA) model based optimal control method is proposed. Firstly, a SCPWA model is constructed where modes evolve in continuous time and continuous states evolve in discrete time. Thanks to this model, a piecewise affine (PWA) system can switch at any time instant whereas mode switching only occurs at sample instants when a completely discrete PWA model is adopted, which improves the prediction accuracy of multi-models. Secondly, the switching condition is relaxed such that operating subspaces have overlaps and switching condition parameters are introduced. As a consequence, an optimal control problem with fixed mode switching sequence is established. Finally, a SCPWA model based model predictive control (MPC) policy is designed for nonlinear systems. The convergence of the MPC algorithm is proved. Compared with widely used mixed logical dynamic (MLD) model based methods, the proposed method not only alleviates mode mismatch, but also lightens the computing burden, hence improves the control performance and reduces the computation time. Some numerical examples are provided as well to show the efficiency of the method.