Nonlinear Model Predictive Control Using Discrete-Time Piecewise Multilinear Models

We propose a nonlinear model predictive controller for discrete-time nonlinear systems using a piecewise model based on feedback linearization. Model predictive control (MPC) has been successfully applied to many industrial processes. However, the stability of unstable linear systems and nonlinear systems is difficult to gurantee. The piecewise model in this study is a nonlinear system, and it can be constructed using only the vertex values of the piecewise rectangle regions without any information about the dynamics. Basically, the stability analysis and the stabilizing controller design of piecewise systems are difficult. This study applies feedback linearization to the transformation from each piecewise model into a linear system known as the Brunovsky canonical form. Thus, designing the controller for the entire piecewise system is easy. The proposed model predictive controller is designed for the piecewise system using feedback linearization. The MPC system satisfies the stability conditions based on a terminal cost. Through computer simulation, an example is shown to confirm the feasibility of our proposals.