Filled Function Method for Nonlinear Model Predictive Control

Abstract

A new method is used to solve the nonconvex optimization problem of the nonlinear model predictive control (NMPC) for Hammerstein model. Using nonlinear models in MPC leads to a nonlinear and nonconvex optimization problem. Since control performances depend essentially on the results of the optimization method, in this work, we propose to use the filled function as a global optimization method to solve the nonconvex optimization problem. Using this method, the control law can be obtained through two steps. The first step consists of determining a local minimum of the objective function. In the second step, a new function is constructed using the local minimum of the objective function found in the first step. The new function is called the filled function; the new constructed function allows us to obtain an initialization near the global minimum. Once this initialization is determined, we can use a local optimization method to determine the global control sequence. The efficiency of the proposed method is proved firstly through benchmark functions and then through the ball and beam system described by Hammerstein model. The results obtained by the presented method are compared with those of the genetic algorithm (GA) and the particle swarm optimization (PSO).