RBF neural network based generalized predictive control for nonlinear stochastic systems

Abstract

Almost all practical systems are nonlinear, which are subject to disturbances and contain uncertainties. In most cases, disturbances and uncertainties can be modeled as stochastic processes, which make it necessary to develop controllers for nonlinear stochastic systems. Due to the disturbances and uncertainties, it is difficult to get the exact model of the nonlinear stochastic systems. Neural network techniques are found to have advantages in system identification. Any unknown function can be approximated to any degree of accuracy by a multiple-layer neural network. In addition, time delay occurs in many real systems. One of the most effective control methods to reduce the impact of delay on the closed-loop systems is predictive control, which is obtained by predicting the future control to minimize the errors. A RBF Neural Network based Generalized Predictive Controller (NNGPC) is introduced to control nonlinear stochastic systems. The input-output relationship of a nonlinear stochastic system is approximated by an RBF neural network. A learning algorithm is developed to train the RBF neural network by updating the neural network parameters, such as centers, widths, and weights, either on-line or off-line. The parameters are updated using the modified gradient decent method to minimize a cost function, which is a quadratic function of errors between the real system output and the output from the neural network. Based on the model obtained from the neural network learning algorithm, a multistep-ahead generalized predictive control algorithm is designed to minimize a cost function, which is constructed using future control signals and errors between future references and future outputs estimated from the model. The optimization problem involved in the predictive control is solved using Nelder-Mead method and Quasi-Newton method. The comparison between these two methods is made using simulation results.