Design of a hierarchical fuzzy model predictive controller

Abstract

In order to control a nonlinear system using Nonlinear Model Predictive Control (NMPC), a nonlinear model from system is required. In this paper, a hierarchical neuro-fuzzy model is used for nonlinear identification of the plant. The use of hierarchical neuro-fuzzy systems makes it possible to overcome the curse of dimensionality. In neuro-fuzzy systems, if the input number increases, then the number of rules increases exponentially. One solution to this problem is making use of Hierarchical Fuzzy System Mamdani (HFS) in which the number of the rules increases linearly. Gradient descent and recursive least square algorithm are used simultaneously to train the parameters of the HFS. Gradient Descent Algorithm is utilized to train the parameters, which appear nonlinearly in the output of HFS, and RLS is used to train the parameters of consequent the part, which appears linearly in the output of HFS. Finally, a model predictive fuzzy controller based on a predictive cost function is proposed. Using Gradient Descent Algorithm, the parameters of the controller are optimized. The proposed controller is simulated on the control of continuous stirred tank reactor. It is shown that the proposed method can control the system with high performance.