Parameter Learning of Neuro-Fuzzy Controller Using Particle Swarm Optimization for Chaotic System Control

Abstract This paper describes the effective utilization of particle swarm optimization (PSO) to train a Takagi–Sugeno (TS)-type network controller for two samples of high nonlinear systems. First sample system is continuous stirred tank reactor (CSTR) and the second is Van-Der-Pole (VDP) oscillator. For the first system first-order, for the second system second-order Sugeno fuzzy controller are learned to hold the selected state variable at fixed set point. While the controller’s antecedent parameters are hold at proper fixed value, its rule (consequent) parameters are optimized with PSO. The superiority of this learning technique is not to need the partial derivative for the parameter learning. The results show that fuzzy controllers learned by PSO have exhibited good control performance. 1. Introduction In recent years, particle swarm optimization (PSO) has been used increasingly as an effective technique for solving complex and difficult problems [1-3]. This optimization technique has been proposed by Eberhart and Kennedy [4]. Optimization starts with random candidate parameter (particle) population, during the each algorithm iteration each particle in a swarm population adjusts its position in the search space based on the best position it has found so far. The principle behind PSO is to use these particles with best known positions to guide the swarm population to converge to a single optimum in the search space. The uniqueness of PSO’s ability in adaptively adjusting particles’ positions based on the dynamic interactions with other particles in the population makes it well suited for learning parameters in neuro-fuzzy control problems. If suitable particles can be determined as the appropriate best particles to control system, neuro-fuzzy controller design problem can be solved. How to choose the best-fit particle to guide each particle in the swarm population is a critical issue, and should be determined according to problem to be solved. For the controller design problems, this criterion can be constituted by a cost function defined based on error between set point and actual system value. This paper describes use of PSO for solving the determining problem of neuro-fuzzy controller’s consequent parameters for controlling CSTR and VDP chaotic system at fixed set point. The paper is organized as follows. Section 2 describes the classic PSO. Section 3 presents natural behavior of the two chaotic systems to be controlled and defines neuro-fuzzy controller’s structure. Section 4 presents the results proposed control approximation. Finally, Section V draws some conclusions and gives directions for future research.