Radial Basis Function Neural Network Trained by Adaptive Chaotic Particle Swarm Optimization to Control Nonlinear Systems

Chaotic particle swarm optimization (CPSO) is a newly developed optimization technique which combines the benefits of particle swarm optimization (PSO) and the chaotic optimization. This combination aims at avoiding the premature convergence of the PSO and the shortcomings of the chaotic optimization, in particular, the slow searching speed and the low accuracy when applied in optimizing a large search space. In addition, unlike conventional artificial neural networks (ANNs), the radial basis function neural network (RBFNN) has a more compact structure and consequently, it requires less training time compared with other ANNs and neuro-fuzzy systems. In this paper, an adaptive CPSO technique is utilized to train a RBFNN to act as a controller for nonlinear dynamical systems. Since the CPSO is a derivative-free optimization method, there is no need for a teaching signal to train the RBFNN to operate as a controller. The adaptive CPSO is employed to optimize all the modifiable parameters of the RBFNN, namely the centers and widths of the radial basis functions as well as the connection weights between the hidden layer and the output layer. As the objective function to be minimized by the adaptive CPSO, the mean square of error (MSE) criterion was used to assess the performance of each particle in the CPSO. In order to show the effectiveness of the proposed control method, three nonlinear systems, including the bioreactor which is a highly nonlinear chemical process, were used to be controlled by the adaptive CPSO-trained RBFNN controller. The simulation results confirm the validity of the proposed controller to control all the considered nonlinear systems with notable control accuracy and generalization ability. The advantage of the adaptive CPSO as the training method over other optimization techniques has been revealed from a comparison with the standard PSO and the genetic algorithm (GA). Furthermore, a comparative study with a neuro-fuzzy controller has shown the superiority of the RBFNN controller in terms of control performance and training speed.