Sliding Mode Control of Discrete Chaotic System Based on Multimodal Function Series Coupling

Abstract

A new sliding mode control model of discrete chaotic systems based on multimodal function series coupling is proposed to overcome the shortcomings of the standard PSO algorithm in multimodal function optimization. Firstly, a series coupled PSO algorithm (PP algorithm) based on multimodal function is constructed, which is optimized by multipeak solution on the basis of the standard PSO algorithm. Secondly, the improved PSO algorithm is applied to search all the extreme points in the feasible domain. Thirdly, the Powell method is used to perform the local optimization of the search results, and the newly generated extreme points are added to the extreme point database according to the same peak judgment operator. Finally, the long training time of PP algorithm can be overcome by the characteristics of fast convergence rate of the cloud mutation model. And also, both the population size and the redundancy can be reduced. Then, the clonal selection algorithm is used to keep the diversity of the population effectively. Simulation results of the sliding mode control of discrete chaotic systems show that the improved PSO algorithm obviously improves the response speed, overshoot, and so on.