An Application of Backtracking Search Algorithm for Chaos Control Using Adaptive Fuzzy PID Controller with H∞ tracking performance

This paper introduces a technique for controlling a class of uncertain chaotic systems using an adaptive fuzzy Proportional-Integrator-Derivative (PID) controller with H∞ tracking performance. The purpose of this work is to achieve optimal tracking performance of the controller using Backtracking Search Algorithm (BSA). BSA، which is a novel heuristic algorithm، has an easy structure with single control parameter. In BSA، three basic genetic operators (selection، mutation and crossover) are utilized to generate trial individuals. To this reason، the control problem in hand is considered as an optimization problem by defining an appropriate objective function. Stability analysis of the control scheme is provided based on Lyapunov theory and modified Riccati-like equation، where the robustness of the closed-loop system is guaranteed by H∞ tracking performance for any predefined level. To evaluate the performance of the proposed control method، it is employed for tracking control of Duffing uncertain chaotic system. Simulation results show the capability of the proposed controller.