Stabilizing Periodic Orbits of Chaotic Systems Using Adaptive Critic-Based Neurofuzzy Controller

Abstract

In this paper design and evaluation of an adaptive critic-based neurofuzzy controller for the stabilizing periodic orbits of chaotic systems has been presented in detail. The main superiority of the proposed controller over previous analogous fuzzy logic controller design approaches, e.g., genetic fuzzy logic controller, is its online tuning characteristic and remarkable reduced amount of computations used for parameter adaptation, which makes it desirable for real time applications. Considering the simplicity of this controller and its independence from the system model, this control method has the advantage of online learning and control, and can be applied to a large variety of systems. The proposed adaptive scheme is used for stabilizing the 2-π and 4-π periodic orbits of a Duffing system to investigate numerically the effectiveness of the method. Also the robustness of the proposed controller was examined using input noise and parameter uncertainty in the system model. Simulation results show that the proposed algorithm can be successfully used for chaos suppression when there is not any crisp mathematical model of the dynamical system.