Flatness-Based Adaptive Neurofuzzy Control of Chaotic Dynamical Systems

Abstract

The paper proposes a solution to the problem of control of nonlinear chaotic dynamical systems, which is based on differential flatness theory and on adaptive fuzzy control. An adaptive fuzzy controller is designed for chaotic dynamical systems, under the constraint that the system’s model is unknown. The control algorithm aims at satisfying the $$H_\infty $$ tracking performance criterion, which means that the influence of the modeling errors and the external disturbances on the tracking error is attenuated to an arbitrary desirable level. After transforming the chaotic system’s model into a linear form, the resulting control inputs are shown to contain nonlinear elements which depend on the system’s parameters. The nonlinear terms which appear in the control inputs are approximated with the use of neuro-fuzzy networks. It is shown that a suitable learning law can be defined for the aforementioned neuro-fuzzy approximators so as to preserve the closed-loop system stability. With the use of Lyapunov stability analysis it is proven that the proposed adaptive fuzzy control scheme results in $$H_{\infty }$$ tracking performance. The efficiency of the adaptive fuzzy control method is checked through simulation experiments, using as case study the Lorenz chaotic oscillator.