Fuzzy-Chaos hybrid controllers for nonlinear dynamic systems

Controlling of chaos is an interesting research topic while employing of deterministic chaos for controlling is more interesting. This chapter focuses on employing and utilizing of inherent chaotic features in a nonlinear dynamical system in a useful manner. When it comes to employing deterministic chaos, there are tremendous advantages such as low-energy consumption, robustness of the controller performance, information security, and simplicity of employing chaos whenever it has chaotic attractive features in the original systems itself. If the original system does not have chaotic properties, deterministic chaos will be introduced to the system. Keeping these objectives, the control algorithm is constructed in order to control nonlinear systems, which exhibit chaotic behavior. We introduce two phases of control: First phase uses open-loop control forming a chaotic attractor or using chaotic inherent features in a system itself. Fuzzy model based controller is employed under state feedback control in the second phase of control. The Henon map and the three-dimensional Lorenz attractor, which have chaotic attractive features in their original systems, are taken into consideration so as to utilize the benefits of chaos. Then, a two-link manipulator is considered to illustrate the design procedure with employing deterministic chaos. Simulation results show the effectiveness of the proposed controller.