Indirect Robust Adaptive Nonlinear Controller Design for a New 3D Chaotic System

A new three-dimensional chaotic system is presented with its basic properties such as equilibrium points, Lyapunovs exponents and Kaplan-Yorke dimension. An Indirect Robust Adaptive Nonlinear Controller for complete synchronization and/or control of the new system considered with mismatch disturbances is designed. The adaptive controller is designed such that it allows simultaneously accurate control and system identification. The same controller design approach proposed in this paper can be applied to the design of controllers for other nonlinear Multi-Input-Multi Output (MIMO) systems with parameters uncertainties. Using the Lyapunovs method, the update rules for system identification are derived. MATLAB simulations results are presented to illustrate the efficiency of the proposed controller.