Adaptive Terminal Sliding Mode Control of Hyper-Chaotic Uncertain 4-Order system with One Control Input

One of the unavoidable issues with various real-time control systems is existence of the external disturbances and uncertainties which is usually unavailable. To deal with these disturbances and uncertainties, various robust control methods have been introduced in the literature such as Sliding Mode Control (SMC), adaptive control method and so on. This paper proposes a novel Adaptive Terminal SMC (ATSMC) method to control the hyper-chaotic 4-order system within a finite-time by utilizing only one control input. The dynamical model of the hyper-chaotic 4-order system is subjected to the mismatched external disturbances and uncertainties which are bounded, but these bounds are unavailable. The adaptive concept is employed to approximate the upper bounds of these unknown mismatched external disturbances and uncertainties within a finite-time and their estimations are used in the control input. The robust controller is designed by utilizing Lyapunov stability theory. The key features of the designed controller are robustness against all mismatched uncertainties and external disturbances, and providing stability within a finite-time. Finally, a numerical simulation is performed in Simulink/MATLAB to verify the effectiveness of the designed controller to suppress the chaotic oscillations. The numerical simulation results reveal that the finite-time stability is achieved accurately as soon as the controller is introduced.