Terminal sliding mode control of chaotic Lorenz system: A discrete-time case (original) (raw)
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This work presents a robust chaotic control strategy for the Lorenz chaos via backstepping design. Backstepping technique is a systematic tool of control law design to provide Lyapunov stability. The concept of extended system is used such that a continuous sliding mode control (SMC) effort is generated using backstepping scheme. In the proposed control algorithm, an adaptation law is applied to estimate the system parameter and the SMC offers the robustness to model uncertainties and external disturbances so that the asymptotical convergence of tracking error can be achieved. Regarding the SMC, an equivalent control algorithm is chosen based on the selection of Lyapunov stability criterion during backstepping approach. The converging rate of error state is relative to the corresponding dynamics of sliding surface. Numerical simulations demonstrate its advantages to a regulation problem and an orbit tracking problem of the Lorenz chaos.
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2018 IEEE Conference on Systems, Process and Control (ICSPC), 2018
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.
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In this paper, a chattering-free sliding mode controller design for uncertain chaotic systems is presented. Since the implementation of the sliding mode control may cause a significant problem of chattering, many modified methodologies have been developed to overcome this drawback. However, each of them has own problems such as lack of robustness against disturbance variations, steady-state error, large convergence time and effect on transient performance. This paper proposes an improved sliding mode control strategy in which a modified sliding condition in a continuous function in control signal is taken into account instead of discontinuous part and also it adds an auxiliary continuous control to the control input. Then, the stability of controlled system is proved by using Lyapunov's direct method. The usefulness of this proposed method for eliminating the chattering phenomenon in transient and steady states, in the face of uncertain chaotic systems with disturbances, is well appeared. For this purpose, the Lorenz system is studied and its simulation results are presented to demonstrate the effectiveness of the proposed control scheme.