Synchronization of noise-perturbed generalized Lorenz system by sliding mode control

This paper designs the controller for uncertain Lorenz system with multiple inputs containing sector nonlinearities and dead zone, and theoretically demonstrates the effectiveness of this controller. By this controller, the controlled Lorenz system can asymptotically drive the system orbits to arbitrarily objective trajectories even with uncertainties and sector nonlinearities and dead zone in the inputs, and thus has strong robustness. Finally, through the emulation studies of controlled Lorenz systems, it demonstrates the effectiveness of this controller.

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COMPOSITE SLIDING MODE CONTROL OF CHAOTIC SYSTEMS WITH UNCERTAINTIES

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127403006984 ◽

2003 ◽

Vol 13 (04) ◽

pp. 863-878 ◽

Cited By ~ 5

Author(s):

CHUN-CHIEH WANG ◽

JUHNG-PERNG SU

Keyword(s):

Sliding Mode Control ◽

High Performance ◽

Chaotic Systems ◽

Lorenz System ◽

Sliding Mode ◽

Dynamic Responses ◽

Significant Feature ◽

New Approach ◽

Mode Control ◽

Control Scheme

This paper presents a new approach to the design of a composite sliding mode control for a class of chaotic systems with uncertainties. A significant feature of this control scheme is the incorporation of a new complementary sliding variable to the conventional sliding variable in order that a high-performance controller can be obtained. It has been shown that the guaranteed steady-state error bounds are reduced by half, as compared with the conventional sliding control. Moreover, the dynamic responses during the reaching phase are also significantly improved. We used a controlled uncertain Lorenz system and a controlled uncertain Chua's circuit as illustrative examples to demonstrate the effectiveness of the design.

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Synchronization of Lorenz System Based on Fast Stabilization Sliding Mode Control

Mathematical Problems in Engineering ◽

10.1155/2015/282919 ◽

2015 ◽

Vol 2015 ◽

pp. 1-6 ◽

Cited By ~ 1

Author(s):

Xu Guowei ◽

Wan Zhenkai ◽

Li Chunqing

Keyword(s):

Sliding Mode Control ◽

Finite Time ◽

Lorenz System ◽

Sliding Mode ◽

External Perturbation ◽

Lyapunov Theory ◽

Continuous Control ◽

Integral Sliding Mode ◽

Control Approach ◽

Mode Control

A sliding mode control approach is achieved for Lorenz system based on optimal finite time convergent and integral sliding mode surface. The system perturbation is divided into two parts: the unmatched and the matched parts. Firstly, we design a discontinuous control for the unmatched part which will not be amplified. Secondly, we design a continuous control, that is, the ideal control to stabilize the Lorenz system error states in finite time stabilization. Then the controller based on integral sliding mode is constructed to ensure the robustness. The proposed method is proven to guarantee the stability and the robustness using the Lyapunov theory in the system uncertainties and external perturbation. Finally, the numerical simulations demonstrate that the proposed controller is effective and robust with respect to the perturbation.

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