Abstract
A sliding mode control design for a class of uncertain chaotic systems subject to sector nonlinear inputs and dead zone is considered in this paper. It is guaranteed that, under the proposed control law, chaotic systems can asymptotically drive the system orbits to arbitrarily desired trajectories even with both uncertainties and input nonlinearities. However, in the sliding mode, the investigated uncertain chaotic system with nonlinear input still possesses advantages of fast response, good transient performance and insensitive to the parameter uncertainties and external disturbances as the systems with linear input. Finally, the Duffing-Holmes chaotic system and the multi-scroll chaotic system are used as an illustrative example to demonstrate the effectiveness of the proposed control scheme.
Highlights
IntroductionChaos has been shown to be an interesting and even common phenomenon in nature
Over many years, chaos has been shown to be an interesting and even common phenomenon in nature
Chaos control approaches can be classified into two categories, namely feedback and non-feedback methods (Soong et al, 2007)
Summary
Chaos has been shown to be an interesting and even common phenomenon in nature. The feedback methods stabilize one of the unstable periodic orbits embedded in its chaotic attractor by applying a small time-dependent perturbation proportional to the deviation between the desired and the actual trajectories calculated at every time instant. Such as occasional proportional feedback technique (Hunt, 1991), delayed feedback method (Pyragas, 1992), neural control (Lin, 2011), adaptive control (Lin et al, 2010), etc., are all typical feedback methods. The slide mode controller for uncertain chaotic systems with input nonlinearities are proposed (Yan, 2007; Wang et al, 2009). Computer simulation for the uncertain Duffing-Holmes system and the multi-scroll chaotic attractors are included to verify and visualize the effect of the sliding mode control
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