Adaptive control of fractional-order unified chaotic systems using a passivity-based control approach
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Feedback passivity-based controller design for stabilization of fractional-order unified chaotic systems is proposed in this paper. Although feedback passivity-based control is a well-known method for integer-order systems, it has not been investigated for fractional-order systems due to a lack of suited mathematical results. In this paper, a recently established lemma for the Caputo fractional derivative of a quadratic function is utilized to facilitate the design. An adaptive mechanism is also employed such that the controller does not need to known the parameter of the systems. Moreover, based on a fractional-order extension of the Lyapunov direct method, the stability of the zero dynamics of the systems is also provided. Numerical simulations are performed to illustrate the effectiveness of the proposed design. The results show that the controller is able to effectively stabilize the chaotic behavior without the knowledge of the system parameter. In addition, it is also found that the transient dynamics of the controlled system and the control effort are markedly influenced by the fractional order of the system.
KeywordsChaos control Fractional-order system Unified chaotic system Adaptive control Passivity-based control