Robust Adaptive Control of Nonlinear Systems with Time-Varying Parameters and Its Application to Chua's Circuit

Hamid R. KOOFIGAR  Saeed HOSSEINNIA  Farid SHEIKHOLESLAM  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E91-A   No.9   pp.2507-2513
Publication Date: 2008/09/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e91-a.9.2507
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and its Applications)
Category: Control and Optimization
Keyword: 
uncertain nonlinear systems,  Chua's circuit,  robust adaptive control,  tracking control,  time-varying parameters,  

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Summary: 
The problem of designing a robust adaptive control for nonlinear systems with uncertain time-varying parameters is addressed. The upper bound of uncertain parameters, considered even in control coefficients, are not required to be known. An adaptive tracking controller is presented and, using the Lyapunov theory, the closed-loop stability and tracking error convergence is shown. In order to improve the performance of the method, a robust mechanism is incorporated into the adaptive controller yielding a robust adaptive algorithm. The proposed controller guarantees the boundedness of all closed-loop signals and robust convergence of tracking error in spite of time-varying parameter uncertainties with unknown bounds. The parametric uncertain systems under consideration describes a wide class of nonlinear circuits and systems. As an application, a novel parametric model is derived for nonlinear Chua's circuit and then, the proposed method is used for its control. The effectiveness of the method is demonstrated by some simulation results.