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Research Papers

Adaptive Robust Stabilization of Rossler System With Time-Varying Mismatched Parameters Via Scalar Input

[+] Author and Article Information
Mohammad Mehdi Arefi

Department of Power and Control Engineering,
School of Electrical and Computer Engineering,
Shiraz University,
Shiraz 71348-51154, Iran
e-mail: arefi@shirazu.ac.ir

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received September 3, 2015; final manuscript received April 6, 2016; published online May 13, 2016. Assoc. Editor: Mohammad Younis.

J. Comput. Nonlinear Dynam 11(4), 041024 (May 13, 2016) (6 pages) Paper No: CND-15-1271; doi: 10.1115/1.4033383 History: Received September 03, 2015; Revised April 06, 2016

This paper presents an adaptive robust controller for a class of uncertain chaotic Rossler system with time-varying mismatched parameters. The proposed controller is designed based on Lyapunov stability theory, and it is shown that using this controller all signals of the closed-loop system are uniformly ultimately bounded (UUB). In addition, the proposed scheme is such that it does not require a priori information about the bound of uncertainties. Furthermore, since all the signals are UUB, the control signal is smooth and feasible to implement. Simulation results on a third-order Rossler system with time-varying parameters confirm the effectiveness of the proposed controller.

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References

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Figures

Grahic Jump Location
Fig. 1

The states of the attractor of the Rossler system

Grahic Jump Location
Fig. 2

Bifurcation diagram for increasing b

Grahic Jump Location
Fig. 3

The state time response of the Rossler system. The control is activated at t=10 s.

Grahic Jump Location
Fig. 4

The input response u(t) of the Rossler system and adaptation parameter β̂. The control is activated at t=10 s.

Grahic Jump Location
Fig. 5

The input response u(t) of the Rossler system using method presented in Estrada et al.

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