Robust Estimation-Based Control of Chaotic Behavior in an Oscillator with Inertial and Elastic Symmetric Nonlinearities

Abstract

In this paper, we study the dynamics of a forced nonlinear oscillator with inertial and elastic symmetric nonlinearities using modern nonlinear, bifurcation and chaos theories. The results for the response have shown that, for a certain combination of physical parameters, this oscillator exhibits a chaotic behavior or a transition to chaos through a sequence of period doubling bifurcations. The main objective of this paper is to control the chaotic behavior for this type of oscillator. A nonlinear estimation-based controller is proposed and the transient performance is investigated. The design of the parameter update mechanism is analyzed while discussing ways to extend its performance to further account for other types of uncertainties. We examine robustness problems as well as ways to tune the controller parameters. Simulation results are presented for the uncontrolled and controlled cases, verifying the effectiveness and the capability of the proposed controller. Finally, a discussion and conclusions are given with possible future extensions.

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