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Adaptive Control for the Stabilization and Synchronization of Nonlinear Gyroscopes

Adaptive Control for the Stabilization and Synchronization of Nonlinear Gyroscopes

B. A. Idowua, *RongweiGuob, U. E. Vincent c,d,* aDepartment of Physics, Lagos State University, Ojo, Nigeria.b School of Mathematics and Physics, Shandong Institute of Light Industry, Jinan250353, P.R. China. c Department of Physics, Redeemers University Nigeria, Ogun State, Nigeria. dNonlinear Biomedical Physics, Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom.

Abstract 

Recently, we introduced a simple adaptive control technique for the synchronizationand stabilization of chaotic systems based on the Lasalle invariance principle. The method is very robust to the effect of noise and can use single-variable feedback toachieve the control goals. In this paper, we extend our studies on this technique tothe nonlinear gyroscopes with multi-system parameters. We show that our proposedadaptive control can stabilize the chaotic orbit of the gyroscope to its stable equilibrium and also realized the synchronization between two identical gyros even whenthe parameters are assumed to be uncertain. The designed controller is very simple relative to the system being controlled, employs only a single-variable feedbackwhen the parameters are known; and the convergence speed is very fast in all cases.We give numerical simulation results to verify the effectiveness of the technique andits robustness in the presence of noise. 

Key words: 

chaos synchronization, adaptive control, Nonlinear gyroscopePACS: 05.45.-a, 05.45.Pq, 05.45.Ac

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