Adaptive synchronization of Chua´s circuit with an uncertain harmonic system

Motivated by an adaptive synchronization problem for the Chua´s circuit with an uncertain harmonic system, we first consider an adaptive stabilization problem for a class of uncertain nonlinear systems with both dynamic and static uncertainties. A sufficient condition on the convergence of the estimated parameter to true parameter is also given. Then we show that the synchronization problem for the Chua´s circuit and the uncertain harmonic system can be converted into the adaptive stabilization problem under consideration. Finally, an adaptive feedback control law is designed such that, the output of the Chua´s circuit can asymptotically synchronize, in the presence of large parameter variations, with a sine function with arbitrary unknown frequency, amplitude, and phase angles.