Adaptive control of a class of nonlinear systems with its application to a synchronization problem

In this paper, 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 the true parameter is also given. Then we show that the synchronization problem for the Chua's circuit and an 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 the output of the uncertain harmonic system.