Adaptive control of uncertain Chua´s circuits

In this brief, we consider the problem of adaptive backstepping control of the Chua\´s circuits with all the parameters unknown. First, we show that several types of Chua\´s circuits, including the Chua\´s oscillator, Chua\´s circuit with cubic nonlinearity, and Murali-Lakshmanan-Chua circuit, can be transformed into a class of nonlinear systems in the nonautonomous "strict-feedback" form. Second, an adaptive backstepping with tuning functions method is extended to this nonautonomous "strict-feedback" system, and then employed to control the output of the Chua\´s circuit to asymptotically track an arbitrarily given reference signal generated from a known, bounded and smooth nonlinear reference model. Both global stability and asymptotic tracking of the closed-loop system are guaranteed. Simulation results are presented to show the effectiveness of the approach.