Adaptive control of uncertain Chua´s circuits

In this paper, the adaptive backstepping with tuning functions method is used for the control of uncertain Chua´s circuits with all the key parameters unknown. First, we show that several Chua´s circuits of different types including Chua´s oscillator, Chua´s circuit with cubic nonlinearity, and Murali-Lakshmanan-Chua circuit, can all be transformed into a class of nonlinear systems in the so-called non-autonomous “strict-feedback” form. Next, an adaptive backstepping with tuning functions method is extended to the non-autonomous “strict-feedback” system, and then used 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