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.