ADT-based adaptive back-stepping control for the switched non-affine nonlinear system with uncertain parameters

The adaptive back-stepping control issue for the switched non-affine nonlinear system with the uncertain parameter is addressed in this paper. Inspired by the “extended state” conception, the integral item is first employed in the original switched nonlinear system to generate an augmented switched non-affine nonlinear system. Then, the non-affine structures in the system dynamics are adopted to devise the virtual controls directly, and the dynamic surface control is integrated to eliminate the “explosion of complexity” caused by the back-stepping design. Furthermore, the estimation of switched unknown parameter is achieved by the continuous variable, and the individual Lyapunov functions including the estimation errors are constructed for each subsystem. Combined with the multiple Lyapunov functions methods, the uniformly ultimately bounded of the closed-loop switched system could be ensured under any switching law, which satisfies the average dwell time condition. Furthermore, system tracking errors would converge to the neighborhood of the zero. Finally, numerical simulations demonstrate the validity of proposed control approaches.