Switched-observer-based adaptive output-feedback control design with unknown gain for pure-feedback switched nonlinear systems via average dwell time

This paper studies the problem of adaptive fuzzy tracking control for a class of pure-feedback switched nonlinear systems with unknown gain. First, the studied system is handled by using the mean value theorem, the initial pure-feedback nonlinear systems become affine nonlinear systems. Then, the unknown signal is handled through a linear transformation, the Nussbaum-type functions are used to design an effective controller for the processed system. To avoid the issue of 'explosion of complexity' caused by mean value theorem and backstepping procedure, a first-order sliding-mode differentiator is employed to simplify the calculation. Combined with the average dwell time (ADT) method, a set of switching signals are given to sure the stability of the system. The Lyapunov theorem is used to verify that all signals are semiglobal uniformly ultimately boundness (SGUUB), and the errors can be regulated arbitrarily small. Finally, simulation results show the effectiveness of the proposed method.