Asymmetric prescribed performance‐barrier Lyapunov function for the adaptive dynamic surface control of unknown pure‐feedback nonlinear switched systems with output constraints

Summary An adaptive dynamic surface control scheme for a class of pure‐feedback nonlinear switched systems possessing completely unknown nonlinearities and output constraints is proposed in this paper. By enabling the barriers to vary with prescribed performance functions in time, an asymmetric prescribed performance‐barrier Lyapunov function (APP‐BLF) is developed to guarantee the prescribed tracking performance simultaneously with constraint satisfaction under arbitrary switching, while the initial conditional requirements are relaxed. To handle the nonaffine problem, an affine variable is constructed to transform pure‐feedback systems into a strict‐feedback form with the nonaffine and switching properties existing in time‐varying bounded parameters by utilizing the mean value theorem at each step of the backstepping design procedure. Next, by incorporating the supremum norm theory, dynamic surface control, and the Nussbaum gain technique, a novel adaptive approach is presented to overcome unknown nonlinearities, unknown control coefficients, and the explosion of complexity. At last, by using the common Lyapunov function approach in combination with the decoupled backstepping method, a common approximation‐free adaptive controller is constructed to guarantee that all the signals in the closed‐loop system are semiglobally uniformly bounded. Moreover, the proposed controller alleviates the problems of overparameterization and the computational burden. Two simulation studies are conducted to demonstrate the effectiveness, robustness, and applicability of the proposed approach.