Adaptive modified prescribed performance constraint control for uncertain nonlinear discrete-time systems

In this work, an adaptive output constraint control scheme-based on modified prescribed performance function is investigated for a class of discrete time nonlinear systems subject to unknown parameters and uncertain dynamics. Unlike the traditional adaptive output constraint approach that employs barrier Lyapunov functions, a modified prescribed performance function is first employed to guarantee that the tracking error can convergence to a predefined and asymmetric neighborhood of zero and that the safety constraint bound of the system output is not violated. In order to reduce the effect of unknown parameters, the multiple model set is constructed and it can improve the transient response of systems. The specific features of the established multiple model method are that it not only can enhance the cooperativity of each identification model, but also reduce the computational burden since it does not require to a large number of models. The neural networks are utilized to approximated unknown dynamics. At the same time, the prescribed performance function, slide variable and second adaptive level technology in a unified framework are employed to design the controller. In order to verify the effectiveness of the established control scheme, the presented output constraint method is implemented to two numerical examples.