Adaptive Fuzzy Predetermined Performance Control of $p$-Normal Systems With Unknown Control Coefficients via Dynamic-Events

The issue of event-based asymmetric predetermined performance control (PPC) has been addressed for $p$-normal nonlinear systems with time-varying unknown control coefficients. A set of Nussbaum functions is introduced, capable of addressing both single and multiple unknown control coefficients. To achieve asymmetric PPC, a switching constraint scheme is proposed. Subsequently, an adaptive fuzzy controller based on dynamic events is developed. Improved techniques for approximating the unknowns of a system using fuzzy logic systems, while dynamic events are employed to reduce the frequency of controller updates. Using Lyapunov stability theory, it is proven that all signals in the closed-loop system remain bounded, and the tracking error is confined within the specified asymmetric boundaries. Eventually, the effectiveness of the present scheme is demonstrated by the simulation of three examples.