Adaptive Fuzzy Practical Tracking Control for Asymmetric Time-Varying Constrained High-Order Nonlinear Systems with Zero Dynamics and Unknown Control Directions

This work investigates the adaptive fuzzy practical tracking control for high-order nonlinear systems with asymmetric time-varying output constraints and zero dynamics in presentation of unknown control directions and input saturation. To address the unknown control direction, Nussbaum functions are constructed. In addition, the fractional barrier Lyapunov function (BLF) is employed to handle the asymmetric time-varying output constraints problem. By utilizing fuzzy systems and adding a power integrator technique, a novel control method is proposed. Finally, it is demonstrated that the asymmetric time-varying output constraints are not violated, all the signals in the closed-loop systems are bounded and the tracking error converges into a small neighborhood of the origin. An example is provided to demonstrate the feasibility of the proposed control method.