Fixed-Time Fuzzy Adaptive Tracking Control for High-Order Systems with Unknown Nonlinearities and Control Directions

This paper presents a fixed-time tracking controller for a class of high-order nonlinear systems with completely unknown nonlinearities and unknown control directions. To perform the high-order practical tracking control objective, which is quite different from both the low-order control ones and the asymptotic stabilization ones, a coordinate transformation related to tracking error is introduced to make the tracking error be constrained to a prescribed interval including the origin in a fixed time by employing a finite-time stable function. A unique adaptive parameter is adopted to approximate the unknown nonlinear functions by applying fuzzy logic functions. Nussbaum functions are utilized to determine the unknown control directions. Based on the domination technique and the method of adding a power integrator, the provided controller can guarantee all the states of the closed-loop systems and control signal are bounded. Three simulation examples show the feasibility and efficiency of the proposed tracking control strategy.