Approximation-based adaptive fixed-time tracking control for uncertain high-order nonlinear systems subject to time-varying parameters and unknown input nonlinearity

In this paper, the fixed-time tracking control (FTTC) problem is discussed for a type of uncertain high-order nonlinear systems. Compared with the existing works, the studied system is affected by time-varying parameters and unknown input nonlinearity. By applying neural network (NN) approximation method together with the adaptive control method, the fixed-time control theory, the backstepping control method, and the Nussbaum gain function (NGF) technique, an adaptive NN-based FTTC scheme is presented to achieve fixed time tracking. Especially, the NGF is utilized to handle the unknown control gain caused by unknown input nonlinearity. Furthermore, some adaptive control laws are formulated to estimate unknown parameters. Under the influence of different input nonlinearity, it can be inferred that the designed control strategy guarantees that the tracking error converges to a small neighborhood of zero within a fixed time, while also maintaining the boundedness of all signals of the closed-loop system. Finally, three simulation cases are presented to validate the availability of the theoretical results.