Finite-time tracking control for fractional-order nonlinear high-order parametric systems with time-varying control gain and external disturbances: an approximation-based adaptive control method

Abstract This paper addresses the finite-time tracking control (FTTC) problem for a class of fractional-order nonlinear high-order parametric systems. The considered system exhibits significant distinctions from existing studies due to the presence of unknown dynamics, including time-varying control gain, parametric nonlinearities and external disturbances. Firstly, the issue of approximating unknown nonlinear functions is solved by utilizing the radial basis function neural network (RBFNN) approximation technique. Moreover, adaptive laws for unknown parameters are designed based on adaptive estimation methods. Furthermore, the Nussbaum gain function (NGF) technique is also used to deal with the unknown time-varying control gain. Subsequently, an NN-based adaptive FTTC law is successfully developed to achieve the finite time convergence. The proposed control law guarantees that the system output tracks the given reference signal and the tracking error can converge to a small neighborhood of zero within a finite time, while also ensuring that all signals of the closed-loop system remain bounded. In the end, the effectiveness of the proposed control law is verified through two simulation examples.