Neural network-based adaptive finite-time tracking control for multiple inputs uncertain nonlinear systems with positive odd integer powers and unknown multiple faults

This paper addresses the adaptive finite-time tracking control (FTTC) problem for multiple-input nonlinear systems (NSs). The system under consideration encompasses high-order nonlinear terms with positive odd integer powers, uncertain dynamics, parametric nonlinear dynamics, multiple unknown faults, and unknown control gains. The proposed adaptive FTTC strategy integrates the neural network (NN) approximation technique with the backstepping control approach. By employing the NN approximator, the challenge of approximating uncertain nonlinear dynamics and unknown nonlinear functions was effectively resolved. Concurrently, adaptive control laws for unknown parameters were formulated using the adaptive estimation method. Furthermore, to address unknown control coefficients arising from unknown faults and unknown control gains within the system, the Nussbaum gain function (NGF) was incorporated into the control design process. Subsequently, NN-based adaptive FTTC strategies were developed for inputs under various fault conditions. The designed control strategies ensured that all signals of the closed-loop system (ASCLS) with multiple faults maintain semi-global practical finite-time stability (SGPFS), and the tracking error of the system converges to a small neighborhood of zero within a finite time (SNZFT). Finally, the efficacy of the developed control method was validated through a simulation example.