Design of Fixed-Time Neural Controller for Uncertain Nonstrict-Feedback Systems with Smooth Switching Functions

The tracking problem of uncertain nonstrict-feedback nonlinear systems(UNFNS) is examined to develop a novel adaptive neural control scheme to ensure fixed-time convergence. In particular,the challenge associated with the unknown nonlinear function can be overcome through neural network(NN) based estimation. Therefore, an NN-based adaptive fixed-time control scheme is established with only one parameter, using the property of the basis function vector to address the algebraic loop problem. Furthermore, the singularity problem can be solved by incorporating a smooth switching function. A rigorous theoretical analysis is performed to demonstrate that the output signal can track the reference signal within a fixed time and that the signals in the control systems are bounded. Finally,numerical simulations are performed to validate the feasibility of the proposed methodology.