Novel prescribed performance-tangent barrier Lyapunov function for neural adaptive control of the chaotic PMSM system by backstepping

Abstract This paper investigates a neural adaptive output tracking prescribed performance control of the chaotic permanent magnet synchronous motor system with output-constrained, time-delays, parameter perturbations and external disturbances. Firstly, a novel prescribed performance-tangent barrier Lyapunov function is created to tackle the prespecified constraints of tracking error and output. Subsequently, backstepping controllers have been suggested. In specific steps, Chebyshev neural networks and the Nussbaum-type function are exploited to solve unknown nonlinearities and the unknown gain sign. Time-delays are tackled by constructing Lyapunov–Krasovskii functions (LKFs). Meanwhile, the “explosion of complexity” caused by the differentiation of virtual input is removed by plugging tracking differentiator into the controller. Furthermore, it is demonstrated that all the closed-loop signals are ultimate boundedness and predefined constraints are not violated. Finally, simulation studies were performed to confirm the validities and robustness of the raised scheme.