Adaptive output feedback control for chaotic PMSMs stochastic system considering constraints

This paper presents an adaptive output feedback controller for chaotic permanent magnet synchronous motors (PMSMs) considering unknown control gain, prescribed output performance constraint, full-state constraint, input constraint, and partial state quantity unmeasurable. To approximate unknown nonlinearities, radial basis neural networks (RBFNN) are employed, and computational complexity is reduced by using an adaptive law for single-parameter weight updates. Additionally, a neural network-based (NN-based) observer is constructed to estimate the unmeasurable states. A novel unified prescribed performance quadratic tangent type barrier Lyapunov function (QT-BLF) is proposed to handle both prescribed output performance constraint and full state constraints. This approach accommodates both constrained (symmetric or asymmetric) and unconstrained cases without altering the control law. Moreover, an auxiliary dynamic system is designed to address the effect of input saturation. The proposed controller is developed using the backstepping technique. To address the issue of "complexity explosion" in the backstepping method, a tracking differentiator (TD) is introduced, and an error compensation system is designed to address filtering errors. Based on the above, the controller design for chaotic systems of PMSM with stochastic disturbance and asymmetric constraints is implemented. The effectiveness of the proposed controller is validated through simulation results, which demonstrate that all signals of the closed- loop system are ultimately bounded, states are restricted to a prescribed region, and chaotic oscillations are effectively suppressed.