Neural Adaptive Backstepping Control of the Chaotic PMSM System with Output Constraint via Tangent Barrier Lyapunov Function

This work devises a neural adaptive backstepping control of the chaotic permanent magnet synchronous motor system with output constraint. In the specific backstepping steps, to resolve the restraint of output tracking error, the Lyapunov function of the tangent barrier is introduced. Chebyshev neural networks and Nussbaum-type function are utilized to deal with uncertain nonlinearities and uncertain gain. The tracking differentiator is exploited to eliminate the "explosion of complexity" of virtual controller. Then, the boundedness of all the closed-loop signals is proved without bypassing the output constraint by Lyapunov synthesis. Eventually, simulation results verify the validities of the presented scheme.