A Dual-Loop Sliding-Mode Scheme for Uncertain Nonlinear Systems*

This paper investigates a novel dual-loop slidingmode control (SMC) scheme to achieve trajectory tracking for a class of nonlinear systems with unknown uncertainties. The inner loop is control loop, which consists of three controllers. An optimal feedback controller based on solving Hamilton-Jacobi-Bellman equation is proposed, which optimizes system performance for the nominal tracking system. A cerebellar model articulation control (CMAC) neural network is introduced for approximating the unknown uncertainties, and is embedded in the so-called CMAC-based sliding-mode controller. An adaptive compensator is used to dispel the negative effect from the approximated error of the CMAC. The outer loop is learning loop, which consists of the CMAC-based approximator and the quasi-sliding-model learning law. We formulate the learning problem of CMAC into a robust control framework of discretetime nonlinear system. A new online learning law based on discrete-time quasi-SMC strategy is developed to ensure the global and fast convergence and eliminates the chattering. It can be shown that the explicit expressions of gain parameters of the dual-loop sliding-mode scheme are derived in terms of the established sufficient conditions. Our proposed techniques are applied to a salient permanent magnet synchronous motor with excellent performance.