FSE-RBFNNs-Based Robust Adaptive DSC Design for a Larger Class of Nonlinear Strict-Feedback Systems

A novel set-invariance adaptive neural dynamic surface (DSC) control scheme is presented for an extended class of the periodically disturbed nonlinear MIMO strict-feedback systems whose control gain functions are possibly unbounded. The most advanced is that the restrictive bounds assumption is removed after introducing appropriate compact sets, which are constructed in such a way that all the closed-loop trajectories stay in those sets all the time. To tackle the tracking control problem in the presence of more general periodic disturbances, a novel function approximator is well constructed by combining the radial basis function neural networks (RBFNNs) with the Fourier series expansion (FSE). In addition, the DSC technique is employed to overcome the problem of "explosion of complexity''. Furthermore, the Lyapunov theory and invariant set theorem are utilized to prove the closed-loop systems semi-globally uniformly ultimately bounded (SGUUB) stability, and the tracking errors can converge to an arbitrarily small residual set after appropriately choosing design parameters. Finally, the simulation results verify the effectiveness of the proposed method.