Globally Exponentially Stable Tracking Control of Self-Restructuring Nonlinear Systems

This article proposes a neural networks (NNs)-based tracking control approach for a class of uncertain high-order self-restructuring nonaffine dynamic systems. Unlike most existing NN-based works that normally ignore the precondition on the functionality and reliability of NN unit and thus can only ensure semiglobal stability, the proposed method explicitly addresses the issue of reliable in-loop operation of NN approximation-based control unit, resulting in a safeguarded NN-based control solution capable of ensuring globally stable tracking. Furthermore, the control method proposed guarantees exponentially globally stable tracking for systems with self-restructuring nonlinearities and uncertainties, distinguishing itself from those that only yield uniformly ultimately bounded (UUB) regulation/tracking results for nonlinear systems with fixed structures. All of these features are achieved by the proposed strategy consisting of two cooperative control units: 1) safeguard control and 2) NN-based control. The role of the safeguard control is to force the states (starting from any initial condition) to enter a stable region, so that the NN-based control can be activated trustworthily and safely. It is such cooperation of the two units that not only ensures the tracking error entering the stable region first within a prespecified finite time but also guarantees the tracking error converging to zero exponentially thereafter, resulting in global zero-error tracking. Both the theoretical analysis and numerical simulation authenticate the effectiveness of the proposed method.