Tracking control and dynamic regulation of time-varying delay nonlinear systems with actuator saturation via multi-dimensional Taylor networks

Abstract

For desirable tracking control and transient optimization of time-varying nonlinear delay systems with actuator saturation, a controller with a fixed structure, i.e., multi-dimensional Taylor networks (MTN) controller, is proposed here. Based on the extension of the Lie derivative, a series of assumptions for most nonlinear time-varying delays systems are identified. Based on the filter variable and Lyapunov–Razumikhin theorem, it is proven that the MTN controller can track the reference satisfactorily, which conforms to the assumption. Furthermore, the dynamic regulation to improve system transient response using the MTN controller is realized through polynomial approximation. Parameters of the controller are determined by means of the appropriate optimization method, and its general design is explored and detailed. As verified by the results from two numerical examples, the proposed approach is feasible and effective. Depending on the conclusion of the interconnected control, the application of MTN controller in MIMO time-varying delays nonlinear system with actuator saturation is discussed.