Robust Time-Delayed Control of a Class of Uncertain Nonlinear Systems

Abstract

Abstract In this paper, the tracking control problem of a class of uncertain nonlinear systems is addressed. The conventional Time-Delayed Control (TDC) approach, as reported in literature, does not provide any selection criterion for sampling interval and controller gains. This design issue of TDC is solved in this paper through a new stability approach based on the Lyapunov-Krasvoskii method and a relation between sampling interval and controller gains has been established. Moreover, a new Robust Time-Delayed Control (RTDC) strategy has been proposed to negotiate the time-delayed error that arises from the approximation of uncertainties in TDC. The RTDC methodology, unlike the existing control methodologies, does not require any predefined bound of the uncertainties. The switching gain of RTDC attempts to circumvent the approximation error through the control input and feedback information of past instances. The maximum allowable length of past data is evaluated from the stability analysis of TDC. Experimental result of the proposed methodology using a nonholonomic wheeled mobile robot (WMR) is presented and improved tracking accuracy of the proposed control law is noted compared to time-delayed control.