On Event-Triggered Tracking of Nonlinear SISO System by Sliding Mode Control

This paper studies tracking via sliding mode control for nonlinear SISO systems, with the provision of control updates by event-triggered method. In the tracking problem, the system dynamics is converted to the normal form based on the system relative degree. Then to implement the sliding mode control, a sliding surface is designed to track the reference trajectory. The resulting control law based on the designed surface will be a function of states and the reference and their derivatives. When system states move on the Sliding surface, system dynamics converge to reference trajectory asymptotically. By the event-triggered method the number of updates is decreased significantly, while the finite-time stability to sliding surface is guaranteed. The contribution of this paper is to draw a general discrete-time triggering-rule based on the states and the reference signal, effectively. As the reference derivative (equal to the system related degree) is effective in the triggering-rule, control system will be agile enough to track any fast maneuvering reference trajectory. To be conservative in the usage of computation resources, instead of the complicated terms of triggering functions, their Lipschitz equivalents have been put into use. Applicability of proposed event-triggered approach is demonstrated via simulation of a control system in tracking multiple references.

Keywords:

sliding mode control , system relative degree , normal form , event-triggered method , inter-execution time , triggering-rule