Dynamic event‐triggering based design of sliding mode control

Abstract

This article presents a new event-triggering based design of sliding mode control (SMC) for the control of a dynamical system against external perturbations. This triggering mechanism aims to generate a sparser sampling pattern than the existing one while achieving the minimum resource utilization. The triggering mechanism employs scalar dynamics, hence it is called the dynamic event-triggering mechanism, which acts as a filter for the triggering condition. The output of this dynamics is used in the event condition in addition to a constant threshold while the part of the event function is fed as an input to this filter. The existing design algorithms for event-triggered SMC may not guarantee an increase in the inter event time for the dynamic event-triggering strategy. An alternative approach to this is proposed for the design of dynamic triggering based SMC where we partially relax the dependency of SMC gain on the event parameter without affecting the steady-state performance for the closed-loop system. It is shown that the proposed design achieves a larger inter event time leading to a sparser triggering sequence. We guarantee the stability by showing the convergence of state trajectories of the closed-loop system within any desired bound around the origin for the proposed triggering mechanism, and also the absence of the Zeno phenomenon in the triggering sequence is established. Finally, an illustration of the proposed scheme is presented in a simulation study for a mass-spring-damper system.