Periodic event-based sliding mode tracking control of Euler-Lagrange systems with dynamic triggering

In this article, we propose the design of a robust tracking controller of perturbed Euler-Lagrange systems (ELSs) based on dynamic event-triggered (DET) sliding mode control (SMC) with periodic evaluation of triggering rule. To ensure robustness, we employ the SMC technique and introduce a dynamic periodic event-triggering strategy to reduce communication frequency significantly. This strategy involves the incorporation of an auxiliary dynamic variable to formulate the event-triggering condition, leading to the generation of sparser triggering instants. An upper bound of the sampling period is also obtained in this design to facilitate the periodic assessment of the event-triggered strategy, alleviating the need for continuous verification of the event condition. This technique is more economical with respect to communication resources and practical than its continuous counterpart due to the relaxation of continuous measurements. The stability of the closed loop system is established using Lyapunov analysis within the dynamically triggered event-based SMC framework. The necessary switching gain for maintaining the stable motion of the sliding variable is derived with the help of Lyapunov analysis. The tracking error is shown to be ultimately bounded, and Zeno-behaviour is excluded to ensure finite sampling. A comparative analysis based on simulation results is included to highlight the effectiveness of the proposed scheme, especially in reducing the network usage in the transient phase of the response while achieving comparable steady-state behaviour. Ultimately, we validate the effectiveness of the proposed algorithm by simulating a two-link manipulator and experimentally implementing it with a one-link manipulator.