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.

中文翻译：

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基于动态事件触发的滑模控制设计

本文介绍了一种新的基于事件触发的滑模控制 (SMC) 设计，用于控制动态系统抵抗外部扰动。这种触发机制旨在生成比现有采样模式更稀疏的采样模式，同时实现最小的资源利用率。触发机制采用标量动力学，因此称为动态事件触发机制，作为触发条件的过滤器。除了恒定阈值之外，此动态的输出还用于事件条件，而事件函数的一部分作为输入馈送到此过滤器。现有的事件触发 SMC 设计算法可能无法保证动态事件触发策略的事件间时间增加。为设计基于动态触发的 SMC 提出了一种替代方法，其中我们部分放宽了 SMC 增益对事件参数的依赖性，而不影响闭环系统的稳态性能。结果表明，所提出的设计实现了更大的事件间时间，从而导致更稀疏的触发序列。触发序列中的芝诺现象成立。最后，在质量-弹簧-阻尼器系统的仿真研究中展示了所提出方案的说明。