arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2201.02090eess.SYcs.SY
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事件触发控制下平面系统事件间时间的渐近行为

Asymptotic Behavior of Inter-Event Times in Planar Systems under Event-Triggered Control

Anusree Rajan, Pavankumar Tallapragada

AI总结:

本文研究事件触发控制下平面线性系统事件间时间的渐近行为,通过角度映射不动点、遍历理论和旋转理论给出收敛性条件,并用数值仿真验证。

摘要:

本文分析平面线性系统在具有一般类尺度不变事件触发规则的事件触发控制下,事件间时间的渐近行为。在该设定下,事件间时间是事件发生时状态角度的函数。这一观点使我们能够通过研究角度映射的不动点来分析事件间时间,其中角度映射表示状态角度从一个事件到下一个事件的演化。我们为在尺度不变事件触发规则下事件间时间收敛或不收敛到稳态值提供了一个充分条件。在此基础上,我们进一步分析了基于阈值的事件触发规则这一特殊情况下的事件间时间行为,并给出了事件间时间收敛或不收敛到常数的各种条件。我们还分析了渐近平均事件间时间作为系统初始状态角度的函数。借助遍历理论,我们为渐近平均事件间时间对系统所有非零初始状态均为常数提供了一个充分条件。然后,我们考虑角度映射为保向同胚的特殊情况。利用旋转理论,我们对事件间时间的渐近行为进行了评述,包括事件间时间是否收敛到周期序列。我们通过数值仿真说明了所提出的结果。

英文摘要:

This paper analyzes the asymptotic behavior of inter-event times in planar linear systems, under event-triggered control with a general class of scale-invariant event triggering rules. In this setting, the inter-event time is a function of the angle of the state at an event. This viewpoint allows us to analyze the inter-event times by studying the fixed points of the angle map, which represents the evolution of the angle of the state from one event to the next. We provide a sufficient condition for the convergence or non-convergence of inter-event times to a steady state value under a scale-invariant event-triggering rule. Following up on this, we further analyze the inter-event time behavior in the special case of threshold based event-triggering rule and we provide various conditions for convergence or non-convergence of inter-event times to a constant. We also analyze the asymptotic average inter-event time as a function of the angle of the initial state of the system. With the help of ergodic theory, we provide a sufficient condition for the asymptotic average inter-event time to be a constant for all non-zero initial states of the system. Then, we consider a special case where the angle map is an orientation-preserving homeomorphism. Using rotation theory, we comment on the asymptotic behavior of the inter-event times, including on whether the inter-event times converge to a periodic sequence. We illustrate the proposed results through numerical simulations.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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