论文标题
事件触发的控制下的平面系统中事件间时期的渐近行为
Asymptotic Behavior of Inter-Event Times in Planar Systems under Event-Triggered Control
论文作者
论文摘要
本文通过一类一般的规模不变事件触发规则在事件触发的控制下分析了平面线性系统中事件间时间的渐近行为。在这种情况下，活动间时间是事件中状态角度的函数。该观点使我们能够通过研究角度图的固定点来分析事件间时间，这代表了状态从一个事件到另一个事件的角度的演变。我们为在规模不变的事件触发规则下，在事件触发规则下，事件间值与稳态价值的收敛或不相关提供了足够的条件。在此之后，我们在基于阈值的事件触发规则的特殊情况下进一步分析了事件间的时间行为，并提供了各种条件，以使事件间时间的收敛或不连贯到一个常数。我们还分析了渐近平均事件间时间与系统初始状态角度的函数。借助厄贡理论，我们为系统的所有非零初始状态提供了足够的条件，使得渐近平均赛间间的时间间隔是一个常数。然后，我们考虑了一个特殊情况，即角度图是方向保护同态的同态。使用旋转理论，我们评论事件间时间的渐近行为，包括事件间时间是否汇聚到周期性序列。我们通过数值模拟说明了提出的结果。
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.
