具有马尔可夫切换耦合和事件触发扩散的耦合动力系统的钉扎网络
Pinning networks of coupled dynamical systems with Markovian switching couplings and event-triggered diffusions
摘要：
本文研究了线性耦合动力系统的反馈牵制稳定性问题。在这里，耦合矩阵和钉扎节点的集合都随时间变化，由具有有限状态的连续时间马尔可夫链引起。在扩散耦合项和反馈钉扎项上采用事件触发规则，有效地减少了计算量，在某些情况下也减少了通信量，并通过其局部邻域状态信息和目标轨迹的最新观测值来实现。下一个观察也是由基于这些状态信息的特定标准（事件）触发的。考虑了两种情况：连续监测是指每个节点以瞬时的方式观察其邻居和目标（如果被钉住）的状态信息，以确定下一个触发事件时间，而离散监测是指每个节点只需要观察上一个事件时间的状态信息，并预测下一个触发事件时间。在这两种情况下，我们都给出了几种事件触发规则，证明了如果具有持续耦合和控制的耦合系统能够镇定的条件满足，那么这些事件触发策略能够镇定系统，并且在某些情况下Zeno行为被排除.数值例子来说明理论结果。
英文摘要：
In this paper, stability of linearly coupled dynamical systems with feedback pinning algorithm is studied. Here, both the coupling matrix and the set of pinned-nodes vary with time, induced by a continuous-time Markov chain with finite states. Event-triggered rules are employed on both diffusion coupling and feedback pinning terms, which can efficiently reduce the computation load, as well as communication load in some cases and be realized by the latest observations of the state information of its local neighborhood and the target trajectory. The next observation is triggered by certain criterion (event) based on these state information as well. Two scenarios are considered: the continuous monitoring, that each node observes the state information of its neighborhood and target (if pinned) in an instantaneous way, to determine the next triggering event time, and the discrete monitoring, that each node needs only to observe the state information at the last event time and predict the next triggering-event time. In both cases, we present several event-triggering rules and prove that if the conditions that the coupled system with persistent coupling and control can be stabilized are satisfied, then these event-trigger strategies can stabilize the system, and Zeno behaviors are excluded in some cases. Numerical examples are presented to illustrate the theoretical results.
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