触发更新机制下多智能体系统上一致性算法的设计与分析

In the applications of networked control systems,how to share the limited computational and communication resources is a big issue. To solve this problem, the so-called event-triggered control scheme is proposed to reduce unnecessary update and excution of the controllers without viloating the control objective of the whole system. In event-triggered control scheme, since the controller is excuted only when certain event occurs, so the design of the triggering events plays a fundamental role. In the existing works, the triggering events are always based on state observation and error measurement. However, when introduced in consensus algorithms in networks of multiagents such a design can not privide satisfactory performance compared to its continuous feedback control counterpart.For example, it can only apply to static networks, and it can not exclude Zeno behavior(occurrence of infinite number of triggering events in a finite time interval). Thus a new design of triggering events is necessary to improve the performance of the algorithm.In this project, different from the existing work, we consider the design of triggering events based on the relation between the event-triggered system and a proper discrete-time system. Concretely, we consider direct discretization whenever possible, otherwise, we try to relate the event-triggered system to a discrete-time system after some proper transformation. The new design will apply to networks with dynamic topologies such as switching topologies, especially stochastically switching topologies as well as networks with arbitrary coupling weights(either positive or negative). At the same time, by employing the switching systems theory, we consider the exclusion of Zeno behavior by extending the inter-event time intervals. After that, by considering the relation between the event-triggered systems and differential systems with discontinuous right-hand sides, we will refine the design of the consensus protocols to accelarate convergence. Particularly, we try to obtain finite-time convergence at least in some special cases. As applications, we consider the design and analysis of event-triggered consensus algorithms that will achieve consensus on a prescribed value by impulsive pinning control technique. Our work will provide a better theoretical framework for the design of event-triggered consensus algorithms on a wider range of networked control systems.

在网络化控制系统中，事件触发更新的控制机制是提高资源利用率的有效方法。而在多主体系统的一致性算法中，利用基于状态观察和误差测量的触发事件设计方法只适用于静态网络，且无法消除Zeno现象，即有限时间内发生无限次触发的现象，严重制约了其实际应用。针对这一问题，我们拟采取新的基于离散化的触发事件设计方法，使之适用于更一般的网络结构，特别是动态网络结构以及任意权重的耦合结构,并结合切换系统理论研究如何增大触发事件的事件间隔从而消除Zeno现象。在此基础上，我们将采用不连续系统理论改善算法的设计从而提高其收敛性能，并实现有限时间收敛。作为应用，我们在触发更新机制下利用脉冲牵制控制实现特定值的一致性算法并分析其收敛性。我们的工作将为网络化控制系统上触发更新机制的一致性算法的设计提供更好的理论框架。

在网络化控制系统中，事件触发更新机制可以通过减少通信及控制器更新次数有效提高网络资源的利用率。而在多主体系统的一致性算法中，现有的基于状态观察和误差测量的触发事件设计方法只适用于静态网络，且难以消除所谓的Zeno现象，即有限时间内触发无限次的现象，严重制约了其实际应用。针对这一问题，本项目从一种新的角度研究了触发更新机制下一致性算法的设计与分析，主要目标是为这类算法的设计与分析提供一种新的理论框架。主要研究内容有：1）研究了新的基于离散化的触发事件设计方法，使之适用于更一般的网络结构并且更容易分析，且易于消除Zeno现象；2）在新的理论框架下研究了动态结构以及任意耦合结构的网络上触发更新的一致性算法的设计,并结合切换系统理论研究了如何增大触发事件的事件间隔从而消除Zeno现象；3）在此基础上，我们进一步研究了利用不连续系统理论改善算法的设计从而提高其收敛性能，并实现有限时间收敛；4）在触发更新机制下利用脉冲牵制控制实现了特定值的一致性算法并对其收敛性进行了分析。这些工作为网络化控制系统上触发更新机制的一致性算法的设计与分析提供了一种新的理论框架。