Distributed event-triggered consensus for multi-agent systems with quantisation

This paper studies the consensus problem for multi-agent systems with quantised information communication via event-triggered control. First, the asynchronous event-triggered control for multi-agent systems is considered based on distributed uniform-quantised protocols. It is shown that practical consensus among agents is guaranteed and occurrence of Zeno behaviour is prevented under the designed event-triggering mechanisms. Second, under the proposed protocols using logarithmic quantised information, both synchronous and asynchronous event-triggered control algorithms are given to solve the practical consensus problem. Meanwhile, Zeno behaviour of the closed-loop systems can be excluded under the proposed event-triggered algorithms. Finally, numerical simulations are given to illustrate the effectiveness of the derived results.     

Event-triggered finite-time dynamic output feedback control for switched affine systems with asynchronous switching

This paper investigates the event-triggered finite-time dynamic output feedback control for switched affine systems (SASs) with asynchronous switching. A key point of the study is to set up a dynamic output feedback switched affine controller together with an event-triggered mechanism (ETM). By using an average dwell time (ADT) approach and resorting to a controller-mode-dependent Lyapunov functional, the finite-time stability (FTS) performance is achieve for the closed-loop SASs. The system dynamics under the proposed ETM are fully discussed during the synchronous and asynchronous switching intervals. The existence of the lower bound on interevent intervals is discussed emphatically, which excludes the occurrence of Zeno behavior. Finally, an application example of the DC-DC converter is given to show effectiveness of the acquired control algorithm.     

Asynchronous decentralised event-triggered control of multi-agent systems

In this paper, the consensus problem of first-order multi-agent systems under linear asynchronous decentralised event-triggered control is investigated. Both undirected and directed topologies are considered. In the analysis, the closed-loop multi-agent systems with the event-triggered control are modelled as switched systems. After proposing the decentralised event-triggered consensus protocols, decentralised state-dependent event conditions are derived, which act as switching signals. The consensus analyses are performed based on graph theory and stability results of switched systems. Under the event-triggered control schemes presented, consensus is reached with enlarged sampling periods and no Zeno behaviour. Simulation examples are given to illustrate the effectiveness of the proposed theoretical results.     

Event-triggered-based integral reinforcement learning output feedback optimal control for partially unknown constrained-input nonlinear systems

In this paper, an adaptive output feedback event-triggered optimal control algorithm is proposed for partially unknown constrained-input continuous-time nonlinear systems. First, a neural network observer is constructed to estimate unmeasurable state. Next, an event-triggered condition is established, and only when the event-triggered condition is violated will the event be triggered and the state be sampled. Then, an event-triggered-based synchronous integral reinforcement learning (ET-SIRL) control algorithm with critic-actor neural networks (NNs) architecture is proposed to solve the event-triggered Hamilton–Jacobi–Bellman equation under the established event-triggered condition. The critic and actor NNs are used to approximate cost function and optimal event-triggered optimal control law, respectively. Meanwhile, the event-triggered-based closed-loop system state and all the neural network weight estimation errors are uniformly ultimately bounded proved by Lyapunov stability theory, and there is no Zeno behavior. Finally, two numerical examples are presented to show the effectiveness of the proposed ET-SIRL control algorithm.     

Event-triggered consensus control for uncertain multi-agent systems with external disturbance

This paper investigates the event-triggered consensus control for a general linear multi-agent system with model uncertainties and external disturbances. A consensus protocol is proposed using the local state information at asynchronous event-triggering time instants, where each agent determines when to perform sampling and control updating using the designed event-triggered condition. Then the robust consensus condition and the feedback matrix design method are derived to make the uncertain multi-agent system reach consensus with a desired disturbance attenuation ability. Furthermore, it is demonstrated that the Zeno behaviour will never occur by giving the lower bound of inter-event time intervals. Finally, a simulation example is given to verify the obtained theoretical results, with the comparison simulation conducted by using the periodic triggering strategy.     

Sparse event-triggered control of linear systems

In event-triggered control, a situation where the control input must be sparse often arises. Therefore, in this study, we propose sparse event-triggered control, meaning that the control input is sparse and updated in an event-triggered manner. First, we present a model-based method for sparse event-triggered control of linear systems, where the event condition is defined by a Lyapunov function. The resulting control input is proven to be sparse and the control system is confirmed to be asymptotically stable. Second, we extend it to a data-driven version, where the event condition is adaptively updated from online data on the state trajectory. Finally, we discuss the possibility of extending our framework to two cases of disturbance and nonlinear dynamics.     

Adaptive event-triggered consensus of singular multi-agent systems based on asynchronous data sampling

This paper is devoted to the problem of event-triggered consensus for a class of singular multi-agent systems with nonlinear dynamics. Firstly, in consideration of the impossibility to reach all agents in some case, an observer is designed to access these agents' states. Secondly, a novel adaptive event-triggered scheme is proposed based on asynchronous data sampling. In this scheme, the trigger parameter can be adjusted dynamically in order to reduce information transmissions among agents. Thirdly, by employing Lyapunov stability theory, a sufficient condition on the consensus of singular multi-agent systems is obtained. Then, the control protocol and event-triggering scheme are designed by solving a linear matrix inequality condition. Finally, an example is given to illustrate the proposed results.     

Reactive Modules

We present a formal model for concurrent systems. The model represents synchronous and asynchronous components in a uniform framework that supports compositional (assume-guarantee) and hierarchical (stepwise-refinement) design and verification. While synchronous models are based on a notion of atomic computation step, and asynchronous models remove that notion by introducing stuttering, our model is based on a flexible notion of what constitutes a computation step: by applying an abstraction operator to a system, arbitrarily many consecutive steps can be collapsed into a single step. The abstraction operator, which may turn an asynchronous system into a synchronous one, allows us to describe systems at various levels of temporal detail. For describing systems at various levels of spatial detail, we use a hiding operator that may turn a synchronous system into an asynchronous one. We illustrate the model with diverse examples from synchronous circuits, asynchronous shared-memory programs, and synchronous message-passing protocols.     

广义马尔科夫跳变系统的事件触发异步故障检测滤波

针对一类具有事件触发机制的离散时间广义马尔科夫跳变系统,解决了异步故障检测滤波问题。 提出了一种事件触发策略,实现了合理利用网络资源,降低通信负担的目的;考虑了系统模态和滤波器模态之间存在的异步现象,使用两种不同的马尔科夫链来分别表示系统模态和滤波器模态,并在此基础上提出了一种异步故障检测滤波器的设计方法。 通过将异步故障检测滤波器的设计问题与事件触发机制相结合,根据Lyapunov稳定性理论,给出了保证残差误差系统具有正则性、因果性和随机稳定的并且满足 性能的充分条件,通过求解一组特定的线性矩阵不等式,得到了期望的异步故障检测滤波器参数。 最后,通过一个仿真例子说明了所设计的异步故障检测滤波器的设计方法是有效的。     

Edge event-triggered control for multi-agent systems under directed communication topologies

The edge event-triggered consensus control for multi-agent systems with single- or double-integrator dynamics under directed communication topologies is investigated in this paper. With the edge event-triggered sampling strategies, a class of novel consensus protocols is proposed to reduce control update frequency. The main features of the proposed edge event-triggered control include three aspects: (i) measurement errors are defined based on directed information flow and thus they allow that the communication topology is directed, (ii) each individual controller updates its output only when the associated edge event occurs and the control actions are independent of other agents, and (iii) the proposed edge event-triggered control does not exhibit Zeno behaviour and it is shown that the inter-event intervals are lower bounded by a positive constant. In the consensus analysis, matrix transformation techniques are used to convert the high-dimensional system into a low-dimensional system, and some sufficient consensus conditions are derived for the multi-agent systems with single- or double-integrator dynamics. Finally, the effectiveness of the edge event-triggered sampling strategies is illustrated by simulations.     

Formal Verification of Activity-Based Specification of Protocols

In this paper, we describe a method to formally verify activity-based specifications such as EBSDL. Starting from EBSDL-like specifications that specify engineering activities in terms of input and output behaviors, we derive programs in an asynchronous language CSP-R. CSP-R programs are then verified by the Maxpar method by composing them with the programs abstracting their environment. EBSDL-like specification and its verification using our method, is illustrated through the example of a fragment of LAPD protocol. The derivation of programs from the specification of activities of the underlying protocols through EBSDL-like specifications provides an important useful tool for formal verification of real-time protocols. We shall also discuss a translation of EBSDL-like specifications to synchronous languages such as Esterel. In the method proposed, it is possible for the user to choose asynchronous or synchronous formalisms depending upon the requirements of verification vis-a-vis logical specification.     

基于事件触发的离散多智能体二分一致性

针对一阶离散多智能体系统,研究了事件触发控制下的二分一致性问题.首先考虑智能体间通信拓扑结构为无向连通结构平衡图的情形,针对各智能体设计事件触发控制,包括仅依赖于自身及邻居智能体采样状态的控制输入,以及仅依赖自身状态的事件触发条件,实现了对通信资源的节约利用.基于图论、离散系统稳定性理论,证明系统能够实现二分一致性.同时,合理设置控制输入及事件触发条件中参数,保证系统不存在Zeno现象.之后,进一步分析设计了包含有向生成树的结构平衡图下,多智能体系统的事件触发控制.最后利用仿真实例验证了理论结果的有效性.     

任意相对阶下非线性切换系统的事件触发漏斗控制

针对一类具有任意相对阶且带有部分非输入到状态稳定逆动态的非线性切换系统, 提出一种动态事件触 发漏斗跟踪控制方案. 首先, 引入一个虚拟输出将任意相对阶的非线性切换系统转换为相对阶为一的非线性切换系 统. 其次, 设计各子系统的事件触发漏斗控制器和切换的动态事件触发机制, 解决候选事件触发漏斗控制器和子系 统之间的异步切换问题, 所提方案消除已有文献中为所有子系统设计共同控制器带来的保守性. 在一类具有平均驻 留时间切换信号的作用下, 保证切换闭环系统的所有信号都是有界的, 且跟踪误差一直在预设的漏斗内演化, 并排 除采样中的奇诺现象. 最后, 一个仿真例子验证方案的实用性和有效性.     

An overview of multirate multisensor systems: Modelling and estimation

In this paper, research advances in modelling and estimation algorithms for multirate multisensor systems are reviewed. Multirate multisensor sampling schemes can be classified into two cases: uniform sampling and nonuniform sampling. A general method to solve an asynchronous estimation problem for multirate multisensor systems is to transform the asynchronous problem into a synchronous one. Then, synchronous estimation algorithms can be applied. Therefore, modelling synchronisation approaches are summarised for uniform and nonuniform sampling cases. Meanwhile, the corresponding estimation algorithms are reviewed according to different synchronised models. Last, future research topics are discussed.     

Decentralised event-triggered cooperative control with limited communication

This note studies event-triggered control of Multi-Agent Systems (MAS) with first-order integrator dynamics. It extends previous work on event-triggered consensus by considering limited communication capabilities through strict peer-to-peer non-continuous information exchange. The approach provides both a decentralised control law and a decentralised communication policy. Communication events require no global information and are based only on local state errors; agents do not require a global sampling period or synchronous broadcasting as in sampled-data approaches. The proposed decentralised event-triggered control technique guarantees that the inter-event times for each agent are strictly positive. Finally, the ideas in this note are used to consider the practical scenario where agents are able to exchange only quantised measurements of their states.     

基于事件触发的网络化T-S模糊系统容错控制

研究了基于事件触发的网络化T-S模糊系统容错控制问题．首先针对一类具有随机执行器故障的网络化T-S模糊系统,提出一种有效减少数据传输量的事件触发机制．然后在综合考虑事件触发机制和控制器与T-S系统前件变量的异步的情况下,建立一种能同时描述事件传送策略、执行器失效、网络诱导时延和异步前件变量的新颖模型．利用李亚普诺夫泛函方法,得到保守性较小的闭环T-S系统均方渐近稳定条件和相应的容错控制器设计方法．实例表明了本文所得结果的有效性．     

离散非线性零和博弈的事件驱动最优控制方案

在求解离散非线性零和博弈问题时,为了在有效降低网络通讯和控制器执行次数的同时保证良好的控制效果,本文提出了一种基于事件驱动机制的最优控制方案.首先,设计了一个采用新型事件驱动阈值的事件驱动条件,并根据贝尔曼最优性原理获得了最优控制对的表达式.为了求解该表达式中的最优值函数,提出了一种单网络值迭代算法.利用一个神经网络构建评价网.设计了新的评价网权值更新规则.通过在评价网、控制策略及扰动策略之间不断迭代,最终获得零和博弈问题的最优值函数和最优控制对.然后,利用Lyapunov稳定性理论证明了闭环系统的稳定性.最后,将该事件驱动最优控制方案应用到了两个仿真例子中,验证了所提方法的有效性.     

非线性零和微分对策的事件触发自适应动态规划算法

针对一类非线性零和微分对策问题,本文提出了一种事件触发自适应动态规划(event-triggered adaptive dynamic programming,ET--ADP)算法在线求解其鞍点.首先,提出一个新的自适应事件触发条件.然后,利用一个输入为采样数据的神经网络(评价网络)近似最优值函数,并设计了新型的神经网络权值更新律使得值函数、控制策略及扰动策略仅在事件触发时刻同步更新.进一步地,利用Lyapunov稳定性理论证明了所提出的算法能够在线获得非线性零和微分对策的鞍点且不会引起Zeno行为.所提出的ET--ADP算法仅在事件触发条件满足时才更新值函数、控制策略和扰动策略,因而可有效减少计算量和降低网络负荷.最后,两个仿真例子验证了所提出的ET--ADP算法的有效性.     

Bearing-based formation stabilization using event-triggered control

This article studies two distributed bearing-based event-triggered schemes to achieve formation stabilization. We focus on systems with double-integrator dynamics with bearings sensing capabilities. Firstly, we propose a bearing-only event-triggered condition (ETC) that is edge-dependent which drives the control updates of the agents using only information dependent on relative sensed quantities. Secondly, along with bearing measurements we make use of local agent state measurements to arrive at an ETC that uses this collective measurement to drive the sensing and control updates of an agent. In doing so, we propose a new control law that renders the final formation stationary. Simulations are provided to verify the validity of the proposed algorithms.