Distributed event-triggered control of multi-agent systems with combinational measurements

doi:10.1016/j.automatica.2012.11.010

Automatica

Volume 49, Issue 2, February 2013, Pages 671-675

https://doi.org/10.1016/j.automatica.2012.11.010 Get rights and content

Abstract

This paper studies the distributed rendezvous problem of multi-agent systems with novel event-triggered controllers. We have proposed a combinational measurement approach to event design and developed the basic event-triggered control algorithm. As a result, control of agents is only triggered at their own event time, which reduces the amount of communication and lowers the frequency of controller updates in practice. Furthermore, based on the convergence analysis of the basic algorithm, we have proposed a new iterative event-triggered algorithm where continuous measurement of the neighbor states is avoided. It is noted that the amount of communication among agents has been significantly reduced without obvious negative effects on the control performances. The effectiveness of the proposed strategies is illustrated by numerical examples in 3D spaces.

Introduction

Nowadays many applications require large sets of robots, vehicles or mobile sensors to work cooperatively and accomplish complex tasks. In view of this, many researchers have devoted themselves to the study of coordination control of multi-agent systems. Typical research in this field includes the problems of consensus (Olfati-Saber et al., 2007, Ren and Beard, 2005), formation control (Fax & Murray, 2004), rendezvous (Cortés et al., 2006, Fan et al., 2011, Lin et al., 2003, Lin et al., 2007a, Lin et al., 2007b), agent flocking (Tanner, Jadbabaie, & Pappas, 2007), and deployment (Nowzari and Cortés, 2012, Song et al., 2011). To lower the cost, each agent may equip with a small embedded micro-processor and capability-limited onboard communication and actuation modules, which usually have only limited energy resources and computing capabilities. These factors motivate researchers to develop event-triggered control schemes for digital platforms, see, for example, De Persis, Sailer, and Wirth (2011), and Wang and Lemmon (2011). For multi-agent systems, the authors in Dimarogonas, Frazzoli, and Johansson (2012) employ the deterministic event-triggered strategy introduced in Tabuada (2007) to develop consensus control algorithms. Furthermore, the lower bounds for the inter-event time are provided to ensure there is no Zeno behavior (Dimarogonas et al., 2012). Event-triggered control has also been addressed in decentralized control over wireless sensor/actuator networks (Mazo & Tabuada, 2011) and multi-agent systems with event-based communication (Seyboth, Dimarogonas, & Johansson, 2012).

In event-triggered control, the measurement error plays an essential role in the event design. When its magnitude reaches the prescribed threshold, an event is triggered and the controller is updated. Generally speaking, the threshold can be state-independent (Mazo and Tabuada, 2011, Seyboth et al., 2012) and state-dependent (Dimarogonas et al., 2012). In the former case, the threshold can be a constant or a time-dependent variable. It is noted that the state-dependent threshold is better and more natural since in the constant threshold case the agent system cannot achieve asymptotic convergence and in the time-dependent variable case the convergence rate is governed by an external signal (Seyboth et al., 2012). However, the drawback of the existing controllers with state-dependent thresholds lies in that each agent is required to be triggered at the neighbors’ event time. This increases the load of communication and brings higher frequency of controller updates.

In this paper we firstly propose a combinational measuring approach to event-design and develop a basic event-triggered control algorithm for rendezvous. In this approach the measurement error of each agent is determined by a convex combination of its neighbors’ states rather than by measuring the agents’ own states. By categorizing the triggering executions, it is proven that each agent will be triggered regularly and the group will asymptomatically achieve rendezvous. Then based on the convergence analysis, we have developed a new iterative event-triggered control algorithm without continuous measuring of the neighbor states to further reduce inter-agent communication. The contribution of this work are as follows. Firstly, by the combinational measuring approach, the controller of each agent is allowed to be triggered only at its own triggering time instants, which reduces the amount of communication and the frequency of controller updates. Secondly, the categorization of triggering executions help investigate the behaviors of the agent system in a solid manner. Thirdly, in the iterative algorithm without continuous measurement, each agent does both of the actions of measuring the neighbor states and sending combined state signals only at its own triggering time instants, which further reduces communication significantly. Compared with the existing work in Dimarogonas et al. (2012), the proposed controller achieves nearly the same convergence performances with much less amount of communication and controller updates.

The rest of this paper is organized as follows. Sections 2 Basic event-triggered algorithm, 3 Rendezvous analysis present the basic event-triggered controller design and the convergence analysis. Section 4 presents the iterative event-triggered algorithm without continuous measurement. In Section 5, numerical simulations are provided. Finally the paper is concluded in Section 6.

Section snippets

Basic event-triggered algorithm

Consider a multi-agent system with $N$ agents, labeled by $1, 2, \dots, N$ . The agents are able to move, compute and communicate, and required to achieve the rendezvous task. Their positions at time $t$ are represented by $x_{i} (t) \in R^{n} (n = 2, 3)$ with kinematics being ${\dot{x}}_{i} (t) = u_{i} (t), i = 1, \dots, N .$ The communication topology of the system is represented by an undirected graph $G = (V, E)$ , where $V$ is the vertex set and $E$ is the edge set. The neighbor set of agent $i$ is denoted by $N_{i} = {j \in V | (j, i) \in E}$ . To introduce the event-triggered

Rendezvous analysis

Consider a system $\dot{x} (t) = f (x (t), u (t)), x (t) \in R^{n}, u (t) \in R^{p}$ under an event-triggered controller $u (t) = u (t_{k}), t \in [t_{k}, t_{k} + 1)$ . Events are designed based on an event-related vector $μ (t) = {(μ_{1} (t), \dots, μ_{m} (t))}^{T} \in R^{m}$ , where $μ_{1} (t), μ_{2} (t), \dots, μ_{m} (t)$ are constant or time-dependent variables or variables dependent on the state $x (t)$ (Seyboth et al., 2012). Let $E \subset R^{m}$ be a closed set containing all feasible event-related vectors, which can be partitioned into two subsets: the triggering event set $E$ and the non-event set $\bar{E} = E ∖ E$ .

Iterative event-triggered algorithm

A significant problem of the basic event-triggered algorithm is that each agent still needs to continuously measure the states of all its neighbors. See the triggering condition (4). In this section, we will propose a distributed iterative algorithm to deal with this problem. As a result, continuous measurement of the neighbor states can be avoided.

There are two major features in the new triggering approach. First, only at each triggering time instant $t_{k}^{i}$ , agent $i$ measures the combined state $q_{i} ($

Simulations

In this section some simulations are provided to illustrate the proposed algorithms. Consider a group of $N = 6$ agents in $R^{3}$ . Each agent is governed by the kinematic (1) and the controller (3). The parameters are given by $ξ_{i} = 0.1$ and $β_{i} = 0.9$ for all agents. The initial positions and the communication graph are shown in Fig. 1(a). When the sum of the distances from the agents to the group center is shorter than 0.01, the group is considered to have achieved rendezvous. The trajectories of agents

Conclusions

In this paper, we have proposed a distributed event-triggered strategy for multi-agent rendezvous where the events are determined by measuring the combinational states of the neighbors. Firstly we have proposed a basic event-triggered algorithm and presented the convergence analysis. Then we have proposed a new iterative event-triggered algorithm where continuous measuring of the neighbor states has been avoided. As a result, communication among agents can be significantly reduced. Future work

References (17)

Y. Fan et al.
A novel approach to coordination of multiple robots with communication failures via proximity graph
Automatica
(2011)
C. Nowzari et al.
Self-triggered coordination of robotic networks for optimal deployment
Automatica
(2012)
C. Song et al.
Decentralized adaptive awareness coverage control for multi-agent networks
Automatica
(2011)
J. Cortés et al.
Robust rendezvous for mobile autonomous agents via proximity graph in arbitrary dimensions
IEEE Transactions on Automatic Control
(2006)
De Persis, C., Sailer, R., & Wirth, F. (2011). On a small-gain approach to distributed event-triggered control. In...
D.V. Dimarogonas et al.
Distributed event-triggered control for multi-agent systems
IEEE Transactions on Automatic Control
(2012)
J.A. Fax et al.
Information flow and cooperative control of vehicle formations
IEEE Transactions on Automatic Control
(2004)
Lin, J., Morse, A.S., & Anderson, B.D.O. (2003). The multi-agent rendezvous problem. In Proceedings of the 42nd IEEE...

There are more references available in the full text version of this article.

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^☆: This work was partially supported by grants from the Research Grants Council of Hong Kong (No. CityU-113209), the National Natural Science Foundation of China (No. 61203027), and the Anhui Provincial Natural Science Foundation (No. 1208085QF108). The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Andrey V. Savkin under the direction of Editor André L. Tits.

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Technical communiqueDistributed event-triggered control of multi-agent systems with combinational measurements☆

Abstract

Introduction

Section snippets

Basic event-triggered algorithm

Rendezvous analysis

Iterative event-triggered algorithm

Simulations

Conclusions

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Distributed event-triggered control of multi-agent systems with combinational measurements☆