Mathematical Problems in Engineering

Volume 2017, Article ID 1318376, 8 pages

https://doi.org/10.1155/2017/1318376

## Event-Triggered Multitarget Formation Control for Multiagent Systems

^{1}Institute of Electrical Engineering, Yanshan University, Qinhuangdao 066004, China^{2}Institute of Mathematics and Information Technology, Hebei Normal University of Science and Technology, Qinhuangdao 066004, China^{3}School of Electronic and Electric Engineering, Shanghai Jiaotong University, Shanghai 200240, China

Correspondence should be addressed to Lingmin Zhang; moc.361@9999nimgnil

Received 23 June 2017; Revised 22 October 2017; Accepted 22 October 2017; Published 5 December 2017

Academic Editor: Leonid Shaikhet

Copyright © 2017 Lingmin Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The problems of multitarget selection and formation for multiagent systems are considered. First of all, an improved multitarget selection method based on auction algorithm is proposed such that each agent can automatically choose its target, and during the process of choosing targets, we apply an event-triggered mode to reduce the communication links between agents. Second, in view of the fact that all agents with the same target need to form a desired formation shape, we provide an event-triggered formation controller for each agent. Finally, we carry out the simulation experiment of the algorithm and the simulation results have illustrated the effectiveness of it.

#### 1. Introduction

In recent years, the problem of multiagent system (MAS) has been widely studied by many researchers [1–4]. These systems can potentially consist of a great number of agents, such as unmanned aerial vehicles (UAG), unmanned underwater vehicles (UUV), and unmanned ground vehicles (UGA). MASs provide many applications in various practical fields, such as intelligent transportation systems, building automation, underwater exploration, and surveillance. Advantages of MASs over single agent include cost reduction, efficiency, and robustness improvement.

One interesting issue of multiagent system is formation control [5–7]. Its objective is to design algorithms to motivate agents to form a desired formation. Meanwhile, study on formation with a single target has become one of the hot spots issues in research of multiagent systems formation control [8–11]. In [8], a methodology for group coordination and cooperative control of agents to achieve a target-capturing task in 3D space was studied, and the proposed approach was based on a cyclic pursuit strategy, where agent simply pursued agent modulo . In [9], the cooperative target pursuit problem by multiple agents based on directed acyclic graph was investigated. The target appeared at a random location and moved only when sensed by the agents, and agents pursued the target once they detected its existence. In [10], the problem of flocking motion combined with topology optimization for mobile multiagent systems was considered, and a distributed multiflocking method was designed based on the partial information exchange. In [11], the cooperative control of a team of robots to estimate the position of a moving target using onboard sensing was investigated. The above works are all based on the common assumption that a group of agents pursue the same target; that is, it is supposed that there is only one target in the workplace. However, this assumption is strict in certain situations. For instance, when more than one target is considered in the workplace, agents will face a dilemma in choosing their targets. Thus, some researchers studied multitarget formation [12–14]. In [12], a team of agents who can accomplish multitarget pursuit formation by using a developed leader-follower strategy was designed. In [13], a flocking algorithm with multitarget tracking for multiagent systems was adopted. It was supposed that each target could accept a certain number of agents. Which target would be chosen by an agent was determined by the distances from the agent to the targets. In [14], to solve this problem, a distributed multiflocking method was adopted based on the partial information exchange. But in the above existing multitarget selection algorithms, the targets assignment is static; that is, each agent selects an invariable target to pursue. However, as the system evolves, each agent may select a different target to pursue according to certain optimal objectives. Therefore, considering systems with dynamic targets assignment will be more significant. Thus how to design a dynamic multitarget selection is a problem to be solved.

In addition, in the existing algorithms of multitarget selection and multiagent systems formation control, time-triggered control mode is widely adopted. Time-triggered control mode is simple, but it may cause large amount of bandwidth and communication. Event-triggered control is an alternative to time-triggered control [15, 16]. The distinct feature of event-triggered control is that control action is updated only when some specific event occurs. Compared with time-triggered control mode, event-triggered control mode has the often cited advantages on communication reduction and energy saving. It has been studied extensively in network control systems and decentralized systems [15, 17, 18]. In many cases, such as formation control, pursuit control, and path planning, it outperforms the traditional time-triggered control [16, 19–22]. Thus, how to apply event-triggered mode to multiagent formation control is another problem to be solved. For the above two problems, this paper focuses on the dynamic multitarget selection and formation of multiagent systems and applies event-triggered control mode to multitarget selection and formation. The main contributions of this paper are as follows:(1)Unlike in most of the existing multitarget selection algorithms, the targets assignment is static and each agent selects an invariable target to pursue; we consider systems with dynamic targets assignment as each agent may select a different target to pursue according to certain optimal objectives. In addition, an improved dynamic selection method based on auction algorithm is adopted, and the event-triggered control mode is applied to the multitarget selection to reduce the communication links between agents.(2)In the process of multitarget formation control for multiagent systems, we adopt the event-triggered control mode instead of time-triggered-control mode. When event-triggered control mode is applied to multiagent systems, the stability of the system can be maintained and compared with time-triggered control mode; it has the advantages of reducing the number of information updating and saving bandwidth resources and energy.

The rest of this paper is organized as follows. In Section 2, system modeling and problem formulation are presented. In Section 3, we apply the event-triggered mode to dynamic target selection and the formation strategy. Simulation studies are provided to illustrate the effectiveness of our method in Section 4. Conclusions are given in Section 5.

#### 2. Preliminaries and Problem Formulation

##### 2.1. Graph Theory

A graph is a pair that consists of a set of vertices and edges . The graph is said to be undirected if . And in order to ensure cooperation and coordinating among agents, each agent has to know the states of other agents. Therefore, agents have to communicate with each other. Given an agent , the set of agents from which it can receive information is called a neighbor set ; that is,

A graph is connected if any two vertices can be joined with an edge. It is assumed that the graph describing the information structure is connected. A graph also admits matrix representations. Some of these matrices, such as the adjacency matrix, the degree matrix, and the Laplacian matrix, will be reviewed subsequently.

The adjacency matrix encoding of the adjacency relationship in the graph is defined as where is the entry of the adjacency matrix . The degree matrix for an undirected graph is a diagonal matrix , where is the cardinality of neighbor set of agent . The adjacency matrix of undirected graph is symmetric because for . The Laplacian matrix associated with an undirected graph is defined as , where and are degree matrix and adjacency matrix of graph , respectively.

##### 2.2. System Modeling and Problem Formulation

*Multiagent Systems*. Define a set of agents as , where is the number of agents. For the agent with two-dimensional coordinate, the position and input vectors are denoted by and , respectively. The dynamics of agent at time are described by the following continuous-time equation: For the dynamic system, the following assumptions are made.

*Assumption 1. *Initially, it is assumed that targets and agents disperse randomly in the workplace. Meanwhile, agents can detect the state information about the target at the initial time.

*Assumption 2. *Each agent can only obtain the state information of its neighbors and each target can only accept a certain number of agents. In the following, we will give an improved auction algorithm based on event-triggered control to complete the target selection; then an event-triggered controller for each agent will be given to form a desired formation shape.

#### 3. Event-Triggered Multitarget Formation

In this section, we will design a team of agents who can accomplish multitarget formation by using an event-triggered formation method. First, we will present an event-triggered dynamic strategy for choosing a target. Second, we will provide an event-triggered controller for each agent to form a desired multiagent systems formation.

##### 3.1. Strategy for Choosing a Target

In the dynamic system, each target is considered as a commodity, and we define the value of the target as . , at the initial time, and the price to catch up with for is . The system designs an open platform, in which all the targets have an auction, and all the agents are involved in the auction. In this mode of auction, the auction platform begins with a given price, and all agents are aware of the current price announced. The price is gradually reduced, until some agent selects it. In the designed auction algorithm, all targets are simultaneously on auction. When an agent’s income is greater than or equal to the outcry of the current system, the agent selects the corresponding target. If target is chosen by agents, the value obtained by agent is When increases, the value obtained from target will be decreased gradually, and thus the agent will tend to choose the target that is chosen by fewer agents. In this way, we can effectively avoid the problem of selecting the same target for many agents.

Building the proceeds functions as follows: where is the cost function for agent to select target and and are positions of agent and target , respectively. After calculating its proceeds for selecting each target, the agent will choose the one with the biggest proceeds as its target. In this way, each agent will tend to choose target relatively close to it, in order to get the final rate of exchange: When the current bid price is less than or equal to , agent will select the corresponding target and drop out of the auction. The remaining agents will continue to achieve the selection until the last agent accomplishes the target selection. After selecting the targets, agents will continue to move and will update the data at the next time node, in order to achieve the dynamic selection and make a response to the changes of the scene. The pseudocode of the auction algorithm is showed in Algorithm 1.