electronics
Review
Multi-Agent Cooperative Control Consensus:
A Comparative Review
Muhammad Majid Gulzar 1,* ID , Syed Tahir Hussain Rizvi 2,* ID , Muhammad Yaqoob Javed 3,
Umer Munir 1 and Haleema Asif 1
1 Department of Electrical Engineering, University of Central Punjab, 54000 Lahore, Pakistan;
engr.umermunir@hotmail.com (U.M.); haleema.asif@ucp.edu.pk (H.A.)
2 Department Dipartimento di Automatica e Informatica (DAUIN), Politecnico di Torino, 10129 Turin, Italy
3 Department of Electrical Engineering, COMSATS Institute of Information Technology, 54000 Lahore,
Pakistan; yaqoobsheikh@gmail.com
* Correspondence: majidgulzar3@gmail.com (M.M.G.); syed.rizvi@polito.it (S.T.H.R.)
Received: 18 December 2017; Accepted: 11 February 2018; Published: 16 February 2018
Abstract: Cooperative control consensus is one of the most actively studied topics within the realm
of multi-agent systems. It generally aims to drive multi-agent systems to achieve a common group
objective. The core aim of this paper is to promote research in cooperative control community by
presenting the latest trends in this field. A summary of theoretical results regarding consensus
for agreement analysis for complex dynamic systems and time-invariant information exchange
topologies is briefly described in a unified way. The application under both non-formation and
formation cooperative control consensus for multi-agent system also investigated. In addition, future
recommendations and some open problems are also proposed.
Keywords: distributed coordination; multi-agent; consensus; formation
1. Introduction
In comparison to an autonomous single agent/mobile robot, which only executes solo missions,
better operational capability and efficiency can be achieved from multi-agent systems that are operating
in a coordinated fashion. Owing to the ability to handle abundant computational resources that are
embedded in an autonomous agent enables it to enhance operational effective capabilities through a
cooperative teamwork of multi-agent in military and civilian applications [1]. So by using multi-agent
systems, certain global objectives can be achieved through sensing, exchange of information using
communication, computation and their control [2,3].
A significant amount of research effort has been put into the cooperative control of multi-agent
systems in the last decade. In the cooperative control consensus, agents share their information
with each other. This information may lead to achieve common group objectives, relative position
information or common control algorithms.
The behavior-based approach has been used for researchers to examine the social characteristics
of animals and insects to apply coordination control findings to the design of multi-agent systems.
In Reference [4] Reynolds presented three basic rules of cohesion, separation and alignment. Where
cohesion means staying close to all nearby neighbors, separation means avoiding collision and
alignment means to match velocities with the remaining agents. By introducing the aggregate motions
of a multi-agent system, the author generated the first animation on the computer. Also, for dynamic
topologies, Viscek’s model is very important, which can be classified as a special type of a distributed
behavioral model with Reynolds’ rules [5].
Cooperative control for multiple agents can be classified as non-formation cooperative control
problems such as role assignment, automated parallel delivery of payload transport, foraging, task
Electronics 2018, 7, 22; doi:10.3390/electronics7020022 www.mdpi.com/journal/electronics
Electronics 2018, 7, 22 2 of 20
handling, air traffic control, cooperative search and timing, or as formation control problems such
as mobile agents involved in surveillance and reconnaissance operations, flying or unmanned
aerial vehicles (UAVs), self-assembly of connected mobile networks, autonomous underwater
vehicles, spacecraft, aircraft, satellites and automated highway systems. To enable these applications
in multi-agent systems, diverse cooperative control techniques need to be built up, including
rendezvous [6,7] flocking [8,9] and swarming [10,11].
The main issues for the multi-agent consensus are coverage problems [12], network consensus [13],
multi-agent navigation [14] and formation control [15]. The main approaches found in recent literature
to solve these problems include algebraic graph theory-based approaches [16], geometric constraint
techniques [17] and the artificial potential field method [18]. In all these approaches, the agents are
assumed to remain entirely connected with each other for communication links and particularly for
formation control they should further form a predefined shape as well.
The ultimate focus of this paper is to present a review of consensus problems in multi-agent
coordination systems with the aim of elevating more and more research in this field by emphasizing
highly cited papers. Finally, applications of multi-agent systems including consensus, flocking and
swarming are also presented.
The paper outline is as follows: A brief background on algebraic graphs and matrix theory is given
in Section 2. Theoretical progress in consensus that includes convergence analysis for the time-invariant
and dynamic state, consensus speed and heterogeneous agents is presented in Section 3. Section 4
demonstrates the convergence constraint due to practical limitations. The application of multi-agent
systems can be seen in Section 5. Finally, conclusions and some open questions are discussed in
Section 6.
2. Preliminaries
In order to exchange information among multi-agent systems, it is natural to model this by way
of an undirected or directed graph, where vertices represent agents and edges are the information
exchange links among agents. A pair (V, E) is called a directed graph where V = f1, . . . , ng is a
nonempty finite node set and E  V  V is called an edge set. The neighbor of ith agent is denoted
by Ni = fj 2 V : (i, j) 2 Eg. For the edge (i, j), i is known as parent node whereas j is mentioned as
the child node. The edge (i, j) 2 E means that agent j can get updates from agent i but for agent i it is
not permissible. Contrary to a directed graph, the undirected graph can be seen as a special type of
directed graph where un-ordered pairs of nodes are allowed. The edge (i, j) 2 E is referred to as agent
i and j and can receive updates from each other so edges (i, j) and (j, i) in the directed graph equate to
an edge (i, j) in the undirected graph [19].
In a directed graph, if there is a directed path from every node to every other node it is known as
“strongly connected”. Similarly, in an undirected graph, if there is an undirected path between every
pair of distinct nodes then it is called “connected graph”. A node is called a root if it has a directed
path to the remaining nodes without having a parent itself. A rooted directed tree is a directed graph
where except for one node remaining nodes should have exactly one parent node [20].
For a directed graph with a node set V = f1, . . . , ng the adjacency matrix A =

aij

2 Rnn is
defined as a “positive weight” where aij = 1 if (j, i) 2 E and aij = 0 for (j, i) /2 E. As all the graphs
have some weights so if weights are not significant in a particular situation, then aij is assumed to be
equal to one for all (j, i) 2 E. Self-edges with positive weight are also allowed. For some aij graph is
referred to as balanced if ån
i=1 aij = ånj
=1 aji for all i. As adjacency matrix is symmetric for undirected
graph thus every undirected graph will be automatically balanced. Thus, the adjacency matrix can be
written as
A = [aij] =
(
1 i f kqj