Citation: Xiong, Z.; Liu, Z.; Luo, Y.;
Xia, J. An Adaptive and Bounded
Controller for Formation Control of
Multi-Agent Systems with
Communication Break. Appl. Sci.
2022, 12, 5602. https://doi.org/
10.3390/app12115602
Academic Editor: Dario Richiedei
Received: 18 April 2022
Accepted: 25 May 2022
Published: 31 May 2022
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Article
An Adaptive and Bounded Controller for Formation Control of
Multi-Agent Systems with Communication Break
Zhigang Xiong, Zhong Liu, Yasong Luo * and Jiawei Xia
College of Weapon Engineering, Naval University of Engineering, Wuhan 430034, China;
xiongzgzm2@163.com (Z.X.); lzhong@163.com (Z.L.); wilson0078@163.com (J.X.)
* Correspondence: yoursbaggio@163.com
Abstract:
AbstractAiming at maneuvering, input saturation, and communication interference in the
controller design for formation control multi-agent systems, a novel nonlinear bounded controller is
proposed. Based on coordinates transformation, reference information is processed, and nonlinear
effects of maneuvering are analyzed. Then a nonlinear controller is established with graph theory,
consensus algorithm, and Lyapunov method, which guarantee the stability of the controller. For input
saturation avoidance, adaptive parameters are put forward with the Lyapunov function. Considering
the communication breaks, various conditions of the sensing graph are discussed for stable formation
control, and a dynamic programming regulator is proposed for unknown position reference needed
for formation keeping. Comparison with the traditional consensus method is provided in numerical
simulation to verify the stability and feasibility of the proposed strategy.
Keywords: formation control; input saturation; Lyapunov function; multi-agent systems
1. Introduction
Formation control [
1
,
2
] is crucial for multi-agent systems. Previously, switching
topology [
3
,
4
], actuator faults [
5
], noise resistance [
6
], time constraints [
7
,
8
], connectivity
maintenance [
9
], and communication delay [
10
] have been widely studied. Inspired by
this research, a stable and feasible controller is critical for the formation control of multi-
agent systems. Although various controllers have been proposed, nonlinearity caused by
maneuvering [
11
–
13
] and saturation [
5
,
14
] is still the challenge. Besides, communication
interference will lead to bad control due to the lack of reference information, which means
extra strategies should be applied for stable formation [
4
]. Therefore, a comprehensive
survey of bounded controllers considering maneuvering and communication interference
is necessary. Previously, optimization-based methods and consensus algorithms with graph
theory have been widely studied for controller design.
As for controller design, Ref. [
14
] proposed the inverse optimality method (IOM) with
Hamilton–Jacobi–Bellman (HJB) equations, which provides a feasible bounded controller
for formation control theoretically, but HJB equations are difficult to be solved for a sim-
ple control law. In [
15
,
16
], intelligent algorithms have been used to optimize velocities
using centralized computing systems. However, time consumption is a big challenge
for intelligent algorithms and saturation constraints are hard to be incorporated into the
objective functions. Recently, model predictive control (MPC) [
17
,
18
] has been widely used
for formation control, various requirements can be converted into inequality constraints.
MPC is easy to implement programmatically, the challenge is the central computer will
assume a great burden with a large number of agents. Then, distributed MPC (DMPC)
has been proposed [
19
,
20
] for low time cost. With less computation and the advantage
of bounded outputs, DMPC has attracted much attention now. The problem with DMPC
is that there must exist nonlinear constraints considering dynamic constraints, such as
Appl. Sci. 2022, 12, 5602. https://doi.org/10.3390/app12115602 https://www.mdpi.com/journal/applsci
