H
∞
Time-Varying Formation Control of Multiple Spacecraft
System
ZHOU Ning
12
, CHEN Riqing
1
, HUANG Jie
†
23
, WEN Guoxing
4
1. College of Computer and Information Sciences, Fujian Agriculture and Forestry University, Fuzhou 350002, P. R. China
E-mail: zhouning2010@gmail.com; riqing.chen@fafu.edu.cn
2. Faculty of Science and Engineering, University of Groningen, Groningen 9747AG, The Netherlands
E-mail: autohuangjie@gmail.com
3. College of Electrical Engineering and Automation, Fuzhou University, Fuzhou 350108, P. R. China
4. College of Science, Binzhou University, Binzhou, Shandong 256600, P. R. China
E-mail: gxwen@live.cn
Abstract: This paper discusses the problem of time-varying formation control for multiple spacecraft while achieving H
∞
per-
formance. Firstly, an elaborate formation task function is designed by using estimator-based null-space based behavioral control
method, and a predesigned desired velocity is calculated for each spacecraft. Then by employing backstepping technique associ-
ated with the universal approximation property of radial basis function neural networks (RBFNN), an adaptive H
∞
coordination
control scheme is presented to drive all the spacecraft to implement the time-varying formation task in switching communica-
tion graph. Finally, rigorous theoretical analysis shows that the proposed algorithm implements the time-varying formation task
successfully with H
∞
performance.
Key Words: Time-Varying Formation, H
∞
Control, Neural Networks Control, Spacecraft System
1 Introduction
Spacecraft formation flying (SFF) is an effective method
to perform space operations flexibly. SFF means a group of
spacecraft flying together with coupled dynamic states. This
technology can be accomplished by a well designed collab-
orative controller which brings out new opportunities and
possibilities of reasonable redundancy, cost reduction, and
improved resolution aspects of onboard payload. In recen-
t years, research on SFF becomes an increasingly attracted
subject due to the important practical significance and ap-
plication prospects. Spacecraft time-varying formation can
described as let all the follower spacecraft form a prede-
fined time-varying formation while tracking the trajectory of
the leader spacecraft. In some practical applications, e.g.,
the source seeking and target enclosing, forming the desired
time-varying formation should be an important step while
tracking leader’s trajectory is also needed to perform the w-
hole mission.
It should be pointed out that some advanced algorithms
have been proposed for the time-varying formation problem
of various control systems during the past decade. For exam-
ple, the time-varying formation control problems for high-
order linear time-invariant swarm systems were discussed
in [1], and a general formation control protocol was pre-
sented in switching interaction topologies. [2] investigat-
ed the time-varying formation control analysis and design
problems for unmanned aerial vehicle (UAV) swarm system-
The work was supported in part by the the National Natural Sci-
ence Foundation of China (No.61603094, 61603095), the China Scholar-
ship Council (No.201707870005), the Natural Science Foundation of Fu-
jian Province (No.2016J01284, 2016J01286), the Research Foundation for
Outstanding Young Scholars in Fujian Agriculture and Forestry University
(No.xjq201612), the Research Foundation for Outstanding Young Schol-
ars in the University of Fujian Province, the Doctoral Scientific Research
Staring Fund of Binzhou University (No.2016Y14), and the Foundation
of Cloud Computing and Big Data for Agriculture and Forestry (No.117-
612014063).
s, in which an explicit expression of the time-varying for-
mation center function was derived. The distributed time-
varying formation (TVF) control problems were studied in
[3] for general linear swarm systems with switching interac-
tion topologies, and an adaptive dynamic protocol including
a feasible formation condition was proposed to determine the
gain matrices of the distributed adaptive formation protocol
by solving a linear matrix inequality for swarm systems. The
time-varying formation tracking problems for second-order
multi-agent systems was studied in [4] with switching in-
teraction topologies, and a formation tracking protocol was
proposed based on the relative information of the neighbor-
ing agents. Under directed interaction topologies, the time-
varying output formation control problems for linear multi-
agent systems was investigated by employing the output de-
composition, observability decomposition and output forma-
tion decomposition in [5]. Under directed interaction topolo-
gies, a continuous fault-tolerant formation control proto-
col was developed for the distributed time-varying forma-
tion control problems of second-order multi-agent systems
[6]. The time-varying formation tracking problems for linear
multi-agent systems with multiple leaders were discussed
in [7], and a formation tracking protocol was constructed
to deal with time-varying formation tracking problems, tar-
get enclosing problems, and consensus tracking problems
with one or multiple targets/leaders. [8] studied the time-
varying formation robust tracking problems for high-order
linear multi-agent systems with a leader of unknown control
input in the presence of heterogeneous parameter uncertain-
ties and external disturbances, and a robust tracking proto-
col was proposed. The fully distributed time-varying for-
mation control problems were addressed for general linear
swarm systems with fixed and switching topologies in [9],
and a node-based time-varying formation control protocol
was constructed via dynamic output feedback. [10] consid-
ered the time-varying formation control for multi-agent sys-
Proceedings of the 37th Chinese Control Conference
Jul
25-27, 2018, Wuhan, China
7076