© The Institution of Engineering and Technology
A formulation of stability for formation flying spacecraft is presented. First, a formation is defined via control interactions between the spacecraft. Then, stability is formulated on the basis of inputtooutput stability with respect to a partitioning of the formation dynamics. The particular form of inputtooutput stability used here is based on the peaktopeak gain of a system from its input to its output. This formulation of stability is shown to be useful in characterising disturbance propagation in the formation as a function of the partition interconnection topology, and also in analysing the robustness of sensing, communication and control topologies. Stability analysis results are presented for hierarchical, cyclic and disturbance attenuating formations in terms of the inputtooutput gains of the partitions in the formation. Finally, Lyapunov stability analysis results are provided in terms of linear matrix inequalities for a general class of formations.
References


1)

Scharf, D.P., Hadaegh, F.Y., Ploen, S.R.: `A survey of spacecraft formation flying guidance and control (Part II): control', Proc. 2004 American Control Conf., June 2004, 4, p. 2976–2985.

2)

Lawson, P.R.: `The terrestrial planet finder', Proc. IEEE Aerospace Conf., 2001, 101, p. 2005–2011.

3)

E.D. Sontag ,
Y. Wang
.
Notions of input to output stability.
Syst. Control Lett.
,
235 
248

4)

E. Sontag ,
Y. Wang
.
Lyapunov characterizations of input to output stability.
SIAM J. Control Optim.
,
226 
249

5)

Sontag, E., Wang, Y.: `A notion of input to output stability', Proc. European Control Conf., July 1997, Brussels.

6)

A. Pant ,
P. Seiler ,
J.K. Hedrick
.
Mesh stability of lookahead interconnected systems.
IEEE Trans. Autom. Control
,
2 ,
403 
407

7)

H.G. Tanner ,
G.J. Pappas ,
V. Kumar
.
Leadertoformation stability.
IEEE Trans Robot. Autom.
,
3 ,
443 
455

8)

Tanner, H.G., Pappas, G.J., Kumar, V.: `Inputtostate stability on formation graphs', Proc. 41st IEEE Conf. on Decision and Control, 2002, 3, p. 2439–2444.

9)

P.K.C. Wang ,
F.Y. Hadaegh
.
Coordination and control of multiple microspacecraft moving in formation.
J. Astronaut. Sci.
,
3 ,
315 
355

10)

D.D. Šiljak
.
(1991)
Decentralized control of complex systems.

11)

A.N. Michel
.
On the status of stability of interconnected systems.
IEEE Trans. Autom. Control
,
6 ,
325 
340

12)

W. Tang ,
A.N. Michel ,
H.W. Hale
.
On structure of interconnected dynamical systems.
IEEE Trans. Autom. Control
,
5 ,
391 
405

13)

S. Boyd ,
L.E. Ghaoui ,
E. Feron ,
V. Balakrishnan
.
(1994)
Linear matrix inequalities in system and control theory.

14)

M.L. Brockman ,
M. Corless
.
Quadratic boundedness of nominally linear systems.
Int. J. Control
,
6 ,
1105 
1117

15)

N. Deo
.
(1974)
Graph theory with applications to engineering and computer science.

16)

E. Sontag ,
Y. Wang
.
New characterisations of the inputtostate stability property.
IEEE Trans. Autom. Control
,
1283 
1294

17)

A. Isidori
.
(1999)
Nonlinear control systems II.

18)

R.A. Horn ,
C.R. Johnson
.
(1991)
Topics in matrix analysis.

19)

H.K. Khalil
.
(1988)
Nonlinear systems.

20)

T. Iwasaki ,
G. Shibata
.
LPV system analysis via quadratic seperator for uncertain implicit systems.
IEEE Trans. Autom. Control
,
1195 
1208

21)

A.B. Açikmeşe ,
M. Corless
.
Robust tracking and disturbance rejection of bounded rate signals for uncertain/nonlinear systems.
Int. J. Control
,
11 ,
1129 
1141

22)

C.W. Scherer
.
LPV control and full block multipliers.
Automatica
,
361 
375

23)

J.F. Sturm
.
Using SeDuMi 1.02, a matlab toolbox for optimization over symmetric cones.
Optim. Methods Softw.
,
6 ,
1105 
1154

24)

J.C. Willems
.
Dissipative dynamical systems I–II.
Arch. Ration. Mech. Anal.
,
321 
393

25)

C. Langbort ,
R.S. Chandra ,
R. D'Andrea
.
Distributed control design for systems interconnected over an arbitrary graph.
IEEE Trans. Autom. Control
,
9 ,
1502 
1519

26)

A. Rantzer
.
On the Kalman–Yakubovic–Popov lemma.
Syst. Control Lett.
,
7 
10

27)

W.H. Clohessy ,
R.S. Wiltshire
.
Terminal guidance system for satellite rendezvous.
J. Aerosp. Sci.
,
9 ,
653 
658
http://iet.metastore.ingenta.com/content/journals/10.1049/ietcta_20050459
Related content
content/journals/10.1049/ietcta_20050459
pub_keyword,iet_inspecKeyword,pub_concept
6
6