Abstract
The decentralized output feedback control problem for a class of large-scale interconnected nonlinear systems is considered. The nonlinear interconnection function of each subsystem is assumed to satisfy a quadratic constraint on the entire state of the large-scale system. A decentralized estimated state feedback controller and a decentralized observer are designed for each subsystem. Sufficient conditions, for each subsystem, under which the proposed controller and observer can achieve exponential stabilization of the overall large-scale system are developed. Simulation results on a numerical example are given to verify the proposed design.
1.
D. D.
Siljak
, 1991, Decentralized Control of Complex Systems
, Academic Press
, New York.2.
J. N. R.
Sandell
, P.
Varaiya
, M.
Athans
, and M. G.
Safanov
, 1978, “Survey of decentralized control methods for large scale systems
,” IEEE Trans. Autom. Control
0018-9286, AC-23
, pp. 108
–128
.3.
M.
Ikeda
, 1989, “Decentralized control of large scale systems
,” Three Decades of Mathematical System Theory
, Springer-Verlag
, pp. 219
–242
.4.
S. Y.
Zhang
, K.
Mizukami
, and H. S.
Wu
, 1996, “Decentralized robust control for a class of uncertain large-scale interconnected nonlinear dynamical systems
,” J. Optim. Theory Appl.
0022-3239, 91
, pp. 235
–256
.5.
Z.
Gong
, 1995, “Decentralized robust control of uncertain interconnected systems with prescribed degree of exponential convergence
,” IEEE Trans. Autom. Control
0018-9286, 40
, pp. 704
–707
.6.
D. D.
Siljak
and D. M.
Stipanovic
, 2000, “Robust stabilization of nonlinear systems: The LMI approach
,” Mathematical Problems in Engineering
, 6
, pp. 461
–493
.7.
N.
Viswanadham
and A.
Ramakrishna
, 1982, “Decentralized estimation and control for interconnected systems
,” Large Scale Syst.
0165-0777, 3
, pp. 255
–266
.8.
C.
Wen
, 1994, “Decentralized adaptive regulation
,” IEEE Trans. Autom. Control
0018-9286, 39
, pp. 2163
–2166
.9.
N.
Abdel-Jabbar
, C.
Kravaris
, and B.
Carnahan
, 1998, “A partially decentralized state observer and its parallel computer implementation
,” Ind. Eng. Chem. Res.
0888-5885, 37
, pp. 2741
–2760
.10.
M.
Aldeen
and J. F.
Marsh
, 1999, “Decentralised observer-based control scheme for interconnected dynamical systems with unknown inputs
,” IEE Proc.: Control Theory Appl.
1350-2379, 146
, pp. 349
–357
.11.
Z. P.
Jiang
, 2000, “Decentralized and adaptive nonlinear tracking of large-scale systems via output feedback
,” IEEE Trans. Autom. Control
0018-9286, 45
, pp. 2122
–2128
.12.
K. S.
Narendra
and N. O.
Oleng
, 2002, “Exact output tracking in decentralized adaptive control systems
,” IEEE Trans. Autom. Control
0018-9286, 47
, pp. 390
–395
.13.
A. N.
Atassi
and H. K.
Khalil
, 1999, “A separation principle for the stabilization of a class of nonlinear systems
,” IEEE Trans. Autom. Control
0018-9286, 44
, pp. 1672
–1687
.14.
D. D.
Siljak
and D. M.
Stipanovic
, 2001, “Autonomous decentralized control
,” in Proceedings of the Internaional Mechanical Engineering Congress and Exposition
, (Nashville, TN).15.
R.
Eising
, 1984, “Between controllable and uncontrollable
,” Syst. Control Lett.
0167-6911, 4
, pp. 263
–264
.16.
D. L.
Boley
and W. S.
Lu
, 1986, “Measuring how far a controllable system is from an uncontrollable one
,” IEEE Trans. Autom. Control
0018-9286, 31
, pp. 249
–251
.17.
M.
Wicks
and R. A.
DeCarlo
, 1991, “Computing the distance to an uncontrollable system
,” IEEE Trans. Autom. Control
0018-9286, 36
, pp. 39
–49
.18.
D. D.
Siljak
, D. M.
Stipanovic
, and A. I.
Zecevic
, 2002, “Robust decentralized turbine/governor control using linear matrix inequalities
,” IEEE Trans. Power Syst.
0885-8950, 17
, pp. 715
–722
.19.
C.
Aboky
, G.
Sallet
, and J. C.
Vivalda
, 2002, “Observers for Lipschitz non-linear systems
,” Int. J. Control
0020-7179, 75
, pp. 204
–212
.20.
R.
Rajamani
, 1998, “Observers for Lipschitz nonlinear systems
,” IEEE Trans. Autom. Control
0018-9286, 43
, pp. 397
–401
.21.
S.
Derese
and E.
Noldus
, 1980, “Design linear feedback law for bilinear systems
,” Int. J. Control
0020-7179, 31
, pp. 219
–237
.22.
T.
Kailath
, 1980, Linear Systems
, Prentice-Hall, Inc.
, Englewood Cliffs, N.J..23.
W. M.
Wonham
, 1968, “On a matrix Riccati equation of stochastic control
,” SIAM J. Control
0036-1402, 6
, pp. 681
–698
.Copyright © 2005
by American Society of Mechanical Engineers
You do not currently have access to this content.