Login | Register

Control of continuous-time LTI systems by means of structurally constrained controllers


Control of continuous-time LTI systems by means of structurally constrained controllers

Lavaei, Javad and Aghdam, Amir G. (2008) Control of continuous-time LTI systems by means of structurally constrained controllers. Automatica, 44 (1). pp. 141-148. ISSN 00051098

Text (application/pdf)
Aghdam2007b.pdf - Accepted Version

Official URL: http://dx.doi.org/10.1016/j.automatica.2007.04.027


This paper deals with the characterization of the fixed modes of multi-channel systems with respect to linear time-invariant (LTI) structurally constrained controllers. Fixed modes can be found numerically for any LTI system with respect to any given control structure, using a random number generator. The existing analytical methods, however, are not capable of characterizing the fixed modes in the most general case of non-strictly proper systems with non-block diagonal (i.e., overlapping) control structure, efficiently. The notion of a decentralized overlapping fixed mode (DOFM) is introduced in this paper to address the above problem in the most general case. To this end, the knowledge of the overlapping control structure is translated into a bipartite graph, whose vertices correspond to the input and output vectors of various control channels. An efficient technique is applied to the obtained graph to identify the DOFMs of the system. It is to be noted that a system is stabilizable via an appropriate LTI decentralized overlapping controller if and only if it does not have any unstable DOFM. Moreover, it is shown how those modes which are not DOFMs can be placed freely in the complex plane using a proper LTI decentralized overlapping controller. The efficacy of this work is demonstrated through an example.

Divisions:Concordia University > Gina Cody School of Engineering and Computer Science > Electrical and Computer Engineering
Item Type:Article
Authors:Lavaei, Javad and Aghdam, Amir G.
Journal or Publication:Automatica
Digital Object Identifier (DOI):10.1016/j.automatica.2007.04.027
Keywords:Decentralized control; Overlapping systems; Stabilizability; Graph theory
ID Code:975166
Deposited On:22 Jan 2013 13:55
Last Modified:18 Jan 2018 17:39


Anderson, 1982 B.D.O. Anderson Transfer function matrix description of decentralized fixed modes IEEE Transactions on Automatic Control, 27 (6) (1982), pp. 1176–1182

Anderson and Clements, 1981 B.D.O. Anderson, D.J. Clements Algebraic characterizations of fixed modes in decentralized systems Automatica, 17 (5) (1981), pp. 703–712

Bakule et al., 2001 L. Bakule, J. Rodellar, J.M. Rossell Controllability–observability of expanded composite systems
Linear Algebra and its Applications, 332–334 (2001), pp. 381–400

Bakule et al., 2003 L. Bakule, J. Rodellar, J.M. Rossell Contractibility of dynamic LTI controllers using complementary matrices IEEE Transactions on Automatic Control, 48 (7) (2003), pp. 1269–1274

Becerril and Aghdam, 2007 R. Becerril, A.G. Aghdam Decentralised nonlinear control with disturbance rejection for on-ramp metering in highways IET Control Theory and Applications, 1 (1) (2007), pp. 253–262

Chu and Šiljak, 2005 D. Chu, D.D. Šiljak A canonical form for the inclusion principle of dynamic systems SIAM Journal on Control and Optimization, 44 (3) (2005), pp. 969–990

Davison and Chang, 1990 E.J. Davison, T.N. Chang Decentralized stabilization and pole assignment for general proper systems IEEE Transactions on Automatic Control, 35 (6) (1990), pp. 652–664

Davison and Wang, 1985 E.J. Davison, S.H. Wang A characterization of decentralized fixed modes in terms of transmission zeros IEEE Transactions on Automatic Control, 30 (1) (1985), pp. 81–82

Gong and Aldeen, 1997 Z. Gong, M. Aldeen Stabilization of decentralized control systems Journal of Mathematical Systems, Estimation, and Control, 7 (1) (1997), pp. 1–16

Groumpos, 1994 P.P. Groumpos Structural modelling and optimisation of large scale systems IEE Control Theory and Applications, 141 (1) (1994), pp. 1–11

Iftar, 1991 Iftar, A. (1991). Decentralized optimal control with overlapping decompositions. In IEEE international conference on systems engineering (pp. 299–302).

Iftar, 1993 A. Iftar Overlapping decentralized dynamic optimal control International Journal of Control, 58 (1) (1993), pp. 187–209

Lafferriere et al., 2004 Lafferriere, G., Caughman, J., & Williams, A. (2004). Graph theoretic methods in the stability of vehicle formations. In American control conference (pp. 3729–3734).

Lavaei et al., 2007 Lavaei, J., Momeni, A., & Aghdam, A. G. (2007). Spacecraft formation control in deep space with reduced communication requirement. IEEE Transactions on Control Systems Technology, to appear.

Leros and Groumpos, 1987 A.P. Leros, P.P. Groumpos The time-invariant BAS decentralized large-scale linear regulator problem International Journal of Control, 46 (1) (1987), pp. 129–152

Li and Wang, 2005 Li, H., & Wang, Y. (2005). Nonlinear robust decentralized control of multimachine power systems. In Proceedings of the seventh international power engineering conference (pp. 1–6).

Li et al., 1999 Li, K., Kosmatopoulos, E. B., Ioannou, P., & Boussalis, H. (1999). Centralized, decentralized, and overlapping control designs for a segmented telescope. In Proceedings of the IEEE international symposium on intelligent control/intelligent systems and semiotics (pp. 173–178).

Mayeda, 1981 H. Mayeda On structural controllability theorem IEEE Transactions on Automatic Control, 26 (3) (1981), pp. 795–798

Movsichoff et al., 2005 B.A. Movsichoff, C.M. Lagoa, H. Che Decentralized optimal traffic engineering in connectionless networks IEEE Journal on Selected Areas in Communications, 23 (2) (2005), pp. 293–303

Pichai et al., 1984 V. Pichai, M.E. Sezer, D.D. Šiljak A graph-theoretic characterization of structurally fixed modes Automatica, 20 (2) (1984), pp. 247–250

Ravi et al., 1995 M.S. Ravi, J. Rosenthal, X.A. Wang On decentralized dynamic pole placement and feedback stabilization IEEE Transactions on Automatic Control, 40 (9) (1995), pp. 1603–1614

Reinschke, 1988 K. Reinschke Multivariable control: A graph-theoretic approach Springer, Berlin (1988)

Šiljak, 1991 D.D. Šiljak Decentralized control of complex systems Academic Press, Cambridge (1991)

Šiljak and Zecevic, 2005 D.D. Šiljak, A.I. Zecevic Control of large-scale systems: Beyond decentralized feedback Annual Reviews in Control, 29 (2) (2005), pp. 169–179

Smith and Hadaegh, 2002 Smith, R.S., & Hadaegh, F.Y. (2002). Control topologies for deep space formation flying spacecraft. In Proceedings of the 2002 American control conference (pp. 2836–2841).

Stankovic et al., 2000 S.S. Stankovic, M.J. Stanojevic, D.D. Šiljak Decentralized overlapping control of a platoon of vehicles IEEE Transactions on Control Systems Technology, 8 (5) (2000), pp. 816–832

Wang and Davison, 1973 S.H. Wang, E.J. Davison On the stabilization of decentralized control systems IEEE Transactions on Automatic Control, 18 (5) (1973), pp. 473–478

Zecevic and Šiljak, 2005 A.I. Zecevic, D.D. Šiljak A new approach to control design with overlapping information structure constraints Automatica, 41 (2) (2005), pp. 265–272
All items in Spectrum are protected by copyright, with all rights reserved. The use of items is governed by Spectrum's terms of access.

Repository Staff Only: item control page

Downloads per month over past year

Back to top Back to top