Abstract
In the control literature, an interconnected system is often referred to a system with a collection of interacting subsystems [1]. In terms of the interaction topology between the subsystems, the class of hierarchical interconnected systems has drawn special attention in recent publications due to its broad applications such as formation flying, underwater vehicles, automated highway, robotics, satellite constellation, etc., which have leader-follower structures or structures with virtual leaders [2, 3, 4, 5, 6]. It is shown in [2] that even if a continuous-time interconnected system does not have a hierarchical structure, under certain conditions its discrete-time equivalent model can be transformed to a hierarchical form. For such a system, it is normally desired to design a set of local controllers corresponding to the individual subsystems, which partially exchange their information [4, 7]. This demand is originated from some practical limitations concerning, for instance, the geographical distribution of the subsystems or the computational complexity associated with a centralized controller [8]. The case when these local controllers operate independently (i.e., they do not interact with each other), is referred to as decentralized feedback control [9, 10, 11].
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
S. Sojoudi, J. Lavaei and A. G. Aghdam, “Optimal information flow structure for control of interconnected systems,” in Proceedings of 2007 American Control Conference, New York, NY, 2007.
A. G. Aghdam, E. J. Davison and R. B. Arreola, “Structural modification of systems using discretization and generalized sampled-data hold functions,” Automatica, vol. 42, no. 11, pp. 1935–1941, 2006.
G. Inalhan, D. M. Stipanovic and C. J. Tomlin, “Decentralized optimization with application to multiple aircraft coordination,” in Proceedings of 41st IEEE Conference on Decision and Control, Las Vegas, NV, 2002.
D. M. Stipanovic, G. Inalhan, R. Teo and C. J. Tomlin, “Decentralized overlapping control of a formation of unmanned aerial vehicles,” Automatica, vol. 40 , no.8, pp. 1285–1296, 2004.
S. S. Stankovic, M. J. Stanojevic and D. D. Šiljak, “Decentralized overlapping control of a platoon of vehicles,” IEEE Transactions on Control Systems Technology, vol. 8, no. 5, pp. 816–832, 2000.
J. A. Fax and R. M. Murray, “Information flow and cooperative control of vehicle formations,” IEEE Transactions on Automatic Control, vol. 49, no. 9, pp. 1465–1476, 2004.
J. Lavaei and A. G. Aghdam, “A necessary and sufficient condition for the existence of a LTI stabilizing decentralized overlapping controller,” in Proceedings of 45th IEEE Conference on Decision and Control, San Diego, CA, 2006.
J. Lavaei and A. G. Aghdam, “High-performance decentralized control design for general interconnected systems with applications in cooperative control,” International Journal of Control, vol. 80, no. 6, pp. 935–951, 2007.
D. D. Šiljak, Decentralized control of complex systems, Boston: Academic Press, 1991.
E. J. Davison and T. N. Chang, “Decentralized stabilization and pole assignment for general proper systems,” IEEE Transactions on Automatic Control, vol. 35, no. 6, pp. 652–664, 1990.
J. Lavaei, A. Momeni and A. G. Aghdam, “A model predictive decentralized control scheme with reduced communication requirement for spacecraft formation, IEEE Transactions on Control Systems Technology, vol. 16, no. 2, pp. 268–278, 2008.
Z. Gong and M. Aldeen, “Stabilization of decentralized control systems,” Journal of Mathematical Systems, Estimation, and Control, vol. 7, no. 1, pp. 1–16, 1997.
J. Lavaei and A. G. Aghdam, “Elimination of fixed modes by means of high-performance constrained periodic control,” in Proceedings of 45th IEEE Conference on Decision and Control, San Diego, CA, 2006.
J. Lavaei and A. G. Aghdam, “Characterization of decentralized and quotient fixed modes via graph theory,” Proceedings of 2007 American Control Conference, New York, NY, 2007.
J. Leventides and N. Karcanias, “Decentralized dynamic pole assignment with low-order compensators,” IMA Journal of Mathematical Control and Information, vol. 24, no. 3, pp. 395–410, 2007.
S. S. Keerthi and H. S. Phatak, “Regional pole placement of multivariable systems under control structure constraints,” IEEE Transactions on Automatic Control, vol. 40, no. 2, pp. 272–276, 1995.
H. T. Toivoneh and P. M. Makila, “A descent anderson-moore algorithm for optimal decentralized control,” Automatica, vol. 21, no. 6, pp. 743–744, 1985.
M. Rotkowitz and S. Lall, “A characterization of convex problems in decentralized Control,” IEEE Transactions on Automatic Control, vol. 51, no. 2, pp. 274–286, 2006.
J. Lavaei and A. Aghdam, “Simultaneous LQ control of a set of LTI systems using constrained generalized sampled-data hold functions,” Automatica, vol. 43, no. 2, pp. 274–280, 2007.
E. J. Davison, “The robust decentralized control of a general servomechanism problem,” IEEE Transactions on Automatic Control, vol. 21, no. 1, pp. 14–24, 1976.
E. J. Davison, “The robust decentralized control of a servomechanism problem for composite systems with input-output interconnections,” IEEE Transactions on Automatic Control, vol. 24, no. 2, pp. 325–327, 1979.
E. J. Davison, and Ü. Özgüner, “Synthesis of the decentralized robust servomechanism problem using local models,” IEEE Transactions on Automatic Control, vol. 27, no. 3, pp. 583–600, 1982.
S. V. Savastuk and D. D. Šiljak, “Optimal decentralized control,” in Proceedings of 1994 American Control Conference, Baltimore, MD, 1994.
D. D. Sourlas and V. Manousiouthakis, “Best achievable decentralized performance,” IEEE Transactions on Automatic Control, vol. 40, no. 11, pp. 1858–1871, 1995.
R. Krtolica and D. D. Šiljak, “Suboptimality of decentralized stochastic control and estimation,” IEEE Transactions on Automatic Control, vol. 25, no. 1, pp. 76–83, 1980.
J. R. Broussard, “An approach to the optimal output feedback initial stabilizing gain problem,” in Proceedings of 29th IEEE Conference on Decision and Control, Honolulu, HI, 1990.
P. M. Makila and H. T. Toivoneh, “Computational methods for parametric LQ problems- a survey,” IEEE Transactions on Automatic Control, vol. 32, no. 8, pp. 658–671, 1987.
A. İftar and Ü. Özgüner, “An optimal control approach to the decentralized robust servomechanism problem,” IEEE Transactions on Automatic Control, vol. 34, no. 12, pp. 1268–1271, 1989.
R. S. Smith and F. Y. Hadaegh, ”Control topologies for deep space formation flying spacecraft,” in Proceedings of 2002 American Control Conference, Anchorage, AK, pp. 2836–2841, 2002.
K. P. Groves, D. O. Sigthorsson, A. Serrani and S. Yurkovich , “Reference command tracking for a linearized model of an air-breathing hypersonic vehicle,” in AIAA Guidance, Navigation, and Control Conference and Exhibit, San Francisco, CA, 2005.
E. J. Davison, “A generalization of the output control of linear multivariable systems with unmeasurable arbitrary disturbances,” IEEE Transactions on Automatic Control, vol. 20, no. 6, pp. 788–792, 1975.
J. Lam and Y. Y. Cao, “Simultaneous linear-quadratic optimal control design via static output feedback,” International Journal of Robust and Nonlinear Control, vol. 9, pp. 551–558, 1999.
H. Kwakernaak and R. Sivan, Linear optimal control systems, John Wiley & sons,1972.
S. C. Eisenstat and I. C. F. Ipsen, “Three absolute perturbation bounds for matrix eigenvalues imply relative bounds,” SIAM Journal on Matrix Analysis and Applications, vol. 20, no. 1, pp. 149–158, 1998.
Jos. L. M. Van Dorsselaer, “Several concepts to investigate strongly nonnormal eigenvalue problems,” SIAM Journal on Scientific Computing, vol. 24, no. 3, pp. 1031–1053, 2003.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2011 Springer US
About this chapter
Cite this chapter
Sojoudi, S., Lavaei, J., Aghdam, A.G. (2011). LQ Decentralized Controllers with Disturbance Rejection Property for Hierarchical Systems. In: Structurally Constrained Controllers. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-1549-8_7
Download citation
DOI: https://doi.org/10.1007/978-1-4419-1549-8_7
Published:
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-1548-1
Online ISBN: 978-1-4419-1549-8
eBook Packages: EngineeringEngineering (R0)