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LQ Decentralized Controllers with Disturbance Rejection Property for Hierarchical Systems

  • Somayeh Sojoudi
  • Javad Lavaei
  • Amir G. Aghdam
Chapter

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].

Keywords

Model Predictive Control Centralize Controller Local Controller Speed Error Virtual Leader 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    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.Google Scholar
  2. 2.
    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.MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    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.Google Scholar
  4. 4.
    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.MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    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.CrossRefGoogle Scholar
  6. 6.
    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.MathSciNetCrossRefGoogle Scholar
  7. 7.
    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.Google Scholar
  8. 8.
    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.MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    D. D. Šiljak, Decentralized control of complex systems, Boston: Academic Press, 1991.Google Scholar
  10. 10.
    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.MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    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.CrossRefGoogle Scholar
  12. 12.
    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.MathSciNetGoogle Scholar
  13. 13.
    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.Google Scholar
  14. 14.
    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.Google Scholar
  15. 15.
    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.MathSciNetMATHCrossRefGoogle Scholar
  16. 16.
    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.MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    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.CrossRefGoogle Scholar
  18. 18.
    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.MathSciNetGoogle Scholar
  19. 19.
    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.MathSciNetMATHCrossRefGoogle Scholar
  20. 20.
    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.MathSciNetMATHCrossRefGoogle Scholar
  21. 21.
    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.MathSciNetMATHCrossRefGoogle Scholar
  22. 22.
    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.MATHCrossRefGoogle Scholar
  23. 23.
    S. V. Savastuk and D. D. Šiljak, “Optimal decentralized control,” in Proceedings of 1994 American Control Conference, Baltimore, MD, 1994.Google Scholar
  24. 24.
    D. D. Sourlas and V. Manousiouthakis, “Best achievable decentralized performance,” IEEE Transactions on Automatic Control, vol. 40, no. 11, pp. 1858–1871, 1995.MathSciNetMATHCrossRefGoogle Scholar
  25. 25.
    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.CrossRefGoogle Scholar
  26. 26.
    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.Google Scholar
  27. 27.
    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.CrossRefGoogle Scholar
  28. 28.
    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.MATHCrossRefGoogle Scholar
  29. 29.
    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.Google Scholar
  30. 30.
    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.Google Scholar
  31. 31.
    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.MathSciNetMATHCrossRefGoogle Scholar
  32. 32.
    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.MathSciNetMATHCrossRefGoogle Scholar
  33. 33.
    H. Kwakernaak and R. Sivan, Linear optimal control systems, John Wiley & sons,1972.Google Scholar
  34. 34.
    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.MathSciNetMATHCrossRefGoogle Scholar
  35. 35.
    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.MATHCrossRefGoogle Scholar

Copyright information

© Springer US 2011

Authors and Affiliations

  • Somayeh Sojoudi
    • 1
  • Javad Lavaei
    • 1
  • Amir G. Aghdam
    • 2
  1. 1.Control & Dynamical Systems Dept.California Institute of TechnologyPasadenaUSA
  2. 2.Dept. Electrical & Computer EngineeringConcordia UniversityMontreal QuébecCanada

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