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Interconnection-Based Performance Analysis for a Class of Decentralized Controllers

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

Abstract

Many real-world systems can be described by large-scale interconnected models [1]. There is a great deal of interest in performance analysis and control synthesis of large-scale systems. A key practical consideration in designing a controller for this type of system is to rely on local information as much as possible. Decentralized control theory was introduced in the literature to address this consideration, and reduce the complexity of the control implementation for large-scale systems. Distinctive aspects of decentralized control systems have been well-documented in the last three decades [2, 3]. A decentralized controller consists of a number of isolated local controllers corresponding to the subsystems of the large-scale system. For the sake of simplicity of the control design problem, it is often desirable that the largescale system possesses a hierarchical structure [4, 5]. Note that a hierarchical model refers to an interconnected system whose subsystems can be renumbered in such a way that the corresponding transfer function matrix becomes lower block-triangular. The control design problem for a hierarchical system can be broken down into a number of parallel design subproblems corresponding to different subsystems. The advantage of such design techniques is twofold: the control design procedure is far simpler for a number of low-order subsystems compared to that for one high-order system, and at the same time parallel computation is very fast.

Keywords

Hierarchical System Lyapunov Equation Local Controller Sylvester Equation Transfer Function Matrix 
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.
    A. C. Antoulas and D.C. Sorensen, “Approximation of large-scale dynamical systems: An overview,” International Journal of Applied Mathematics and Computer Science, vol. 11, no. 5, pp. 1093–1121, 2001.MathSciNetMATHGoogle Scholar
  2. 2.
    D. D. Šiljak, Decentralized Control of Complex Systems, Boston: Academic Press, 1991.Google Scholar
  3. 3.
    M. Jamshidi, Large-Scale Systems: Modeling, Control, and Fuzzy Logic, Prentice-Hall, NJ, 1997.Google Scholar
  4. 4.
    S. S. Stankovic and D. D. Šiljak, “Sequential LQG optimization of hierarchically structured systems,” Automatica, vol. 25, no. 4, pp. 545–559, 1989.MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    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
  6. 6.
    H. G. Tanner, G. J. Pappas and V. Kumar, “Leader to formation stability,” IEEE Transactions on Robotics and Automation, vol. 20, no. 3, pp. 443–455, 2004.CrossRefGoogle Scholar
  7. 7.
    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
  8. 8.
    D. J. Stilwell and B. E. Bishop, “Platoons of underwater vehicles,” IEEE Control Systems Magazine, vol. 20, no. 6, pp. 45–52, 2000.CrossRefGoogle Scholar
  9. 9.
    A. G. Aghdam, E. J. Davison and R. Becerril, “Structural modification of systems using discretization and generalized sampled-data hold functions,” Automatica, vol. 42, no. 11, pp. 1935–1941, 2006.MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    J. Lavaei, A. Momeni and A. G. Aghdam, “High-performance decentralized control for formation flying with leader-follower structure,” in Proceedings of 45th IEEE Conference on Decision and Control, San Diego, CA, 2006.Google Scholar
  11. 11.
    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
  12. 12.
    A. Iftar, “Overlapping decentralized dynamic optimal control,” International Journal of Control, vol. 58, no. 1, pp. 187–209, 1993.MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    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
  14. 14.
    D. D. Šiljak and A. I. Zecevic, “Control of large-scale systems: Beyond decentralized feedback,” Annual Reviews in Control, vol. 29, no. 2, pp. 169–179, 2005.CrossRefGoogle Scholar
  15. 15.
    A. I. Zecevic and D. D. Šiljak, “A new approach to control design with overlapping information structure constraints,” Automatica, vol. 41, no. 2, pp. 265–272, 2005.MathSciNetMATHCrossRefGoogle Scholar
  16. 16.
    D. Chu and D. D. Šiljak, “A canonical form for the inclusion principle of dynamic systems,” SIAM Journal on Control and Optimization, vol. 44, no. 3, pp. 969–990, 2005.MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    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
  18. 18.
    M. E. Sezer and D. D. Šiljak “Nested e-decompositions and clustering of complex systems,” Automatica, vol. 22, no. 3, pp. 321–331, 1986.MathSciNetMATHCrossRefGoogle Scholar
  19. 19.
    M. E. Sezer and D. D. Šiljak “Nested epsilon decompositions of linear systems: Weakly coupled and overlapping blocks,” SIAM Journal of Matrix Analysis and Applications, vol. 12, pp. 521–533, 1991.MATHCrossRefGoogle Scholar
  20. 20.
    A. I. Zecevic and D. D. Šiljak “A block-parallel Newton method via overlapping epsilon decompositions,” SIAM Journal of Matrix Analysis and Applications, vol. 15, pp. 824–844, 1994.MATHCrossRefGoogle Scholar
  21. 21.
    J. Löfberg, “A toolbox for modeling and optimization in MATLAB,” in Proceedings of the CACSD Conference, Taipei, Taiwan, 2004 (available online at http://control.ee.ethz.ch/~joloef/yalmip.php).Google Scholar
  22. 22.
    S. Prajna, A. Papachristodoulou, P. Seiler and P. A. Parrilo, “SOSTOOLS sum of squares optimization toolbox for MATLAB,” Users guide, 2004 (available online at http://www.cds.caltech.edu/sostools).Google Scholar
  23. 23.
    C. H. Lee, “Solution bounds of the continuous and discrete Lyapunov matrix equations,” Journal of Optimization Theory and Applications, vol. 120, no. 3, pp. 559–578, 2004.MathSciNetMATHCrossRefGoogle Scholar
  24. 24.
    L. Bakule, J. Rodellar and J. M. Rossell, “Inclusion principle for uncertain discrete-time systems with guaranteed cost,” in Proceedings of 43rd IEEE Conference on Decision and Control, Atlantis, Paradise Island, Bahamas, 2004.Google Scholar
  25. 25.
    L. Bakule, J. Rodellar, J. M. Rossell and P. Rubió “Preservation of controllability-observability in expanded systems,” IEEE Transactions on Automatic Control, vol. 46, no. 7, pp. 1155–1162, 2001.MATHCrossRefGoogle Scholar
  26. 26.
    L. N. Trefethen and D. Bau, “Numerical Linear Algebra,” SIAM, 1997.Google Scholar
  27. 27.
    M. K. Tippett and D. Marchesin,“Upper bounds for the solution of the discrete algebraic Lyapunov equation,” Automatica, vol. 35, no. 8, pp. 1485–1489, 1999.MathSciNetMATHCrossRefGoogle Scholar
  28. 28.
    P. Benner,“Large-scale matrix equations of special type,” Numerical Linear Algebra with Applications, vol. 15, no. 9, pp. 747–754, 2008.MathSciNetCrossRefGoogle 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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