Advertisement

Decentralized Control

  • John Swigart
  • Sanjay Lall
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 406)

Abstract

Decentralized control has been a large area of open research for over forty years. To cover every aspect of it would require a vast knowledge of applied mathematics and considerable time. Consequently, in this tutorial we will attempt to restrict our attention to optimal control of systems which are linear with Gaussian random noise and disturbances, where the objective is a quadratic cost function. This encompasses a very general, and commonly encountered, class of systems. While the results herein will be aimed at this class, much of our discussion may be applied more generally to other problems. Most of the results in this chapter are, of course, not new and can be found in the references.

To begin our discussion we will highlight some of the key features of decentralized control with a few motivating examples. From there, we will address what will be called static systems, and show that decentralized problems of this nature admit tractable solutions. Our discussion will then turn to the class of dynamic problems, involving feedback. Decentralized feedback problems in general are known to be difficult. Nevertheless, there exist some problems for which optimal solutions may be obtained. We will end our discussion with some methods for solving these types of problems.

Keywords

Optimal Controller Linear Controller Sparsity Structure Spectral Factorization Decentralize Control 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bamieh, B., Voulgaris, P.G.: Optimal distributed control with distributed delayed measurements. In: Proceedings of the IFAC World Congress (2002)Google Scholar
  2. 2.
    Blondel, V.D., Tsitsiklis, J.N.: A survey of computational complexity results in systems and control. Automatica 36(9), 1249–1274 (2000)MATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)MATHGoogle Scholar
  4. 4.
    Gupta, V.: Distributed Estimation and Control in Networked Systems. PhD thesis, California Institute of Technology (2006)Google Scholar
  5. 5.
    Ho, Y.-C., Chu, K.C.: Team decision theory and information structures in optimal control problems – Part I. IEEE Transactions on Automatic Control 17(1), 15–22 (1972)MATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Sandell Jr., N., Athans, M.: Solution of some nonclassical LQG stochastic decision problems. IEEE Transactions on Automatic Control 19(2), 108–116 (1974)MATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    Qi, X., Salapaka, M., Voulgaris, P., Khammash, M.: Structured optimal and robust control with multiple criteria: A convex solution. IEEE Transactions on Automatic Control 49(10), 1623–1640 (2004)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Radner, R.: Team decision problems. Annals of mathematical statistics 33, 857–881 (1962)MATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    Rantzer, A.: Linear quadratic team theory revisited. In: Proceedings of American Control Conference, pp. 1637–1641 (June 2006)Google Scholar
  10. 10.
    Rotkowitz, M.: Information structures preserved under nonlinear time-varying feedback. In: Proceedings of the American Control Conference, pp. 4207–4212 (2006)Google Scholar
  11. 11.
    Rotkowitz, M., Cogill, R., Lall, S.: A simple condition for the convexity of optimal control over networks with delays. In: Proceedings of the IEEE Conference on Decision and Control, pp. 6686–6691 (2005)Google Scholar
  12. 12.
    Rotkowitz, M., Lall, S.: A characterization of convex problems in decentralized control. IEEE Transactions on Automatic Control 51(2), 274–286 (2002)MathSciNetGoogle Scholar
  13. 13.
    Rotkowitz, M., Lall, S.: Decentralized control information structures preserved under feedback. In: Proceedings of the IEEE Conference on Decision and Control, pp. 569–575 (2002)Google Scholar
  14. 14.
    Rotkowitz, M., Lall, S.: Affine controller parameterization for decentralized control over banach spaces. IEEE Transactions on Automatic Control 51(9), 1497–1500 (2006)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Scherer, C.W.: Structured finite-dimensional controller design by convex optimization. Linear Algebra and its Applications 351(352), 639–669 (2002)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Swigart, J., Lall, S.: Dynamic programming with non-classical information structures. In: Proceedings of Mathematical Theory of Networks and Systems, pp. 457–462 (2008)Google Scholar
  17. 17.
    Swigart, J., Lall, S.: A graph-theoretic approach to distributed control over networks. In: Proceedings of the IEEE Conference on Decision and Control (2009)Google Scholar
  18. 18.
    Swigart, J., Lall, S.: Spectral factorization of non-classical information structures under feedback. In: Proceedings of the American Control Conference, pp. 457–462 (2009)Google Scholar
  19. 19.
    Swigart, J., Lall, S.: An explicit state-space solution for a decentralized two-player optimal linear-quadratic regulator. Submitted to American Control Conference, pp. 457–462 (2010)Google Scholar
  20. 20.
    Vouglaris, P.: Control of nested systems. In: Proceedings of the American Control Conference, vol. 6, pp. 4442–4445 (2000)Google Scholar
  21. 21.
    Witsenhausen, H.S.: A counterexample in stochastic optimum control. SIAM Journal of Control 6(1), 131–147 (1968)MATHMathSciNetCrossRefGoogle Scholar
  22. 22.
    Zelazo, D., Mesbahi, M.: \(\mathcal{H}_2\) analysis and synthesis of networked dynamic systems. In: Proceedings of the American Control Conference, pp. 2966–2971 (2009)Google Scholar

Copyright information

© Springer London 2010

Authors and Affiliations

  • John Swigart
    • 1
  • Sanjay Lall
    • 2
  1. 1.Department of Aeronautics and AstronauticsStanford UniversityStanfordUSA
  2. 2.Department of Electrical Engineering and Department of Aeronautics and AstronauticsStanford UniversityStanfordUSA

Personalised recommendations