Advertisement

Robust control of systems with a single input lag

  • Gilead Tadmor
Chapter
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 228)

Abstract

A state space design methodology is developed for various H problems and gap optimization in systems with a single input lag. The main contribution is in converting associated operator Riccati equation and abstract model compensator realizations to algebraic and differential matrix Riccati equations of a fixed order and finite dimensional, integro-differential realizations.

Keywords

Robust Control Differential Game Delay System Infinitesimal Generator Distribute Parameter System 
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.
    J. A. Ball and N. Cohen. Sensitivity minimization in an H norm: parameterization of suboptimal solutions. Int. J. Control, 46:785–816, 1987.Google Scholar
  2. 2.
    J. A. Burns, T. L. Herdman, and H. W. Stetch. Linear functional differential equations as semigroups on product spaces. SIAM J. Math. Anal., 14:98–116, 1983.Google Scholar
  3. 3.
    R. F. Curtain and A. J. Pritchard. Infinite Dimensional Linear Systems Theory. Springer, 1978.Google Scholar
  4. 4.
    R. F. Curtain and H. J. Zwart. An Introduction to Infinite Dimensional Linear Systems Theory. Springer, 1995.Google Scholar
  5. 5.
    J.C. Doyle, K. Glover, P.P. Khargonekar, and B.A. Francis. State space solutions to standard H 2 and H control problems. IEEE Transactions on Automatic Control, AC-34:831–847, 1989.Google Scholar
  6. 6.
    H. Dym, T. T. Georgiou, and M. C. Smith. Explicit formulas for optimally robust controllers for delay systems. IEEE Transactions on Automatic Control, AC-40:656–669, 1995.Google Scholar
  7. 7.
    D. Flamm and S. Mitter. H Sensitivity minimization for delay systems. System and Control letters, 9:17–24, 1987.Google Scholar
  8. 8.
    C. Foias, A. Tannenbaum, and G. Zames. Weighted sensitivity minimization for delay systems. IEEE Transactions on Automatic Control, AC-31:763–766, 1986.Google Scholar
  9. 9.
    T. T. Georgiou and M. C. Smith. Optimal robustness in the gap metric. IEEE Transactions on Automatic Control, AC-35:673–686, 1990.Google Scholar
  10. 10.
    A. Ichikawa. Optimal control and filtering of evolution equations with delays in conrol and observation. Technical Report 53, Control Theory centre, university of warwick, 1977.Google Scholar
  11. 11.
    A. Ichikawa. Quadratic control of evolution equations with delays in control. SIAM J. Control and Optim, pages 645–668, 1982.Google Scholar
  12. 12.
    P. P. Khargonekar, K. M. Nagpal, and K. R. Poolla. H control with transients. SIAM J. Control and Optim, 29:1373–1393, 1991.Google Scholar
  13. 13.
    P. P. Khargonekar and K. Zhou. on the weighted sensitivity minimization problem for delay systems. System and Control letters, 8:307–312, 1987.Google Scholar
  14. 14.
    A. Kojima and S. Ishijima. Robust controller design for delay systems in the gap metric. In Proceedings of the American Control Conference, pages 1939–1944, 1994.Google Scholar
  15. 15.
    K. M. Nagpal and R. Ravi. H Control and estimations problems with delayed measurements: state space solutions. In Proceedings of the American Control Conference, pages 2379–2383, 1994.Google Scholar
  16. 16.
    O. Toker and H. Özbay. Suboptimal robustness in the gap metric for MIMO delay systems. In Proceedings of the American Control Conference, pages 3183–3187, 1994.Google Scholar
  17. 17.
    H. Özbay and A. Tannenbaum. A skew Toeplitz approach to the H optimal control of multivariable distributed systems. SIAM J. Control and Optim, 28:653–670, 1990.Google Scholar
  18. 18.
    A. Pazy. Semigroups of Linear Operators and Relations to Differential Equations. Springer, 1983.Google Scholar
  19. 19.
    A. J. Pritchard and D. Salamon. The linear-quadratic problem for retarded systems with delays in the control and observation. IMA Journal of Mathematical Control and Information, pages 335–362, 1985.Google Scholar
  20. 20.
    D. Salamon. Control And Observation of Neutral Systems. Pitman, 1984.Google Scholar
  21. 21.
    G. Tadmor. An interpolation problem associated with H optimization in systems with distributed lags. System and Control letters, 8:313–319, 1987.Google Scholar
  22. 22.
    G. Tadmor. H Interpolation in systems with commensurate input lags. SIAM J. Control and Optim, 27:511–526, 1989.Google Scholar
  23. 23.
    G. Tadmor. Worst case design in the time domain: the maximum principle and the standard H problem. Math. Control, Signals and Systems, 3:301–324, 1990.Google Scholar
  24. 24.
    G. Tadmor. H Optimal sampled data control in continuous time systems. Int. J. Control, 56:99–141, 1992.Google Scholar
  25. 25.
    G. Tadmor. The standard H problem and the maximum principle: the general linear case. SIAM J. Control and Optim, 31:831–846, 1993.Google Scholar
  26. 26.
    G. Tadmor. The standard H problem and the maximum principle: the general linear case. SIAM J. Control and Optim, 31:831–846, 1993.Google Scholar
  27. 27.
    G. Tadmor. The standard H problem in systems with a single input delay. Technical Report, 1994.Google Scholar
  28. 28.
    G. Tadmor. H Control in systems with a single input lag. In Proceedings of the American Control Conference, pages 321–325, 1995.Google Scholar
  29. 29.
    G. Tadmor. The nehari problem in systems with distributed input delays is inherently finite dimensional. System and Control letters, 26:11–16, 1995.Google Scholar
  30. 30.
    G. Tadmor. Robust control in the gap: a state space solution in the presence of a single input delay. IEEE Transactions on Automatic Control, in press.Google Scholar
  31. 31.
    G. Tadmor. Weighted sensitivity minimization in systems with a single input delay: a state space solution. SIAM J. Control and Optim, in press.Google Scholar
  32. 32.
    G. Tadmor and J. Turi. Neutral equations and associated semigroups. J. Differential Eqs., 116:59–87, 1995.Google Scholar
  33. 33.
    G. Tadmor and M. Verma. Factorization and the Nehari theorem in time varying systems. Math. Control, Signals and Systems, 5:419–452, 1992.Google Scholar
  34. 34.
    B. van Keulen. H control for infinite dimensional systems: a state space approach. PhD thesis, University of Groningen, 1993.Google Scholar
  35. 35.
    K. Zhou and P. P. Khargonekar. On the weighted sensitivity minimization problem for delay systems. System and Control letters, 8:307–312, 1987.Google Scholar

Copyright information

© Springer-Verlag London Limited 1998

Authors and Affiliations

  • Gilead Tadmor
    • 1
  1. 1.ECE DepartmentNortheastern UniversityBostonUSA

Personalised recommendations