Advertisement

General Formulae for Suboptimal H Control over a Finite Horizon

Chapter
Part of the Systems Control: Foundations & Applications book series (SCFA)

Abstract

In this chapter a general suboptimal control problem is posed, and an expression for a suboptimal controller is derived solving the saddle point conditions. Based on this, a formula for a state feedback suboptimal controller can be derived by solving a dynamic Riccati equation. Then an expression for a suboptimal output feedback controller is developed in a general case via the solution of two dynamic Riccati equations.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Doyle, J. C., Glover, K., Khargonekar, P. P., and Francis, B. A., “State-space solutions to standard H2 and H∞ control problems,” IEEE Transactions on Automatic Control, 34, 1989, pp. 831–847.MathSciNetzbMATHCrossRefGoogle Scholar
  2. [2]
    Khargonekar, P. P., “State-space H∞ Control Theory,” in Mathematical System Theory: The Influence of R. E. Kalman, edited by A. C. Antoulas, Springer-Verlag, Berlin, 1991.Google Scholar
  3. [3]
    Khargonekar, P. P., Nagpal, K. M., and Poolla, K. R., “H∞ control with transients,” SIAM Journal on Control and Optimization, 29, 1991, pp. 1373–1393.MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    Ravi, R., Nagpal, K. M., and Khargonekar, P. P., “H∞ control of linear time-varying systems: A state space approach,” SIAM Journal on Control and Optimization, 29, 1991, pp. 1394–1413.MathSciNetzbMATHCrossRefGoogle Scholar
  5. [5]
    Tadmor, G., “Worst-case design in the time domain: the maximum principle and the standard HQQ problem,” Mathematics of Control, Signals, and Systems, 3, 1990, pp. 301–324.MathSciNetzbMATHCrossRefGoogle Scholar
  6. [6]
    Subrahmanyam, M. B., Optimal Control with a Worst-Case Performance Criterion and Applications, Lecture Notes in Control and Information Sciences, No. 145, Springer-Verlag, Berlin, 1990.Google Scholar
  7. [7]
    Subrahmanyam, M. B., “Optimal disturbance rejection and performance robustness in linear systems,” Journal of Mathematical Analysis and Applications, 164, 1992, pp. 130–150.MathSciNetzbMATHCrossRefGoogle Scholar
  8. [8]
    Subrahmanyam, M. B., “Synthesis of finite-interval H∞ controllers by state-space methods,” AIAA Journal of Guidance, Control, and Dynamics, 13, 1990, pp. 624–629.MathSciNetzbMATHCrossRefGoogle Scholar
  9. [9]
    Subrahmanyam, M. B., “Worst-case performance measures for linear control problems,” Proc. IEEE Conference on Decision and Control, Honolulu, U.S.A., 1990, pp. 2439–2443.Google Scholar
  10. [10]
    Subrahmanyam, M. B. and Steinberg, M., “Model reduction with a finite-interval H∞ criterion,” Proc. AIAA Guidance, Navigation and Control Conference, Portland, U.S.A., 1990, pp. 1419–1427.Google Scholar
  11. [11]
    Safonov, M. G., Limebeer, D. J. N., and Chiang, R. Y., “Simplifying the H∞ theory via loop-shifting, matrix-pencil and descriptor concepts,” International Journal of Control, 50, 1989, pp. 2467–2488.MathSciNetzbMATHCrossRefGoogle Scholar
  12. [12]
    Subrahmanyam, M. B., “Worst-case optimal control over a finite horizon,” Journal of Mathematical Analysis and Applications, 171, 1992, pp. 448–460.MathSciNetzbMATHCrossRefGoogle Scholar
  13. [13]
    Pontryagin, L. S., Boltyanski, V. G., Gamkrelidze, R. V., and Mischenko, E. F., The Mathematical Theory of Optimal Processes, Interscience Publishers, New York, 1962.zbMATHGoogle Scholar

Copyright information

© Birkhäuser Boston 1995

Authors and Affiliations

  1. 1.Flight Dynamics and Control Branch Air Vehicle & Crew Systems Technoly Dept.Naval Warfare Center Aircraft DivisionWarminsterUSA

Personalised recommendations