Advertisement

Synthesis of Suboptimal H Controllers over a Finite Horizon

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

Abstract

In this chapter a finite horizon H optimal control problem is posed and solved. A criterion which is useful for the evaluation of the infimal H norm in the finite horizon case is given. Also, a differential equation is derived for the measure of performance in terms of the final time. A general suboptimal control problem is then posed, and an expression for a suboptimal controller is derived solving the saddle point conditions. An expression for a feedback controller can be derived by solving a dynamic Riccati equation. Also, a criterion that yields the actual performance of the suboptimal controller is given. In the time-invariant case, the finite horizon controller converges to a static controller as the final time becomes large. Examples are given to illustrate the usefulness of the theory.

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]
    Francis, B. A. and Doyle, J. C., “Linear Control Theory with an H∞ Optimality Criterion,” SIAM J. Control and Optimization, 25, 1987, pp. 815–844.MathSciNetzbMATHCrossRefGoogle Scholar
  3. [3]
    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
  4. [4]
    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
  5. [5]
    Perkins, W. R. and Medanic, J. V., “Systematic Low Order Controller Design for Disturbance Rejection with Plant Uncertainties,” Report #WRDC-TR-90-3036, Wright-Patterson AFB, U.S.A., 1990.Google Scholar
  6. [6]
    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
  7. [7]
    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
  8. [8]
    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
  9. [9]
    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
  10. [10]
    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
  11. [11]
    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
  12. [12]
    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
  13. [13]
    Tadmor, G., “Worst-case design in the time domain: the maximum principle and the standard H∞ problem,” Mathematics of Control, Signals, and Systems, 3, 1990, pp. 301–324.MathSciNetzbMATHCrossRefGoogle 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