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Optimal infinite-horizon feedback laws for a general class of constrained discrete-time systems: Stability and moving-horizon approximations

  • S. S. Keerthi
  • E. G. Gilbert
Contributed Papers

Abstract

Stability results are given for a class of feedback systems arising from the regulation of time-varying discrete-time systems using optimal infinite-horizon and moving-horizon feedback laws. The class is characterized by joint constraints on the state and the control, a general nonlinear cost function and nonlinear equations of motion possessing two special properties. It is shown that weak conditions on the cost function and the constraints are sufficient to guarantee uniform asymptotic stability of both the optimal infinite-horizon and moving-horizon feedback systems. The infinite-horizon cost associated with the moving-horizon feedback law approaches the optimal infinite-horizon cost as the moving horizon is extended.

Key Words

Discrete-time systems infinite-horizon optimal control moving-horizon control state-control constraints nonquadratic cost functions stability 

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References

  1. 1.
    Bertsekas, D. P.,Dynamic Programming and Stochastic Optimal Control, Academic Press, New York, New York, 1976.Google Scholar
  2. 2.
    Kwakernaak, H., andSivan, R.,Linear Optimal Control Systems, Wiley-Interscience, New York, New York, 1972.Google Scholar
  3. 3.
    Kleinman, D. L.,An Easy Way to Stabilize a Linear Constant System, IEEE Transactions on Automatic Control, Vol. AC-15, p. 692, 1970.Google Scholar
  4. 4.
    Thomas, Y., andBarraud, A.,Commande Optimale à Horizon Fuyant, Revue RAIRO, Vol. J1, pp. 126–140, 1974.Google Scholar
  5. 5.
    Thomas, Y. A.,Linear Quadratic Optimal Estimation and Control with Receding Horizon, Electronics Letters, Vol. 11, pp. 19–21, 1975.Google Scholar
  6. 6.
    Kwon, W. H., andPearson, A. E.,A Modified Quadratic Cost Problem and Feedback Stabilization of a Linear System, IEEE Transactions on Automatic Control, Vol. AC-22, pp. 838–842, 1977.Google Scholar
  7. 7.
    Kwon, W. H., andPearson, A. E.,On Feedback Stabilization of Time-Varying Discrete Linear Systems, IEEE Transactions on Automatic Control, Vol. AC-23, pp. 479–481, 1978.Google Scholar
  8. 8.
    Kwon, W. H., Bruckstein, A. M., andKailath, T.,Stabilizing State-Feedback Design via the Moving Horizon Method, International Journal of Control, Vol. 37, pp. 631–643, 1983.Google Scholar
  9. 9.
    Keerthi, S. S., andGilbert, E. G.,Moving-Horizon Approximations for a General Class of Optimal Nonlinear Infinite-Horizon Discrete-Time Systems, Conference on Information Sciences and Systems, Princeton, New Jersey, 1986.Google Scholar
  10. 10.
    Keerthi, S. S.,Optimal Feedback Control of Discrete-Time Systems with State-Control Constraints and General Cost Functions, PhD Dissertation, University of Michigan, Ann Arbor, Michigan, 1986.Google Scholar
  11. 11.
    Knudsen, J. K. H.,Time-Optimal Computer Control of a Pilot Plant Evaporator, Proceedings of the 6th IFAC World Congress, Part 2, pp. 4531–4536, 1975.Google Scholar
  12. 12.
    DeVlieger, J. H., Verbruggen, H. B., andBruijn, P. M.,A Time-Optimal Control Algorithm for Digital Computer Control, Automatica, Vol. 18, pp. 239–244, 1982.Google Scholar
  13. 13.
    Gutman, P. O.,On-Line Use of a Linear Programming Controller, IFAC Software for Computer Control, Madrid, Spain, pp. 313–318, 1982.Google Scholar
  14. 14.
    Willems, J. L.,Stability Theory of Dynamical Systems, Thomas Nelson and Sons, London, England, 1970.Google Scholar
  15. 15.
    Kalman, R. E., andBertram, J. E.,Control System Analysis and Design via the Second Method of Lyapunov, II: Discrete-Time Systems, Transactions of the ASME, Journal of Basic Engineering, Vol. 82, pp. 394–400, 1960.Google Scholar
  16. 16.
    Keerthi, S. S., andGilbert, E. G.,An Existence Theorem for Discrete-Time Infinite-Horizon Optimal Control Problems, IEEE Transactions on Automatic Control, Vol. AC-30, pp. 907–909, 1985.Google Scholar
  17. 17.
    Keerthi, S. S., andGilbert, E. G.,Optimal Infinite-Horizon Control and the Stabilization of Discrete-Time Systems: State-Control Constraints and Nonquadratic Cost Functions, IEEE Transactions on Automatic Control, Vol. AC-31, pp. 264–266, 1986.Google Scholar
  18. 18.
    Hwang, W. G., andSchmitendorf, W. E.,Controllability Results for Systems with a Nonconvex Target, IEEE Transactions on Automatic Control, Vol. AC-29, pp. 794–802, 1984.Google Scholar
  19. 19.
    Barrodale, I., andRoberts, F. D. K.,Solution of the Constrained l 1 Linear Approximation Problem, ACM Transactions on Mathematical Software, Vol. 6, pp. 231–235, 1980.Google Scholar
  20. 20.
    Lawson, C. L., andHanson, R. J.,Solving Least Squares Problems. Prentice-Hall, Englewood Cliffs, New Jersey, 1974.Google Scholar
  21. 21.
    Gutman, P. O., andHagander, P.,A New Design of Constrained Controllers for Linear Systems, IEEE Transactions on Automatic Control, Vol. AC-30, pp. 22–33, 1985.Google Scholar

Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • S. S. Keerthi
    • 1
  • E. G. Gilbert
    • 2
  1. 1.School of AutomationIndian Institute of ScienceBangaloreIndia
  2. 2.Department of Aerospace EngineeringUniversity of MichiganAnn Arbor

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