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

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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.

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References

  1. Bertsekas, D. P.,Dynamic Programming and Stochastic Optimal Control, Academic Press, New York, New York, 1976.

    Google Scholar 

  2. Kwakernaak, H., andSivan, R.,Linear Optimal Control Systems, Wiley-Interscience, New York, New York, 1972.

    Google Scholar 

  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. Thomas, Y., andBarraud, A.,Commande Optimale à Horizon Fuyant, Revue RAIRO, Vol. J1, pp. 126–140, 1974.

    Google Scholar 

  5. Thomas, Y. A.,Linear Quadratic Optimal Estimation and Control with Receding Horizon, Electronics Letters, Vol. 11, pp. 19–21, 1975.

    Google Scholar 

  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. 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. 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. 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.

  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. 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.

  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. 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. Willems, J. L.,Stability Theory of Dynamical Systems, Thomas Nelson and Sons, London, England, 1970.

    Google Scholar 

  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. 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. 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. 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. 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. Lawson, C. L., andHanson, R. J.,Solving Least Squares Problems. Prentice-Hall, Englewood Cliffs, New Jersey, 1974.

    Google Scholar 

  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 

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Authors and Affiliations

  1. School of Automation, Indian Institute of Science, Bangalore, India

    S. S. Keerthi (Assistant Professor)

  2. Department of Aerospace Engineering, University of Michigan, Ann Arbor, Michigan

    E. G. Gilbert (Professor)

Authors
  1. S. S. Keerthi
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  2. E. G. Gilbert
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Communicated by J. L. Speyer

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Keerthi, S.S., Gilbert, E.G. Optimal infinite-horizon feedback laws for a general class of constrained discrete-time systems: Stability and moving-horizon approximations. J Optim Theory Appl 57, 265–293 (1988). https://doi.org/10.1007/BF00938540

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  • DOI: https://doi.org/10.1007/BF00938540

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