Skip to main content
Log in

A finite-state, finite-memory minimum principle

  • Contributed Papers
  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

A class of finite-state, finite-memory stochastic control problems is considered. A minimum principle is derived. Signaling strategies are defined and related to the necessary conditions of the minimum principle. Min-H algorithms for the problem are described.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Sandell, N. R. Jr.,Control of Finite-State, Finite-Memory Stochastic Systems, Massachusetts Institute of Technology, PhD Thesis, 1974.

  2. Sandell, N. R., Jr., andAthans, M.,Control of Finite-State, Finite-Memory Stochastic Systems, Princeton Conference on Information Sciences, Princeton, New Jersey, 1974.

  3. Witsenhausen, H. S.,A Standard Form for Sequential Stochastic Control, Mathematical Systems Theory, Vol. 7, No. 1, 1973.

  4. Mullis, C. T., andRoberts, R. A.,Finite-Memory Problems and Algorithms, IEEE Transactions on Information Theory, Vol. IT-20, No. 4, 1974.

  5. Kashyap, R. L.,Optimization of Stochastic Finite State Systems, IEEE Transactions on Automatic Control, Vol. AC-11, No. 4, 1966.

  6. Kuhn, H. W.,Extensive Games and the Problem of Information., Contributions to the Theory of Games II, Princeton University Press, Princeton, New Jersey, 1953.

    Google Scholar 

  7. Halmos, P. R.,Measure Theory. D. Van Nostrand Company, New York, New York, 1950.

    Google Scholar 

  8. Thompson, G. L.,Signalling Strategies in n-Person Games, Contributions to the Theory of Game II, Princeton University Press, Princeton, New Jersey, 1953.

    Google Scholar 

  9. Witsenhausen, H. S.,On Information Structures, Feedback and Causality, SIAM Journal on Control, Vol. 9, No. 2, 1971.

  10. Aoki, M.,Optimization of Stochastic Systems, Academic Press, New York, New York, 1967.

    Google Scholar 

  11. Astrom, K. J.,Optimal Control of Markov Processes with Incomplete State Information, Journal of Mathematical Analysis and Applications, Vol. 10, No. 1, 1965.

  12. Striebel, C. T.,Sufficient Statistics in the Optimum Control of Stochastic Systems, Journal of Mathematical Analysis and Applications, Vol. 12, No. 3, 1965.

  13. Sandell, N. R., Jr., andAthans, M.,Solution of Some Non-Classical LQG Stochastic Decision Problems, IEEE Transactions on Automatic Control, Vol. AC-19, No. 2, 1974.

  14. Kelley, H. J.,Method of Gradients, Optimization Techniques, Edited by G. Leitmann, Academic Press, New York, New York, 1962.

    Google Scholar 

  15. Platzman, L. K.,On the Iterative Design of Optimal and Suboptimal Controllers, Massachusetts Institute of Technology, MS Thesis, 1973.

  16. Witsenhausen, H. S.,A Counterexample in Stochastic Optimal Control, SIAM Journal on Control, Vol. 6, No. 1, 1968.

  17. Ho, Y. C., andChu, K. C.,Team Decision Theory and Information Structures in Optimal Control Problems—Part I, IEEE Transactions on Automatic Control, Vol. AC-17, No. 1, 1972.

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by P. Varaiya

This research has been conducted in the MIT Electronic Systems Laboratory with support from AFOSR Grant No. 72-2273, NASA/AMES Grant No. NGL-22-009(124), and NSF Grant No. GK-25781.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sandell, N.R., Athans, M. A finite-state, finite-memory minimum principle. J Optim Theory Appl 25, 289–305 (1978). https://doi.org/10.1007/BF00933218

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00933218

Key Words

Navigation