Mathematical systems theory

, Volume 7, Issue 1, pp 5–11 | Cite as

A standard form for sequential stochastic control

  • H. S. Witsenhausen


Causal discrete-time stochastic control problems with nonclassical information patterns are not necessarily sequential in the sense that the order of the various control actions is fixed in advance. When this sequential condition does hold, then they can be reduced to a (theoretical) standard form which enables the establishment of a maximum principle, a reachable set concept and dynamic programming, all in a straightforward and transparent way.


Control Problem Computational Mathematic Dynamic Programming Control Action Maximum Principle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    P. R. Halmos,Measure Theory, Van Nostrand, Princeton, 1950.Google Scholar
  2. [2]
    H. Hermes andJ. P. LaSalle,Functional Analysis and Time Optimal Control, Academic Press, New York, 1969.Google Scholar
  3. [3]
    H. S. Witsenhausen, On information structures, feedback and causality,SIAM J. Control 9 (1971), 149–160.Google Scholar
  4. [4]
    H. S. Witsenhausen, Separation of estimation and control for discrete-time systems,Proc. IEEE,59 (1971), 1557–1566.Google Scholar
  5. [5]
    R. Bellman,Dynamic Programming, Princeton Univ. Press, Princeton, N.J., 1957.Google Scholar
  6. [6]
    L. Hormander, Sur la fonction d'appui des ensembles convexes dans un espace localement convexe,Arkiv Mat. 3 (1954), 181–186.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1973

Authors and Affiliations

  • H. S. Witsenhausen
    • 1
  1. 1.Bell Telephone LaboratoriesMurray HillUSA

Personalised recommendations