Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-13T05:40:38.156Z Has data issue: false hasContentIssue false
  • English
  • Français

Simultaneous communication and control

Published online by Cambridge University Press:  01 July 2016

P. Whittle  and
J. F. Rudge
P. Whittle
Affiliation:
University of Cambridge
J. F. Rudge
Affiliation:
University of Cambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

A dynamic co-operative two-person game with imperfect information is considered, in which the conflicting aspects of an optimal policy (choice of actions to minimise ‘own cost’, and choice of actions to optimise communication of information) can to a large extent be decoupled and solved separately. In deriving a strategy which is asymptotically optimal (in a sense explained) we derive formulae for the capacity of a vector Gaussian channel and the rate-distortion of a vector Gaussian source.

It is shown that the optimal strategy is in general non-linear in observables, but a numerical example shows that, at least in one rather special but non-trivial case, the best linear strategy may be very nearly optimal. This conclusion is made explicit by the analysis of Section 7.

Keywords

TEAM GAMECOMMUNICATIONLOG PROBLEMS
Type
Research Article
Information
Advances in Applied Probability , Volume 8 , Issue 2 , June 1976 , pp. 365 - 384
Copyright
Copyright © Applied Probability Trust 1976 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aoki, M. (1967) Optimisation of Stochastic Systems. Academic Press, New York.Google Scholar
Berger, A. (1971) Rate Distortion Theory. Prentice-Hall, Princeton, N. J. Google Scholar
Brandenburg, L. H. and Wyner, A. D. (1974) Capacity of the Gaussian channel with memory: the multivariate case. Bell Syst. Tech. J. 53, 745–778.Google Scholar
Gallagher, R. G. (1968) Information Theory and Reliable Communication. Wiley, New York.Google Scholar
Ho, Y. C. and Chu, K. C. (1972) Team decision theory and information structures in optimal control problems — Part I. I.E.E.E. Trans. Automatic Control AC–17, 15–22.Google Scholar
Pinsker, M. S. (1964) Information and Information Stability of Random Variables and Processes. Holden-Day, San Francisco.Google Scholar
Shannon, C. E. (1957) Certain results in coding theory for noisy channels. Information and Control 1, 6–25.CrossRefGoogle Scholar
Tsybakov, B. S. (1969) Linear information coding. Radio Engrg. Electron. Phys. 7, 22–33.Google Scholar
Witsenhausen, H. (1968) A counterexample in stochastic optimum control. SIAM J. Control 6, 131–146.Google Scholar