Abstract
This paper deals with a linear-quadratic-Gaussian zero-sum game in which one player has delayed and noisy information and the other has perfect information. Assuming that the player with perfect information can deduce his opponent's state estimate, the optimal closed-loop control laws are derived. Then, it is shown that the separation theorem is satisfied for the player with imperfect information and his optimal state estimate is given by a delay-differential equation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Witsenhausen, H. S.,On Information Structures, Feedback, and Causality, SIAM Journal on Control, Vol. 9, No. 2, 1971.
Witsenhausen, H. S.,Separation of Estimation and Control for Discrete Time System, Proceedings of the IEEE, Vol. 59, No. 11, 1971.
Behn, R. D., andHo, Y. C.,On a Class of Linear Stochastic Differential Games, IEEE Transactions on Automatic Control, Vol. AC-13, No. 3, 1968.
Rhodes, I. B., andLuenberger, D. G.,Differential Games with Imperfect State Information, IEEE Transactions on Automatic Control, Vol. AC-14, No. 1, 1969.
Rhodes, I. B., andLuenberger, D. G.,Stochastic Differential Games with Constrained State Estimators, IEEE Transactions on Automatic Control, Vol. AC-14, No. 5, 1969.
Willman, W. W.,Formal Solutions for a Class of Stochastic Pursuit-Evasion Games, IEEE Transactions on Automatic Control, Vol. AC-14, No. 5, 1969.
Ciletti, M. D.,Results in the Theory of Linear Differential Games with an Information Lag, Journal of Optimization Theory and Applications, Vol. 5, No. 5, 1970.
Gikhman, I. I., andSkorokhod, A. V.,Introduction to the Theory of Random Processes, W. B. Saunders Company, Philadelphia, Pennsylvania, 1969.
Striebel, C.,Sufficient Statistics in the Optimum Control of Stochastic Systems, Journal of Mathematical Analysis and Applications, Vol. 12, No. 3, 1965.
Dynkin, E. B.,Markov Processes, Academic Press, New York, New York, 1965.
Wonham, W. M.,On the Separation Theorem of Stochastic Control, SIAM Journal on Control, Vol. 6, No. 2, 1968.
Ho, Y. C., Bryson, A. E., andBaron, S.,Differential Games and Optimal Pursuit-Evasion Strategies, IEEE Transactions on Automatic Control, Vol. AC-10, No. 4, 1965.
Author information
Authors and Affiliations
Additional information
Communicated by G. Leitmann
Rights and permissions
About this article
Cite this article
Mori, K., Shimemura, E. Linear differential games with delayed and noisy information. J Optim Theory Appl 13, 275–289 (1974). https://doi.org/10.1007/BF00934865
Issue Date:
DOI: https://doi.org/10.1007/BF00934865