Abstract
Four stochastic pursuit-evasion differential games involving two players, P and E, moving in the plane are considered. The difference between the games lies in their information structures. In each of the games, sufficient conditions on optimal feedback strategies, in the cases of complete information, and on weak optimal feedback strategies, in the cases of incomplete information, are derived. Optimal strategies are computed for the cases of complete information and weak suboptimal strategies for the cases of incomplete information. The results indicate that the correct measurement of the direction of the segment PE is more important than the measurement of the distance (P, E).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Pachter, M., andYavin, Y.,Simple-Motion Pursuit-Evasion Differential Games in the Plane, National Research Institute for Mathematical Sciences, Pretoria, South Africa, Technical Report TWISK 336.
Stroock, D. W., andVaradhan, S. R. S.,Diffusion Processes with Continuous Coefficients, Communications on Pure and Applied Mathematics, Vol. 22, pp. 345–400 and Vol. 22, pp. 479–530, 1969.
Pachter, M., andYavin, Y.,A Stochastic Homicidal Chaueffeur Pursuit-Evasion Differential Game, Journal of Optimization Theory and Applications, Vol. 34, pp. 405–424, 1981.
Friedman, M., andYavin, Y.,Computation of Optimal Controls for a Nonlinear Stochastic Third-Order System, Journal of Optimization Theory and Applications, Vol. 21, pp. 213–223, 1977.
Huisman, W. C., andYavin, Y.,Numerical Studies of the Performance of an Optimally Controlled Nonlinear Stochastic Oscillator, Computer Methods in Applied Mechanics and Engineering, Vol. 21, pp. 171–191, 1980.
Kumar, P. R.,A Differential Game with Jump Process Observations, Journal of Optimization Theory and Applications, Vol. 31, pp. 219–231, 1980.
Kumar, P. R., andVan Schuppen, J. H.,On Nash Equilibrium Solutions in Stochastic Dynamic Games, IEEE Transactions on Automatic Control, Vol. AC-25, pp. 1146–1149, 1980.
Basar, T.,On the Saddle-Point Solution of a Class of Stochastic Differential Games, Journal of Optimization Theory and Applications, Vol. 33, pp. 539–556, 1981.
Bagchi, A., andOlsder, G. J.,Linear-Quadratic Stochastic Pursuit-Evasion Games, Applied Mathematics and Optimization, Vol. 7, pp. 95–123, 1981.
Yavin, Y.,Feedback Strategies for Partially Observable Stochastic Systems, Springer-Verlag, Berlin, Germany, 1983.
Fagerlund, S.,Target Tracking Based on Bearing Only Measurements, MIT, Laboratory for Information and Decision Systems, Cambridge, Massachusetts, Technical Report No. LIDS-R-1003, 1980.
Liu, P. T., andBongiovanni, P. L.,On a Passive Vehicles Tracking Problem and Max-Minimization, IEEE Transactions on Automatic Control, Vol. AC-28, pp. 233–235, 1983.
Stroock, D. W., andVaradhan, S. R. S.,Multidimensional Diffusion Processes, Springer-Verlag, New York, New York, 1979.
Author information
Authors and Affiliations
Additional information
Communicated by G. Leitmann
Rights and permissions
About this article
Cite this article
Yavin, Y. Stochastic pursuit-evasion differential games in the plane. J Optim Theory Appl 50, 495–523 (1986). https://doi.org/10.1007/BF00938634
Issue Date:
DOI: https://doi.org/10.1007/BF00938634