Abstract
A solution of a pursuit-evasion problem is obtained for two controlled moving points for the case where the coordinates of the evader are measured with bounded errors and the controls chosen by the evader are assumed to be known up to their membership in a given compact set. Moreover, the conditions of a guaranteed solution of the pursuit-evasion problem are obtained for the worst values of measurement errors and controls of the evader.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
L. S. Pontryagin and N. M. Mishchenko, “A linear differential game of pursuit (an analytical theory),” Mat. Sb., 13 No. 2, 131-158 (1986).
N. N. Krasovskii and A. I. Subbotin, Positional Differential Games [in Russian], Nauka, Moscow (1974).
N. N. Krasovskii and A.I. Subbotin, Game-Theoretical Control Problems, Springer-Verlag, New York (1988).
B. N. Pshenichnyi and V. V. Ostapenko, Differential Games [in Russian], Naukova Dumka, Kiev (1992).
G. J. Olsder (ed.), New Trends in Dynamic Games and Applications, Birkhäuser, Boston–Basel–Berlin (1995).
G. Olsder, P. Hagedorn, and H. Knobloch (ed.), Differential Games and Applications, Springer-Verlag, Berlin (1977).
N. N. Krasovskii, Control over a Dynamic System [in Russian], Nauka, Moscow (1974).
L. S. Pontryagin, Selected Scientific Works [in Russian], Nauka, Moscow (1988).
A. Friedman, Differential Games, Wiley, New York (1971).
O. Hajek, Pursuit Games, Acad. Press, New York (1975).
A. A. Chikrii, Conflict-Controlled Processes [in Russian], Naukova Dumka, Kiev (1992).
A. A. Chikrii, Conflict-Controlled Processes, Kluwer, Boston–London–Dordrecht (1997).
V. M. Kuntsevich and B. N. Pshenichnyi, “Solution of a class of pursuit and evasion problems under uncertainty,” Kibern. Sist. Anal., No. 3, 63-70 (1995).
V. M. Kuntsevich and B. N. Pshenichnyi, “Minimal invariant sets of dynamic systems with additive bounded disturbances,” Kibern. Sist. Anal., No. 1, 74-81 (1996).
V. M. Kuntsevich and B. N. Pshenichnyi, “Analysis of some classes of nonlinear discrete systems under bounded disturbances,” in: Proc. 4th IFAC Symp. on Nonlinear Control Systems Design, 1 (1998), pp. 275-280.
A. V. Kuntsevich, “Analysis and synthesis of discrete control systems under conditions of nonstochastic uncertainty,” Kibern. Sist. Anal., No. 6, 50-56 (1998).
V. M. Kuntsevich and A. V. Kuntsevich, “Analysis and synthesis of optimal and robustly optimal control systems under bounded disturbances,” in: Proc. 14th IFAC World Congress (Beijing, 1999), Vol. F: Nonlinear Systems I (1999), pp. 163-168.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kuntsevich, V.M., Kuntsevich, A.V. Optimal Control over the Approach of Conflicting Moving Objects under Uncertainty. Cybernetics and Systems Analysis 38, 230–237 (2002). https://doi.org/10.1023/A:1016395429276
Issue Date:
DOI: https://doi.org/10.1023/A:1016395429276