Abstract
A generalization of L.S.Pontryagin’s test example from the theory of differential games is considered. The study is based on Pontryagin’s first direct method, which was developed for the constructive solution of linear pursuit–evasion differential games of kind.
Similar content being viewed by others
References
L. S. Pontryagin, “On the theory of differential games,” Russ. Math. Surv. 21 (4), 193–246 (1966).
L. S. Pontryagin and E. F. Mishchenko, “Linear differential games,” Dokl. AN SSSR 174 (1), 27–29 (1967).
L. S. Pontryagin, “On linear differential games. I,” Dokl. AN SSSR 174 (6), 1278–1280 (1967).
L. S. Pontryagin, “On linear differential games. II,” Dokl. AN SSSR 175 (4), 764–766 (1967).
L. S. Pontryagin, “Linear differential games of pursuit,” Math. USSR Sb. 40 (3), 285–303 (1981).
L. S. Pontryagin, “A linear differential evasion game,” Proc. Steklov Inst. Math. 112, 27–60 (1971).
M. S. Nikol’skii, Pontryagin’s First Direct Method in Differential Games (Izd. Mosk. Gos. Univ., Moscow, 1984) [in Russian].
R. Isaacs, Differential Games (Wiley, New York, 1965; Mir, Moscow, 1967).
B. N. Pshenichnyi, “Linear differential games,” Automat. Remote Control, No. 1, 55–67 (1968).
N. N. Krasovskii and A. I. Subbotin, Positional Differential Games (Nauka, Moscow, 1974) [in Russian].
V. I. Blagodatskikh, Introduction to Optimal Control: Linear Theory (Vyssh. Shkola, Moscow, 2001) [in Russian].
F. R. Gantmakher, The Theory of Matrices ((Fizmatlit, Moscow, 2004) [in Russian].
V. I. Arnold, Ordinary Differential Equations (Izd. Udmurt. Gos. Univ., Izhevsk, 2000) [in Russian].
A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis (Nauka, Moscow, 1976; Dover, New York, 1999).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © M.S. Nikol’skii, 2016, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2016, Vol. 22, No. 2.
Rights and permissions
About this article
Cite this article
Nikol’skii, M.S. A Study of the Generalized Pontryagin Test Example from the Theory of Differential Games. Proc. Steklov Inst. Math. 299 (Suppl 1), 158–164 (2017). https://doi.org/10.1134/S0081543817090188
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0081543817090188