Guaranteed Result in Differential Games with Terminal Payoff
We suggest a method of solving differential games with terminal payoff. The method consists of applying Fenchel-Moreau  duality ideas to the general scheme of the Resolving Functions method . The gist of the suggested method is presentation of the Resolving Function by means of the function conjugate to the payoff, and employing of involutory property of the conjugation operator for closed convex functions to obtain guarantee estimation of terminal value of the payoff. This estimation can be represented by the initial payoff value and Resolving Function integral. This paper involves the ideas of , adjoins [3–9] and turns out to be a new aspect of Convex Analysis application to differential games.
Unable to display preview. Download preview PDF.
- Rockafellar R. T. Convex Analysis. Princeton University Press, 1970.Google Scholar
- Chikrii A. A. Conflict-controlled processes. Naukova Dumka, Kiev, 1992. (in Russian).Google Scholar
- Pshenichnii B. N., Chikrii A. A., and Rappoport J. S. An efficient method of solving differential games with many pursuers. Dokl. Acad. Nauk SSSR, 256 (3): 530–535, 1981.Google Scholar
- Pshenichnii B. N., Chikrii A. A., and Rappoport J. S. Pursuit by several controlled objects in the presence of phase constraints. Dokl. Acad. Nauk SSSR, 259 (4). 138–141, 1981.Google Scholar
- Pshenichnii B. N., Chikrii A. A., and Rappoport J. S. Group pursuit in differential games. Technische Hochschule Leipzig, 6: 13–27, 1982.Google Scholar
- Pontryagin L. S. Selected scientific works, volume 2. Nauka, Moscow, 1988. (in Russian).Google Scholar
- Pshenichnii B. N. Convex Analysis and Extremal Problems. Nauka, Moscow, 1974. (in Russian).Google Scholar