Estimation of a Guaranteed Result in Nonlinear Differential Games of Encounter
A nonlinear differential game of encounter is considered. Estimation of the function of a guaranteed result (u — stable function) is proposed. The problem is considered in the framework of formalization [1, 2].
The paper is related to the works done in [3–16]. It is assumed that Hamiltonians of initial (nonlinear) and auxiliary systems are connected by special relationships. Unlike [11,12], in this paper the u-stable function for the auxiliary system is nondifferentiable. Conditions imposed on the connection between Hamiltonians of initial and auxiliary systems are not so severe as they were in .
An example, where the function of the guaranteed result is constructed by means of proposed approach is given.
KeywordsViscosity Solution Lipschitz Condition Differential Game Auxiliary System Guarantee Result
Unable to display preview. Download preview PDF.
- Subbotin, A.I., Chentzov, A.G. Optimization of A Guaranteed Result in Control Problems. Moscow, Nauka, 1981, 287 pp. (in Russian)Google Scholar
- Subbotin, A.I., Taras’yev, A.M. Conjugate Derivatives of the Payoff Function of a Differential Game. Dokl. Akad. Nauk SSSR, 283, no. 3, pp. 559–564, 1985 (in Russian).Google Scholar
- Subbotin, A.I., Taras’yev, A.M. Stability properties of the value function of a differential game and viscosity solution of Hamilton—Jacobi equations. Probl. Control and Inform. Theory, vol. 15, no 6, pp. 451463, 1986.Google Scholar
- Barron, E.N., Evans, L.C., Yentsen, R. Viscosity solution of Isaacs equations and differential games with Lipschitz controls. J. Different. Equat., vol. 53, no. 2, pp. 213–233, 1984.Google Scholar
- Krasovskii, N.N. Differential games. Approximation and formal models. Mathematicheskii Sbornik, vol. 107, no. 4, pp. 541–571, 1978 (in Russian).Google Scholar
- Pontryagin, L.S. Linear differential pursuit game. Math.sb., vol. 112, no. 3, pp. 307–330, 1980 (in Russian).Google Scholar
- Isaacs, R. Differential Games. New York, John Wiley and Sons, 479 pp., 1965.Google Scholar
- Pashkov, A.G. On the sufficient condition for nonlinear positional games of encounter. PMM, 40, 1, pp. 168–171, 1976.Google Scholar
- Pashkov, A.G. On an approach to solving certain nonlinear positional differential games. Izv. Akad. Nauk SSSR, Tekhn.Kibernetika, 1, pp. 17–22, 1979.Google Scholar
- Pashkov, A.G. Comparison of the solutions of linear and nonlinear positional differential games of encounter. PMM, 50, 4, pp. 551–560, 1986.Google Scholar
- Levchenkov, A.Yu., Pashkov, A.G., A Game of optimal approach with two inertial pursuers and a noninertial evader. PMM, 49, 4, pp. 536547, 1985.Google Scholar
- Pashkov, A.G., Terekhov, S.D. Differential approach game involving two dynamic objects and a third. Izv. AN SSSR, MTT, vol. 21, no. 3, pp. 66–71, 1986.Google Scholar
- Pashkov, A.G., Terekhov, S.D. A differential game of approach with two pursuers and one evader. J. Optimiz. Theory and Applic., vol. 55, no. 2, pp. 303–311, 1987.Google Scholar