Evasion Differential Game of Many Evaders and Many Pursuers with Integral Constraints

Name: Wong Dai Di

a. IntroductionThe pursuers wish to catch evaders, while evaders want to avoid the capture.

b. Objective/Statement of ProblemTo study evasion of a game in a plane. The result will be extended to .

c. BackgroundFirst, we need to construct strategies of evaders by using controls of the pursuers with time lag.Second, the strategies have to be shown as admissible.Finally, we show that evasion is possible.

d. Importance of researchThey are applicable to economics, military task and other areas.

One airplane pursuing another airplane.

e. Library ResearchA. Y. Azimov, A linear differential evasion game with integral constraints on the controls, USSR Computational Mathematics and Mathematical Physics, vol. 14, no. 6, pp. 5665, 1974.A. A. Azamov and B. Samatov, -Strategy. An Elementary Introduction to the Theory of Differential Games, NUU press, Tashkent, Uzbekistan, 2000.G. I. Ibragimov and R. M. Hasim, Pursuit and evasion differential games in Hilbert space, International Game Theory Review, vol. 12, no. 3, pp. 239251, 2010.G. I. Ibragimov, A. A. Azamov, and M. Khakestari, Solution of a linear pursuit-evasion game with integral constraints, ANZIAM Journal, vol. 52, pp. E59E75, 2010.G. I. Ibragimov, M. Salimi, andM. Amini, Evasion from many pursuers in simple motion differential game with integral constraints, European Journal of Operational Research, vol. 218, no. 2, pp. 505511, 2012.P. B. Gusiatnikov and E. Z. Mohonko, On 1-escape in a linear many-person differential game with integral constraints, Journal of Applied Mathematics and Mechanics, vol. 44, no. 4, pp. 436440, 1980.

g. Methodology and Proposed Schedule of Work

h. Contribution of Research to the NationThis research is important to the nation such as for military strategy, economy, technology efficiency and others.

f. Research Scope/Outline of Research

Introduction to differential game problems. Here we present lion and man game problem and construct strategy for the evader which guarantees evasion from the pursuer. Literature review of related work in this area. Study control and trajectory of an object called P-Strategy.Investigate a pursuit-evasion differential game of one pursuer and one evader with integral constraint.Investigate a pursuit-evasion differential game of many pursuers and one evader with integral constraint.Investigate a pursuit-evasion differential game of many pursuers and many evaders with integral constraint.General conclusion and ideas of future research