Pursuit and Evasion Differential Games of Many Pursuers and one evader of coordinate –wise with Integral Constraints

Name: Wong Dai DiMatrix: GS37725

Supervisor: Associate Professor Ibragimov Gafurjan

a. Introduction•The pursuers wish to catch evader, while evader want to avoid the capture.

b. Objective/Statement of Problem•To study pursuit and evasion of a game in a plane.

c. Background•First, we need to construct strategies of pursuers and evader by using controls of the evader and pursuers with time lag.•Second, the strategies have to be shown as admissible.•Finally, we show that pursuit can be completed or evasion is possible.

d. Importance of research•They are applicable to economics, military task and other areas.

•One airplane pursuing another airplane.

e. Library Research1.A. Y. Azimov, “A linear differential evasion game with integral constraints on the controls,” USSR

Computational Mathematics and Mathematical Physics, vol. 14, no. 6, pp. 56–65, 1974.

2.A. A. Azamov and B. Samatov, π-Strategy. An Elementary Introduction to the Theory of Differential

Games, NUU press, Tashkent, Uzbekistan, 2000.

3.G. I. Ibragimov and R. M. Hasim, “Pursuit and evasion differential games in Hilbert space,”

International Game Theory Review, vol. 12, no. 3, pp. 239–251, 2010.

4.G. I. Ibragimov, A. A. Azamov, and M. Khakestari, “Solution of a linear pursuit-evasion game with

integral constraints,” ANZIAM Journal, vol. 52, pp. E59–E75, 2010.

5.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. 505–511, 2012.

6.P. B. Gusiatnikov and E. Z. Mohon’ko, “On 1∞-escape in a linear many-person differential game

with integral constraints,” Journal of Applied Mathematics and Mechanics, vol. 44, no. 4, pp. 436–

440, 1980.

f. Research Scope/Outline of Research1.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.

2.Literature review of related work in this area.

3.Study control and trajectory of an object called P-Strategy.

4.Investigate a pursuit-evasion differential game of one pursuer and one evader with

integral constraint.

5.Investigate a pursuit-evasion differential game of many pursuers and one evader with

integral constraint.

6.Investigate a pursuit-evasion differential game of many pursuers and many evaders

with integral constraint.

7.General conclusion and ideas of future research

g. Methodology and Proposed Schedule of Work

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