A Design of Strategies in Alternative Pursuit Games

Authors

  • Igor Shevchenko TINRO-Center; Far East Federal University
  • Dusan M. Stipanovic University of Illinois at Urbana-Champaign

Abstract

In this work we consider the games where  P can terminate pursuit at will on any of two terminal manifolds. If the optimal feedback strategies for every variant of termination are known, an obvious pursuit strategy assigns the control that corresponds to the alternative with less value at every state. On the manifold with equal alternative values, this strategy may become discontinuous even when the value functions themselves are smooth. We describe smooth approximations for the minimum functions that allow to construct smooth alternative strategies and to deal with generalized solutions for differential equations with discontinuous right-hand sides. However, as shown by an example, the state may stay on a equivalued manifold and the game never terminates.

Keywords:

approximations of minimum and maximum functions, alternative pursuit, generalized solutions for differential equations with discontinuous right-hand sides

Downloads

Download data is not yet available.

References

Bernhard, P. (1977). Singular Surfaces in Differential Games: An Introduction. In Differential Games and Applications. Springer Lecture Notes in Information and Control Sciences (Hargedorn P., H.W. Knobloch and G.H. Olsder, eds), Berlin: Springer, Vol. 3, 1–33.

Breakwell, J.V. and P. Hagedorn (1979). Point Capture of Two Evaders in Succession. JOTA, 27 (1), 90–97.

Filippov, A. F. (1988). Differential Equations with Discontinuous Righthand Sides. Kluwer: Dordrecht.

Isaacs, R. (1967). Differential Games. John Wiley: New York.

Isbell, J.R. (1967). Pursuit Around a Hole. Naval Research Quarterly, Vol. 14, 569–571.

Krasovskii, N.N. and A. I. Subbotin (1988). Game-Theoretical Control Problems. Springer-Verlag: New York.

Shevchenko, I. (2009). Strategies for Alternative Pursuit Games. Advances in Dynamic Games Theory and Their Applications: Analytical and Numerical Developments. (Bernhard P., V. Gaitsgory and O. Pourtallier eds.) (Annals of the International Society of Dynamic Games, Vol. 10. Birkh¨auser, 121–131.

Shevchenko, I. (2012). Locally Optimizing Strategies for Approaching the Furthest Evader, Contributions to Game Theory & Management, Vol. 5, 293-303.

Shevchenko, I. (2014). Guaranteed strategies with memory for alternative pursuit, Automation and Remote Control, 75(10), 1861–1868.

Stipanovi´c, D.M., A. Melikyan and N. Hovakimyan (2009). Some Sufficient Conditions for Multi-Player Pursuit-Evasion Games with Continuous and Discrete Observations, Annals of the International Society of Dynamic Games, Vol. 10, 1-13.

Stipanovi´c, D.M., A. Melikyan and N. Hovakimyan (2010). Guaranteed strategies for non-linear multi-player pursuit-evasion games, International Game Theory Review, 12(1), 1–17.

Stipanovi´c, D.M., C. J. Tomlin and G. Leitmann (2012). Monotone Approximations of Minimum and Maximum Functions and Multi-Objective Problems, Applied Mathematics & Optimization, Vol. 66, 455–473.

Stipanovi´c, D.M., C. Valicka and A.E. Abbas (2014). Control Strategies For Players In Pursuit-Evasion Games Based On Their Preferences. International Game Theory Review, 16(02), 1440008.

Downloads

Published

2022-05-01

How to Cite

Shevchenko, I., & M. Stipanovic, D. (2022). A Design of Strategies in Alternative Pursuit Games. Contributions to Game Theory and Management, 9. Retrieved from https://gametheory.spbu.ru/article/view/13356

Issue

Vol. 9 (2016)

Section

Articles

License

Articles of "Contributions to Game Theory and Management" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.