Pursuit-evasion games with state constraints: dynamic programming and discrete-time approximations

Martino Bardi; Shigeaki Koike; Pierpaolo Soravia

doi:10.3934/dcds.2000.6.361

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2000, Volume 6, Issue 2: 361-380. Doi: 10.3934/dcds.2000.6.361

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Pursuit-evasion games with state constraints: dynamic programming and discrete-time approximations

1.
Dipartimento di Matematica P. e A., Universita di Padova, via Belzoni 7, 35131 Padova
2.
Department of Mathematics, Saitama University, 255 Shimo-Okubo, Urawa, Saitama 338-8570
3.
Dipartimento di Matematica Pura e Applicata, Università di Padova, Belzoni 7, 1-35131, Padova

Received: December 1998

Revised: June 1999

Published: April 2000

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Abstract

In this paper we study the boundary value problem for the Hamilton-Jacobi-Isaacs equation of pursuit-evasion differential games with state constraints. We prove existence of a continuous viscosity solution and a comparison theorem that we apply to establish uniqueness of such a solution and its uniform approximation by solutions of discretized equations.

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Mathematics Subject Classification: 35F30, 49L20, 49L25.

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