April  2000, 6(2): 361-380. doi: 10.3934/dcds.2000.6.361

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, Japan

3. 

Dipartimento di Matematica Pura e Applicata, Università di Padova, Belzoni 7, 1-35131, Padova, Italy

Received  December 1998 Revised  June 1999 Published  January 2000

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.
Citation: Martino Bardi, Shigeaki Koike, Pierpaolo Soravia. Pursuit-evasion games with state constraints: dynamic programming and discrete-time approximations. Discrete & Continuous Dynamical Systems - A, 2000, 6 (2) : 361-380. doi: 10.3934/dcds.2000.6.361
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