The solution infinite horizon noncooperative differential game with nonlinear dynamics without the Hamilton-Jacobi-Bellman equation

2009/01/10 by Jaykov Foukzon, Foukzon, Jaykov
Mathematics · #FOS: Mathematics #Optimization and Control (math.OC) #math.OC

paper · pdf · doi:10.48550/arxiv.0901.1383

65pages

arxiv created 2009/01/31 · arxiv updated 2009/12/01

Abstract

For a non-cooperative m-persons differential game, the value functions ofthe various players satisfy a system of Hamilton-Jacobi-Bellman equations.Nashequilibrium solutions in feedback form can be obtained by studying a related system of P.D.E's.A new approach, which is proposed in this paper allows one to construct the feedback optimal control and cost functions J_i(t,x),i=1,...,m directly,i.e.,without any reference to the corresponding Hamilton-Jacobi-Bellman equations.

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