In this paper we present some numerical methods for the solution of two-persons zerosum deterministic differential games. The methods are based on the dynamic programming approach. We first solve the Isaacs equation associated to the game to get an approximate value function and then we use it to reconstruct approximate optimal feedback controls and optimal trajectories. The approximation schemes also have an interesting control interpretation since the time-discrete scheme stems from a dynamic programming principle for the associated discrete time dynamical system. The general framework for convergence results to the value function is the theory of viscosity solutions. Numerical experiments are presented solving some classical pursuit-evasion games. © World Scientific Publishing Company.
Numerical methods for differential games based on partial differential equations / Falcone, Maurizio. - In: INTERNATIONAL GAME THEORY REVIEW. - ISSN 0219-1989. - STAMPA. - 8:2(2006), pp. 231-272. [10.1142/s0219198906000886]
Numerical methods for differential games based on partial differential equations
FALCONE, Maurizio
2006
Abstract
In this paper we present some numerical methods for the solution of two-persons zerosum deterministic differential games. The methods are based on the dynamic programming approach. We first solve the Isaacs equation associated to the game to get an approximate value function and then we use it to reconstruct approximate optimal feedback controls and optimal trajectories. The approximation schemes also have an interesting control interpretation since the time-discrete scheme stems from a dynamic programming principle for the associated discrete time dynamical system. The general framework for convergence results to the value function is the theory of viscosity solutions. Numerical experiments are presented solving some classical pursuit-evasion games. © World Scientific Publishing Company.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.