We study a new class of two-player,zero-sum,deterministic differential games where each player uses both continuous and impulse controls in an infinite horizon with discounted payoff.We assume that the form and cost o...We study a new class of two-player,zero-sum,deterministic differential games where each player uses both continuous and impulse controls in an infinite horizon with discounted payoff.We assume that the form and cost of impulses depend on nonlinear functions and the state of the system,respectively.We use Bellman's dynamic programming principle(DPP)and viscosity solutions approach to show,for this class of games,the existence and uniqueness of a solution for the associated Hamilton-Jacobi-Bellman-Isaacs(HJBI)partial differential equations(PDEs).We then,under Isaacs'condition,deduce that the lower and upper value functions coincide,and we give a computational procedure with a numerical test for the game.展开更多
基金supported by the National Center for Scientific and Technical Research CNRST,Rabat,Morocco[grant number 17 UIZ 19].
文摘We study a new class of two-player,zero-sum,deterministic differential games where each player uses both continuous and impulse controls in an infinite horizon with discounted payoff.We assume that the form and cost of impulses depend on nonlinear functions and the state of the system,respectively.We use Bellman's dynamic programming principle(DPP)and viscosity solutions approach to show,for this class of games,the existence and uniqueness of a solution for the associated Hamilton-Jacobi-Bellman-Isaacs(HJBI)partial differential equations(PDEs).We then,under Isaacs'condition,deduce that the lower and upper value functions coincide,and we give a computational procedure with a numerical test for the game.
