Abstract:
This paper focuses on two approaches for calculating optimal controls in cooperative differential games with hybrid structure: namely, the (joint) payoff function has a form of sum of integrals with different but adjoint time intervals.
Our methods had been applied for the game-theoretical model with random time horizon $T$ where $T$ has a discrete structure. But the area of application can be more wide.
Keywords:differential games, random duration, discontinuous cumulative distribution function, discrete random variable, optimal control, Pontryagin's maximum principle.