Discrete control processes, dynamic games and multicriterion control problems. (Q698946)

The author proposes a recursive definition for numerically evaluating an ``objective cost'' (or state evaluation) at each state of a dynamic system. The dynamic system is assumed to be deterministic with the current state uniquely determined by state and control parameters at the previous time instance. Consequently the state evaluation of the system at each time point is determined uniquely by the state and control parameters at the previous time instance. This general scheme includes several previous models of discrete dynamic control problems including an integral-time criterion, a discrete control problem on a network, a game control model with multiple players and a multi-criterion control problem. It is possible to devise a dynamic-programming-like algorithm for obtaining an optimal controller when the numerical function used in the recursive definition satisfies a monotonicity condition with respect to the previous cost evaluation at the previous state and time.