Bellman functions in the optimization of dynamic systems under uncertainty
The author discusses a specific optimization problem of dynamic systems under uncertainty namely, the ''game of two cars'' of \textit{R. Isaacs} [Differential games (1965; Zbl 0125.380)]. It is shown that the well known sufficient optimality conditions expressed in terms of the solution to Bellman's equation (Bellman's function) for a deterministic system do not hold here. However, assuming that no allowed disturbances can move the path of the system out of the domain of definition of the obtained Bellman function before this path reaches the terminal set of the system, then sufficient optimality conditions for the deterministic case hold even for the nondeterministic system.
scientific article; zbMATH DE number 3986040