Multiple-objective risk-sensitive control and its small noise limit
This paper deals with a multiple-objective, risk-sensitive control problem. The authors study asymptotic properties of the value function, as the noise approaches \(0\), and introduce a new class of two-player, zero-sum, deterministic differential games whose cost functional is multiple-objective, being composed of the risk-neutral integral costs associated with the original risk-sensitive control. In this game, the opposing player seeks to maximize the most vulnerable member of a given set of cost functionals, while the original controller seeks to minimize the worst damage that the opponent can do over this set. Using the dynamic programming approach and the viscosity solution, they show the connection between the original risk-sensitive control and the differential game. In particular, they prove that the differential game is independent of the weights on the different objective in the original risk-sensitive control and moreover an efficient risk-sensitive controller can be determined asymptotically by solving the differential game. Applying their results to the single-objective case, they generalize some known results.
multiple-objective optimization differential games
scientific article; zbMATH DE number 1900994
scientific article