Min-max certainty equivalence principle and differential games
Résumé
This paper presents a version of the certainty equivalence principle, usable for nonlinear, variable end-time, partial observation zero-sum differential games, which states that under the unicity of the solution to the auxiliary problem, optimal controllers can be derived from the solution of the related perfect observation game. An example is provided where in one region, the new extended result holds, giving an optimal control and in another region, the unicity condition is not met, leading indeed to a non-certainty equivalent optimal controller.