Mixed control problem under partial observation
This paper is concerned with a mixed control problem under partial observations; in this terminology ``mixed'' means that we choose a strategy composed of a control process \(U_ t\) and a stopping time \(S\), in order to minimize a criterion function. The partial observations mean that the controlled process is a controlled Markov process \((x_ t)\) with values in a Lusin space \(E\), while the observation process is an integer point process \((y_ t)\) whose intensity is a function of \((x_ t)\). The author proves that in the separated problem in canonical formulation (control-stopping rules), the dynamic programming principle holds. From this principle a criterion of optimality for control-stopping rules, and a characterization of an \(\varepsilon\)-optimal stopping time are deduced. Then with the compactness of control-stopping rules, and the continuity of the criterion, existence of an optimal Markovian rule is obtained under some regularity assumptions. Finally the last section is devoted to the filtering equation and applications to the comparison theorem between the control problems (relative to strict controls, relaxed generalized partially observable controls, and separated controls).
mixed control problem under partial observations
scientific article; zbMATH DE number 147400
scientific article