WITH AN EXPONENTIAL COST CRITERION
C.R. Jaensch, Jason Lee Speyer · 1988
This paper considers stochastic control problems with an exponential cost criterion. In particular, the solution of the centralized LinearExponential-Gaussian (LEG) control problem with the hypothesis that the controller is constructed from the past information and the current observation of the state is presented. Furthermore, the decentralized LEG control problem of a two member team with a one-step delayed information-sharing pattern is considered. In contrast to the centralized derivation where a type of certainty equivalence holds, a summary of all the data must be swept forward to the terminal time stage. Then, it is decomposed in a backward recursion inorder to construct the decentralized controller gains In addition, it is shown that the optimal control Law of the i-th member is an affine function of his own Observation at the current time and the one-step delayed state estimate. Finally, the derivation procedure indicates a strong connection between stochastic control theory and game theory for this class of problems.