Centralized and decentralized stochastic control problems with an exponential cost criterion

The authors consider stochastic control problems with an exponential cost criterion. In particular, the centralized linear-exponential-Gaussian (LEG) control problem is solved with the hypothesis that the controller is constructed from the past information and the current observation of the state. 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 in order to construct the decentralized controller gains. The derivation procedure indicates a strong connection between stochastic control theory and game theory for this class of operations