A decentralized team decision problem with an exponential cost criterion

A static decentralized team problem is represented by the nodes of a network working together to optimize the expected value of an exponential of a quadratic function of the state and control variables. The information is assumed to be given linear functions of the normally distributed state plus Gaussian noise. For certain ranges of the system parameters the conditions for optimality are satisfied by a linear decision rule. For this optimizing decision rule, the control gains on the available information are obtained from the stationary conditions which reduce to a set of algebraic equations and a matrix inequality condition. Since the quadratic performance criterion produces the only previously known closed form decentralized decision rule, the exponential criterion is an important generalization.