A decentralized team decision problem with an exponential cost criterion

A static decentralized team 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 consists of known linear functions of the normally distributed state corrupted by additive Gaussian noise. For certain ranges of the system parameters, the stationary condition for optimality is satisfied by a linear decision rule operating on the available information. These stationary conditions reduce to a set of algebraic matrix equations and a matrix inequality condition from which the values of the decision gains are determined. Although the stationary conditions are necessary for the linear control law to be minimizing in the class of nonlinear control laws, sufficiency is obtained for our linear controller to be minimizing in the class of linear control laws. Since the quadratic performance criterion produces the only previously known closed form decentralized decision rule, the exponential criterion is an important generalization.