Team decision theory for linear continuous-time systems

This paper develops a team decision theory for linear-quadratic (LQ) continuous-time systems. First, a counterpart of the well-known result of Radner on quadratic static teams is obtained for two-member continuous-time LQ static team problems when the statistics of the random variables involved are not necessarily Gaussian. An iterative convergent scheme is developed, which in the limit yields the optimal team strategies. For the special case of Gaussian distributions, the team-optimal solution is affine in the information available to each DM, and for the further special case when the team cost function does not penalize the intermediate values of state, the optimal strategies can be obtained by solving a Liapunov type time-invariant matrix equation. This static theory is then extended to LQG continuous-time dynamic teams with sampled observations under the one-step-delay observation sharing pattern. The unique solution is again affine in the information available to each DM, and further, it features a certainty-equivalence property.