Performance bounds for robust decentralized control

We consider the decentralized output feedback control of stochastic linear systems, subject to robust linear constraints on both the state and input trajectories. For problems with partially nested information structures, we establish an upper bound on the minimum achievable cost by computing the optimal affine decentralized control policy as a solution to a finite-dimensional conic program. For problems with general (possibly nonclassical) information structures, we construct another finite-dimensional conic program whose optimal value stands as a lower bound on the minimum achievable cost. With this lower bound in hand, one can bound the suboptimality incurred by any feasible decentralized control policy. A study of a partially nested system reveals that affine policies can be close to optimal, even in the presence state/input constraints and non-Gaussian disturbances.