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In decentralized control systems with linear dynamics, quadratic cost, andGaussian disturbance (also called decentralized LQG systems) linear controlstrategies are not always optimal. Nonetheless, linear control strategies areappealing due to analytic and implementation simplicity. In this paper, weinvestigate decentralized LQG systems with partial history sharing informationstructure and identify finite dimensional sufficient statistics for suchsystems. Unlike prior work on decentralized LQG systems, we do not assumepartially nestedness or quadratic invariance. Our approach is based on thecommon information approach of Nayyar \emph{et al}, 2013 and exploits thelinearity of the system dynamics and control strategies. To illustrate ourmethodology, we identify sufficient statistics for linear strategies indecentralized systems where controllers communicate over a strongly connectedgraph with finite delays, and for decentralized systems consisting of coupledsubsystems with control sharing or one-sided one step delay sharing informationstructures.

Sufficient statistics for linear control strategies in decentralized systems with partial history sharing