Abstract: The synthesis of optimal decentralized controllers is a longstanding open problem. Conventional controls analysis breaks down when multiple controllers have access to different information. With the advent of complex interconnected systems, what has long been recognized as a difficult mathematical problem is now a pertinent one as well. It is shown that when a simple condition holds, the optimal controllers may be found via convex programming. This condition unifies the few previously identified tractable problems, and elucidates many new ones. The implications for optimal control subject to sparsity constraints will be shown, as will those for interconnected systems subject to communication delays. Many physical problems of practical interest are clearly included as thusly admitting tractable solutions. We then discuss recent work which extends these ideas to nonlinear control and time-varying control. In addition, we further see how these recent results may allow this work to extend beyond the field of decentralized control, to all types of constrained control problems
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