Abstract

A canonical decentralized optimal control problem with quadratic cost criteria can be cast as an LQR problem in which the stabilizing controller is restricted to lie in a constraint set. We characterize a wide class of systems and constraint sets for which the canonical problem is tractable. We employ the notion of operator algebras to study the structural properties of the canonical problem. Examples of some widely used operator algebras in the context of distributed control include the subspace of infinite and finite dimensional spatially decaying operators, lower (or upper) triangular matrices, and circulant matrices. For a given operator algebra, we prove that if the trajectory of the solution of an operator differential equation starts inside the operator algebra, it will remain inside for all times. Using this result, we show that if the constraint set is an operator algebra, the canonical problem is solvable and equivalent to the standard LQR problem without the information constraint.

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