The goal of this paper is to derive a modified formulation of the finite-horizon LQR problem, which can be cast as semidefinite programming problems (SDPs). In addition, based on the the Lagrangian duality, its dual problem is studied. We establish connections between the proposed primal-dual conditions with existing results. As an application of the proposed results, the decentralized LQR analysis and design problems are addressed. Especially, using the structure of the derived LQR formulations, a sufficient but simple and convex surrogate problem is developed for solving decentralized LQR design problems.


LQR problem, duality, semidefinite programming, optimal control, decentralized control

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