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Abstract-This tutorial paper provides a comprehensive characterization of information structures in team decision problems and their impact on the tractability of team optimization. Solution methods for team decision problems are presented in various settings where the discussion is structured in two foci: The first is centered on solution methods for stochastic teams admitting state-space formulations. The second focus is on norm-optimal control for linear plants under information constraints.

Abstract-An iterative algorithm to solve Algebraic RiccatiEquations with an indefinite quadratic term is proposed. The global convergence and local quadratic rate of convergence of the algorithm are guaranteed and a proof is given. Numerical examples are also provided to demonstrate the superior effectiveness of the proposed algorithm when compared with methods based on finding stable invariant subspaces of Hamiltonian matrices. A game theoretic interpretation of the algorithm is also provided. Index Terms-Algebraic Riccati equation (ARE),Riccati equations, indefinite quadratic term, iterative algorithms.

Quadratic invariance is a condition which has been shown to allow for optimal decentralized control problems to be cast as convex optimization problems. The condition relates the constraints that the decentralization imposes on the controller to the structure of the plant. In this paper, we consider the problem of finding the closest subset and superset of the decentralization constraint which are quadratically invariant when the original problem is not. We show that this can itself be cast as a convex problem for the case where the controller is subject to delay constraints between subsystems, but that this fails when we only consider sparsity constraints on the controller. For that case, we develop an algorithm that finds the closest superset in a fixed number of steps, and discuss methods of finding a close subset. arXiv:1109.6259v1 [math.OC]

We consider the problem of constructing decentralized control systems. We formulate this problem as one of minimizing the closed-loop norm of a feedback system subject to constraints on the controller structure. We define the notion of quadratic invariance of a constraint set with respect to a system, and show that if the constraint set has this property, then the constrained minimum norm problem may be solved via convex programming. We also show that quadratic invariance is necessary and sufficient for the constraint set to be preserved under feedback.We develop necessary and sufficient conditions under which the constraint set is quadratically invariant, and show that many examples of decentralized synthesis which have been proven to be solvable in the literature are quadratically invariant. As an example, we show that a controller which minimizes the norm of the closed-loop map may be efficiently computed in the case where distributed controllers can communicate faster than the propagation delay of the plant dynamics. University, Stanford CA 94305-4035, U.S.A. The first author was partially supported by a Stanford Graduate Fellowship. Both authors were partially supported by the Stanford URI Architectures f . 7 Secure and Robust DIstnbuted Infmstructures, AFOSR DoD award number 49620-01-1-0365. f ( P , K ) = P I I + S z K ( I -P z z K ) -' P z I 0-7803-7516-5/02/$17.00 a2002 IEEE