On the closest quadratically invariant constraint

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...

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Published inProceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference pp. 1607 - 1612
Main Authors Rotkowitz, M.C., Martins, N.C.
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.12.2009
Subjects
Constraint optimization
Control systems
Delay effects
Distributed control
Educational institutions
Hamming distance
Interconnected systems
System testing
Upper bound
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Summary: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.
ISBN:9781424438716
1424438713
ISSN:0191-2216
DOI:10.1109/CDC.2009.5400367