Alborz Alavian

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We consider a class of mixed integer programs where the problem is convex except for a vector of discrete variables. Two methods based on the Alternating Direction Method of Multipliers (ADMM) are presented. The first, which has appeared in the recent literature, duplicates the discrete variable, with one copy allowed to vary continuously. This results in a(More)
A seminal result in decentralized control is the development of fixed modes by Wang and Davison in 1973 that plant modes which cannot be moved with a static decentralized controller cannot be moved by a dynamic one either, and that the other modes which can be moved can be shifted to any chosen location with arbitrary precision. These results were developed(More)
This work considers the determination of non-binary measures of controllability or robustness with respect to decentralized controllers. A measure developed by Vaz and Davison in 1988 nicely captures the distance from a plant to the closest one with a fixed mode, and ties it to eigenvalue assignability; that is, how much effort is at most required to move(More)
We consider the problem of minimizing a particular singular value of a matrix variable, which is then subject to some convex constraints. Convex heuristics for this problem are discussed, including some counter-intuitive results regarding which is best, which then provide upper bounds on the value of the problem. The use of polynomial optimization(More)
A seminal result in decentralized control is the development of fixed modes by Wang and Davison in 1973 that plant modes which cannot be moved with a static decentralized controller cannot be moved by a dynamic one either, and that the other modes which can be moved can be shifted to any chosen location with arbitrary precision. These results were developed(More)