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- Alborz Alavian, Michael Rotkowitz
- 2017 51st Annual Conference on Information…
- 2017

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)

- Alborz Alavian, Michael Rotkowitz
- CDC
- 2014

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)

- Alborz Alavian, Michael Rotkowitz
- ACC
- 2016

This paper discusses the controllability of linear time-invariant (LTI) systems with decentralized controllers. Whether an LTI system is controllable (by LTI controllers) with respect to a given information structure can be determined by testing for fixed modes, but this gives a binary answer with no information about robustness. Measures have been… (More)

We consider the problem of finding decentralized controllers to optimize an H∞norm. This can be cast as a convex optimization problem when certain conditions are satisfied, but it is an infinite-dimensional problem that still cannot be addressed with existing methods. We useQ-parametrization to approach the original problem with a sequence of… (More)

- Alborz Alavian, Michael Rotkowitz
- 2016 54th Annual Allerton Conference on…
- 2016

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)

- Alborz Alavian, Michael Rotkowitz
- ACC
- 2015

- Alborz Alavian, Michael Rotkowitz
- 2016 54th Annual Allerton Conference on…
- 2016

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)

- Alborz Alavian, Michael Rotkowitz
- ArXiv
- 2017

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)