Sparsity-promoting optimal control for a class of distributed systems

We consider a linear quadratic optimal control problem with an additional penalty on the number of communication links in the distributed controller. We reformulate this combinatorial optimization problem as a sequence of weighted l 1 problems, where the weighted l 1 norm approximates the counting o...

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Bibliographic Details
Published inProceedings of the 2011 American Control Conference pp. 2050 - 2055
Main Authors Fardad, Makan, Fu Lin, Jovanovic, Mihailo R.
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.06.2011
Subjects
Communication architecture
convex optimization
Lead
Minimization
Optimal control
Optimization
reweighting
semidefinite program
sparsity-promoting optimal control
State feedback
Symmetric matrices
Vehicles
vehicular formations
ℓ 1 minimization
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ISBN1457700808
9781457700804
ISSN0743-1619
DOI10.1109/ACC.2011.5991020

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Summary:We consider a linear quadratic optimal control problem with an additional penalty on the number of communication links in the distributed controller. We reformulate this combinatorial optimization problem as a sequence of weighted l 1 problems, where the weighted l 1 norm approximates the counting of the communication links. We identify a class of systems for which the weighted l 1 problem can be formulated as a semideflnite program and therefore its solution can be computed efficiently. Application of the developed algorithm to the optimal control of vehicular formations reveals communication topologies that become sparser as the price of inter-vehicular communications is increased.
ISBN:1457700808
9781457700804
ISSN:0743-1619
DOI:10.1109/ACC.2011.5991020