TY - GEN
T1 - On the design of optimal structured and sparse feedback gains via sequential convex programming
AU - Fardad, Makan
AU - Jovanovic, Mihailo
PY - 2014/1/1
Y1 - 2014/1/1
N2 - We consider the problem of finding optimal feedback gains in the presence of structural constraints and/or sparsity-promoting penalty functions. Such problems are known to be difficult due to their lack of convexity. We provide an equivalent reformulation of the optimization problem such that its source of nonconvexity is isolated in one nonconvex matrix inequality of the form Y X -1. Furthermore, we preserve the feedback gain as an optimization variable in the reformulated problem. Via linearizations of the nonconvex constraint, we introduce an iterative algorithm that solves a semidefinite program at every stage and for which the nonconvex constraint is satisfied upon convergence. We elaborate on the modular nature of the proposed scheme and show that it can be used in a wide range of network control problems.
AB - We consider the problem of finding optimal feedback gains in the presence of structural constraints and/or sparsity-promoting penalty functions. Such problems are known to be difficult due to their lack of convexity. We provide an equivalent reformulation of the optimization problem such that its source of nonconvexity is isolated in one nonconvex matrix inequality of the form Y X -1. Furthermore, we preserve the feedback gain as an optimization variable in the reformulated problem. Via linearizations of the nonconvex constraint, we introduce an iterative algorithm that solves a semidefinite program at every stage and for which the nonconvex constraint is satisfied upon convergence. We elaborate on the modular nature of the proposed scheme and show that it can be used in a wide range of network control problems.
KW - Communication architecture
KW - optimization
KW - semidefinite programming
KW - sequential convex programming
KW - sparsity-promoting control
KW - structural constraints
UR - http://www.scopus.com/inward/record.url?scp=84905674754&partnerID=8YFLogxK
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U2 - 10.1109/ACC.2014.6859120
DO - 10.1109/ACC.2014.6859120
M3 - Conference contribution
AN - SCOPUS:84905674754
SN - 9781479932726
T3 - Proceedings of the American Control Conference
SP - 2426
EP - 2431
BT - 2014 American Control Conference, ACC 2014
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2014 American Control Conference, ACC 2014
Y2 - 4 June 2014 through 6 June 2014
ER -