TY - GEN
T1 - Sparsity-promoting optimal control of spatially-invariant systems
AU - Zoltowski, David M.
AU - Dhingra, Neil
AU - Lin, Fu
AU - Jovanović, Mihailo R.
PY - 2014
Y1 - 2014
N2 - We study the optimal design of sparse and block sparse feedback gains for spatially-invariant systems on a circle. For this class of systems, the state-space matrices are jointly diagonalizable via the discrete Fourier transform. We exploit this structure to develop an ADMM-based algorithm that significantly reduces the computational complexity relative to standard approaches. Specifically, the complexity of the developed algorithm scales linearly with the number of subsystems. This is in contrast to a cubic scaling when circulant structure is not exploited. Two examples are provided to illustrate the effectiveness of the developed approach.
AB - We study the optimal design of sparse and block sparse feedback gains for spatially-invariant systems on a circle. For this class of systems, the state-space matrices are jointly diagonalizable via the discrete Fourier transform. We exploit this structure to develop an ADMM-based algorithm that significantly reduces the computational complexity relative to standard approaches. Specifically, the complexity of the developed algorithm scales linearly with the number of subsystems. This is in contrast to a cubic scaling when circulant structure is not exploited. Two examples are provided to illustrate the effectiveness of the developed approach.
KW - Alternating direction method of multipliers
KW - Fourier transform
KW - sparsity-promoting optimal control
KW - spatially-invariant systems
KW - structured feedback control
UR - http://www.scopus.com/inward/record.url?scp=84905695124&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84905695124&partnerID=8YFLogxK
U2 - 10.1109/ACC.2014.6859491
DO - 10.1109/ACC.2014.6859491
M3 - Conference contribution
AN - SCOPUS:84905695124
SN - 9781479932726
T3 - Proceedings of the American Control Conference
SP - 1255
EP - 1260
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 -