TY - GEN
T1 - Sparse feedback synthesis via the alternating direction method of multipliers
AU - Lin, Fu
AU - Fardad, Makan
AU - Jovanovic, Mihailo R.
PY - 2012
Y1 - 2012
N2 - We study the design of feedback gains that strike a balance between the H2 performance of distributed systems and the sparsity of controller. Our approach consists of two steps. First, we identify sparsity patterns of feedback gains by incorporating sparsity-promoting penalty functions into the H2 problem, where the added terms penalize the number of communication links in the distributed controller. Second, we optimize feedback gains subject to structural constraints determined by the identified sparsity patterns. In the first step, we identify sparsity structure of feedback gains using the alternating direction method of multipliers, which is a powerful algorithm well-suited to large optimization problems. This method alternates between optimizing the sparsity and optimizing the closed-loop H2 norm, which allows us to exploit the structure of the corresponding objective functions. In particular, we take advantage of the separability of sparsity-promoting penalty functions to decompose the minimization problem into sub-problems that can be solved analytically. An example is provided to illustrate the effectiveness of the developed approach.
AB - We study the design of feedback gains that strike a balance between the H2 performance of distributed systems and the sparsity of controller. Our approach consists of two steps. First, we identify sparsity patterns of feedback gains by incorporating sparsity-promoting penalty functions into the H2 problem, where the added terms penalize the number of communication links in the distributed controller. Second, we optimize feedback gains subject to structural constraints determined by the identified sparsity patterns. In the first step, we identify sparsity structure of feedback gains using the alternating direction method of multipliers, which is a powerful algorithm well-suited to large optimization problems. This method alternates between optimizing the sparsity and optimizing the closed-loop H2 norm, which allows us to exploit the structure of the corresponding objective functions. In particular, we take advantage of the separability of sparsity-promoting penalty functions to decompose the minimization problem into sub-problems that can be solved analytically. An example is provided to illustrate the effectiveness of the developed approach.
KW - Alternating direction method of multipliers
KW - cardinality minimization
KW - communication architectures
KW - distributed systems
KW - homotopy
KW - l minimization
KW - sparsity-promoting optimal control
KW - sum-of-logs penalty
UR - http://www.scopus.com/inward/record.url?scp=84869402529&partnerID=8YFLogxK
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M3 - Conference contribution
AN - SCOPUS:84869402529
SN - 9781457710957
T3 - Proceedings of the American Control Conference
SP - 4765
EP - 4770
BT - 2012 American Control Conference, ACC 2012
T2 - 2012 American Control Conference, ACC 2012
Y2 - 27 June 2012 through 29 June 2012
ER -