TY - JOUR
T1 - Distributed solver for linear matrix inequalities
T2 - an optimization perspective
AU - Li, Weijian
AU - Deng, Wen
AU - Zeng, Xianlin
AU - Hong, Yiguang
N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to South China University of Technology, Academy of Mathematics and Systems Science, CAS and Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2021/11
Y1 - 2021/11
N2 - In this paper, we develop a distributed solver for a group of strict (non-strict) linear matrix inequalities over a multi-agent network, where each agent only knows one inequality, and all agents co-operate to reach a consensus solution in the intersection of all the feasible regions. The formulation is transformed into a distributed optimization problem by introducing slack variables and consensus constraints. Then, by the primal–dual methods, a distributed algorithm is proposed with the help of projection operators and derivative feedback. Finally, the convergence of the algorithm is analyzed, followed by illustrative simulations.
AB - In this paper, we develop a distributed solver for a group of strict (non-strict) linear matrix inequalities over a multi-agent network, where each agent only knows one inequality, and all agents co-operate to reach a consensus solution in the intersection of all the feasible regions. The formulation is transformed into a distributed optimization problem by introducing slack variables and consensus constraints. Then, by the primal–dual methods, a distributed algorithm is proposed with the help of projection operators and derivative feedback. Finally, the convergence of the algorithm is analyzed, followed by illustrative simulations.
KW - Distributed computation
KW - Distributed optimization
KW - Linear matrix inequalities
KW - Primal–dual method
UR - https://www.scopus.com/pages/publications/85117949925
U2 - 10.1007/s11768-021-00061-z
DO - 10.1007/s11768-021-00061-z
M3 - Article
AN - SCOPUS:85117949925
SN - 2095-6983
VL - 19
SP - 507
EP - 515
JO - Control Theory and Technology
JF - Control Theory and Technology
IS - 4
ER -