An Accelerated Proximal Alternating Direction Method of Multipliers for Optimal Decentralized Control of Uncertain Systems
arxiv(2023)
摘要
To ensure the system stability of the ℋ_2-guaranteed cost
optimal decentralized control problem (ODC), an approximate semidefinite
programming (SDP) problem is formulated based on the sparsity of the gain
matrix of the decentralized controller. To reduce data storage and improve
computational efficiency, the SDP problem is vectorized into a conic
programming (CP) problem using the Kronecker product. Then, a proximal
alternating direction method of multipliers (PADMM) is proposed to solve the
dual of the resulted CP. By linking the (generalized) PADMM with the (relaxed)
proximal point algorithm, we are able to accelerate the proposed PADMM via the
Halpern fixed-point iterative scheme. This results in a fast convergence rate
for the Karush-Kuhn-Tucker (KKT) residual along the sequence generated by the
accelerated algorithm. Numerical experiments further demonstrate that the
accelerated PADMM outperforms both the well-known CVXOPT and SCS algorithms for
solving the large-scale CP problems arising from
ℋ_2-guaranteed cost ODC problems.
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