A chordal decomposition approach to scalable design of structured feedback gains over directed graphs
A chordal decomposition approach to scalable design of structured feedback gains over directed graphs
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DOI：
10.1109/cdc.2016.7799333
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发表时间：
2016-12
期刊：
影响因子：
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通讯作者：
Yang Zheng;Richard P. Mason;A. Papachristodoulou
中科院分区：
文献类型：
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作者：
Yang Zheng;Richard P. Mason;A. Papachristodoulou
本文考虑了在先验结构约束下的静态反馈增益设计问题，这一般是一个非凸问题。通过利用问题的稀疏性，并使用弦分解，提出了一种可扩展的算法来计算大系统的结构稳定反馈增益的有向图。首先给出了块半定矩阵的弦分解定理。松弛，然后使用重铸的结构化反馈增益的设计成一个凸问题。结合分解和松弛，我们提出了一个顺序设计算法，以获得结构化的反馈增益团的团树的基础弦图。数值仿真验证了该方法的有效性。
This paper considers the problem of designing static feedback gains subject to a priori structural constraints, which is in general a non-convex problem. By exploiting the sparsity properties of the problem, and using chordal decomposition, a scalable algorithm is proposed to compute structured stabilizing feedback gains for large-scale systems over directed graphs. Specifically, we first present a chordal decomposition theorem for block-semidefinite matrices. A relaxation is then used to recast the design of structured feedback gains into a convex problem. Combining the decomposition with the relaxation, we propose a sequential design algorithm to obtain structured feedback gains clique-by-clique over a clique tree of the underlying chordal graph. Numerical simulations demonstrate the efficiency of the proposed method.