Scalable Design of Structured Controllers Using Chordal Decomposition

We consider the problem of designing static feedback gains subject to a priori structural constraints, which is a nonconvex problem in general. Previous work has focused on either characterizing special structures that result into convex formulations, or employing certain techniques to allow convex...

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Vydáno v:IEEE transactions on automatic control Ročník 63; číslo 3; s. 752 - 767
Hlavní autoři: Yang Zheng, Mason, Richard P., Papachristodoulou, Antonis
Médium: Journal Article
Jazyk:angličtina
Vydáno: IEEE 01.03.2018
Témata:
Algorithm design and analysis
Chordal decomposition
Computational modeling
Data models
Large-scale systems
Matrix converters
Matrix decomposition
scalable design
structured feedback gains
Symmetric matrices
ISSN:0018-9286, 1558-2523
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Shrnutí:We consider the problem of designing static feedback gains subject to a priori structural constraints, which is a nonconvex problem in general. Previous work has focused on either characterizing special structures that result into convex formulations, or employing certain techniques to allow convex relaxations of the original problem. In this paper, by exploiting the underlying sparsity properties of the problem, and using chordal decomposition, we propose a scalable algorithm to obtain structured feedback gains to stabilize a large-scale system. We first extend the chordal decomposition theorem for positive semidefinite matrices to the case of matrices with block-chordal sparsity. Then, a block-diagonal Lyapunov matrix assumption is used to convert the design of structured feedback gains into a convex problem, which inherits the sparsity pattern of the original problem. Combining these two results, we propose a sequential design method to obtain structured feedback gains clique-by-clique over a clique tree of the block-chordal matrix, which only needs local information and helps ensure privacy of model data. Several illustrative examples demonstrate the efficiency and scalability of the proposed sequential design method.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2017.2726578