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A double homotopy approach for decentralized H ∞ control of civil structures
Author(s) -
Qu Chunxu,
Huo Linsheng,
Li Hongnan,
Wang Yang
Publication year - 2014
Publication title -
structural control and health monitoring
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.587
H-Index - 62
eISSN - 1545-2263
pISSN - 1545-2255
DOI - 10.1002/stc.1552
Subject(s) - controller (irrigation) , control theory (sociology) , mathematics , decentralised system , homotopy , mathematical optimization , control (management) , computer science , artificial intelligence , pure mathematics , agronomy , biology
This paper presents a decentralized H ∞ controller design for the vibration control of civil structures. The formulation through double homotopy is proposed in discrete time domain and considers feedback time delay. It is well‐known that through bounded real lemma, H ∞ controller design can be transformed to an optimization problem with bilinear matrix inequality (BMI) constraints. To obtain a decentralized H ∞ controller constrained by special block‐diagonal patterns on controller matrices, there is generally no off‐the‐shelf package or numerical algorithm to solve the BMI problem. This paper proposes a double homotopy method to solve the BMI problem in discrete time domain. The method approximates the BMI problem to a series of linear matrix inequality problems along two homotopic paths, and gradually deforms a centralized controller to a decentralized controller. The proposed method is first studied numerically with a six‐story building example, and then validated experimentally through shaking table tests of a two‐story frame with active mass dampers. Copyright © 2013 John Wiley & Sons, Ltd.