A double homotopy approach for decentralized H∞ control of civil structures. Issue 3 (8th May 2013)

• Record Type: Journal Article
• Authors: Qu, Chunxu; Huo, Linsheng; Li, Hongnan; Wang, Yang
• Is Part Of: Structural control and health monitoring. Volume 21:Issue 3(2014)
• Page Start: 269
• Page End: 281
• Publication Date: 2013-05-08
• Subjects: Structural engineering -- Periodicals; Structural control (Engineering) -- Periodicals; Automatic data collection systems -- Periodicals; Detectors -- Periodicals; 624.17
• DOI: 10.1002/stc.1552
• Languages: English
• ISSNs: 1545-2255

Abstract

<abstract abstract-type="main"> <title>ABSTRACT</title> <p>This paper presents a decentralized <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgg4sqqbfb8" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math altimg="urn:x-wiley:15452255:media:stc1552:stc1552-math-0003" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="script">H</mml:mi><mml:mi>∞</mml:mi></mml:msub></mml:math></alternatives> 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, <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgg4sqqbf9q" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math altimg="urn:x-wiley:15452255:media:stc1552:stc1552-math-0004" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="script">H</mml:mi><mml:mi>∞</mml:mi></mml:msub></mml:math></alternatives> controller design can be transformed to an optimization problem with bilinear matrix inequality (BMI) constraints. To obtain a decentralized <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgg4sqqbf7m" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math altimg="urn:x-wiley:15452255:media:stc1552:stc1552-math-0005" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="script">H</mml:mi><mml:mi>∞</mml:mi></mml:msub></mml:math></alternatives> 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.</p> </abstract>