A double homotopy approach for decentralized H∞ control of civil structures

Abstract

This paper presents a decentralized 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, controller design can be transformed to an optimization problem with bilinear matrix inequality (BMI) constraints. To obtain a decentralized 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.