Time-delayed decentralized H∞ controller design for civil structures: A homotopy method through linear matrix inequalities

Traditional structural feedback control systems are centralized systems. The applications of these systems to large scale structures usually encounter a number of difficulties regarding system reliability, cost, and feedback latency. Decentralized control strategies offer promising alternatives that can address some of these difficulties. When making control decisions, decentralized controllers may only require data from sensors located in the neighborhood of a control device. Control decentralization lowers the demand on communication range in the sensing and control network, reduces feedback latency, and removes the risk associated with a centralized controller where single-point failure can paralyze the entire control system. This paper presents a time-delayed decentralized structural control strategy that aims to minimize the H_infin norm of the closed-loop system. Feedback time delay is included in the formulation for the decentralized controller design, which employs a homotopy method through linear matrix inequalities (LMI). Corresponding to certain decentralized feedback patterns, the homotopy method gradually degenerates a centralized control design into a decentralized control scheme. At each homotopy step, LMI constraints are satisfied to guarantee the performance requirement for the closed-loop H_infin norm. The proposed algorithm is validated through numerical simulations with an example structure.