Time-Delayed Decentralized H-Infinity Controller Design for Civil Structures: a Homotopy Method Through Linear Matrix Inequalities

Traditional structural feedback control systems are centralized systems, whose applications to large scale structures encounter a number of practical difficulties in terms of 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 can be designed to acquire 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-infinity 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-infinity norm. The proposed algorithm is validated through numerical simulations with an example structure.