Abstract
This article investigates the decentralized optimal linear quadratic regulation (LQR) control for large-scale systems. The large-scale system is defined over a weakly connected graph. Assume that the information is transmitted along the edges in the graph, and one sampling period is required for the information to travel across an edge. Under the above setup, the LQR control problem for the strongly connected graph case has been fully solved. However, for the weakly connected graph case, the existing results fail. In this article, a new decomposition approach for noise history is proposed. Then, the LQR control problem of large-scale systems defined over a weakly connected graph can be well solved. In addition, the decentralized realization of the control input is derived based on the decentralized information hierarchy graph (DIHG). The DIHG construction algorithm is also provided. Finally, the effectiveness of the developed design scheme is illustrated by a numerical example.
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