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In this paper, a cooperative Linear Quadratic Regulator (LQR) problem isinvestigated for multi-input systems, where each input is generated by an agentin a network. The input matrices are different and locally possessed by thecorresponding agents respectively, which can be regarded as different ways foragents to control the multi-input system. By embedding a fully distributedinformation fusion strategy, a novel cooperative LQR-based controller isproposed. Each agent only needs to communicate with its neighbors, rather thansharing information globally in a network. Moreover, only the jointcontrollability is required, which allows the multi-input system to beuncontrollable for every single agent or even all its neighbors. In particular,only one-time information exchange is necessary at every control step, whichsignificantly reduces the communication consumption. It is proved that theboundedness (convergence) of the controller gains is guaranteed fortime-varying (time-invariant) systems. Furthermore, the control performance ofthe entire system is ensured. Generally, the proposed controller achieves abetter trade-off between the control performance and the communicationoverhead, compared with the existing centralized/decentralized/consensus-basedLQR controllers. Finally, the effectiveness of the theoretical results isillustrated by several comparative numerical examples.

Linear Quadratic Regulator Design for Multi-input Systems with A Distributed Cooperative Strategy