Distributed Cooperative LQR Design for Multi-Input Linear Systems

In this article, a cooperative linear quadratic regulator (LQR) problem is investigated for multi-input systems, where each input is generated by an agent in a network. The input matrices are different and locally possessed by the corresponding agents, respectively, which can be regarded as different ways for agents to control the multi-input system. By embedding a fully distributed information fusion strategy, a novel cooperative LQR-based controller is proposed. Each agent only needs to communicate with its neighbors, rather than sharing information globally in a network. Moreover, only joint controllability is required, which allows the multi-input system to be uncontrollable for every single agent. In particular, only one-time information exchange is necessary at every control step, which significantly reduces the communication consumption. It is proved that the boundedness (convergence) of the controller gains is guaranteed for time-varying (time-invariant) systems. Furthermore, the performance of the entire system is ensured. Generally, the proposed controller achieves a better tradeoff between the control performance and the communication overhead compared with existing distributed LQR-based controllers. Finally, the effectiveness of the theoretical results is illustrated by several comparative numerical examples.