多输入系统分布式协调线性二次型调节器设计
Linear Quadratic Regulator Design for Multi-input Systems with A Distributed Cooperative Strategy
摘要：
研究了多输入系统的合作线性二次型调节器（LQR）问题，其中每个输入由网络中的智能体产生。多输入系统的输入矩阵是不同的，并且分别由相应的智能体局部拥有，这可以看作是智能体控制多输入系统的不同方式。通过嵌入全分布式信息融合策略，提出了一种基于LQR的协同控制器。每个代理只需要与它的邻居进行通信，而不是在网络中全局共享信息。此外，只有联合可控性是必需的，这使得多输入系统是不可控的，为每个单一的代理，甚至所有的邻居。特别地，在每个控制步骤中仅需要一次信息交换，这显著地减少了通信消耗。对于时变（时不变）系统，证明了控制器增益的有界性（收敛性）。此外，还保证了整个系统的控制性能。一般来说，所提出的控制器实现了更好的控制性能和通信开销之间的权衡，与现有的集中式/分散式/基于共识的LQR控制器相比。最后，通过几个比较数值例子说明了理论结果的有效性。
英文摘要：
In this paper, 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 the joint controllability is required, which allows the multi-input system to be uncontrollable for every single agent or even all its neighbors. 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 control performance of the entire system is ensured. Generally, the proposed controller achieves a better trade-off between the control performance and the communication overhead, compared with the existing centralized/decentralized/consensus-based LQR controllers. Finally, the effectiveness of the theoretical results is illustrated by several comparative numerical examples.
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