分布式线性二次型最优控制：局部计算全局作用
Distributed Linear Quadratic Optimal Control: Compute Locally and Act Globally
摘要：
在本文中，我们考虑了单积分动态代理网络的分布线性二次控制问题。我们首先建立了一个一般的制定分布式LQ问题，并表明，最优控制增益依赖于网络上的全球信息。因此，最佳协议只能以集中的方式计算。为了克服这一缺点，我们提出了以分散方式计算的协议的设计。我们将把全局成本泛函写成局部成本泛函的和，每个局部成本泛函与一个代理相关联。为了实现受控网络的“良好”性能，每个代理然后计算自己的本地增益，使用其相邻代理的采样信息。这种分散的计算只会导致次优的全局网络行为。然而，我们将证明由此产生的网络将达成共识。最后给出了一个仿真例子来说明该协议的性能。
英文摘要：
In this paper we consider the distributed linear quadratic control problem for networks of agents with single integrator dynamics. We first establish a general formulation of the distributed LQ problem and show that the optimal control gain depends on global information on the network. Thus, the optimal protocol can only be computed in a centralized fashion. In order to overcome this drawback, we propose the design of protocols that are computed in a decentralized way. We will write the global cost functional as a sum of local cost functionals, each associated with one of the agents. In order to achieve 'good' performance of the controlled network, each agent then computes its own local gain, using sampled information of its neighboring agents. This decentralized computation will only lead to suboptimal global network behavior. However, we will show that the resulting network will reach consensus. A simulation example is provided to illustrate the performance of the proposed protocol.
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