Passive dynamics in mean field control
Passive dynamics in mean field control
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平均场控制中的被动动力学
DOI：
10.1109/cdc.2014.7039805
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Sean P. Meyn
中科院分区：
文献类型：
--
作者：
A. Bušić;Sean P. Meyn
平均场模型在许多领域都是一种流行的工具。它们提供了对大量粒子或人或其他“自利主体”之间相互作用的影响的理解，并且是分布式控制中日益流行的工具。本文考虑了我们在最近的工作中引入的一种特殊的随机分布式控制体系结构。数值结果表明，相关联的平均场模型具有较好的控制性能。特别地，当将其视为一个输入输出系统时，发现其线性化是最小相位。在本文中，我们将仔细研究控制模型。结果表明：(1)将Todorov的Markov决策过程框架扩展到连续时间模型，其中“控制成本”是基于相对熵的。这是构造一系列马尔可夫生成器的基础，由标量ζ E r参数化。（ii）提出了一种分散的控制体系结构，其中每个代理都演变为受控的马尔可夫过程。中央机构向每个代理广播一个公共控制信号{ζt}。中央机构根据马尔可夫代理的聚合标量输出选择{ζt}。这是平均场模型的基础。（iii）如果无控制系统（ζ 0）是可逆的马尔可夫过程，则线性化得到的传递函数G的等式成立，Re (G(jω)) = PSDY(ω)≥0 ω E R，其中右手边表示任意一个马尔可夫过程（ζ 0）输出的功率谱密度。
Mean-field models are a popular tool in a variety of fields. They provide an understanding of the impact of interactions among a large number of particles or people or other “self-interested agents”, and are an increasingly popular tool in distributed control. This paper considers a particular randomized distributed control architecture introduced in our own recent work. In numerical results it was found that the associated meanfield model had attractive properties for purposes of control. In particular, when viewed as an input-output system, its linearization was found to be minimum phase. In this paper we take a closer look at the control model. The results are summarized as follows: (i) The Markov Decision Process framework of Todorov is extended to continuous time models, in which the “control cost” is based on relative entropy. This is the basis of the construction of a family of Markovian generators, parameterized by a scalar ζ E R. (ii) A decentralized control architecture is proposed in which each agent evolves as a controlled Markov process. A central authority broadcasts a common control signal {ζt} to each agent. The central authority chooses {ζt} based on an aggregate scalar output of the Markovian agents. This is the basis of the mean field model. (iii) Provided the control-free system (with ζ 0) is a reversible Markov process, the following identity holds for the transfer function G obtained from the linearization, Re (G(jω)) = PSDY(ω) ≥ 0 ω E R , where the right hand side denotes the power spectral density for the output of any one of the individual Markov processes (with ζ 0).