Mean-field models are a popular tool in a variety of fields. They provide an un-derstanding 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 in-troduced in our own recent work. In numerical results it was found that the associated mean-field 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 ∈ 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 sig-nal {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 lineariza-tion, Re (G(jω)) = PSDY (ω) ≥ 0 ω ∈ 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).

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