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This paper presents an approach to recursively estimate the simplest linear model that approximates the time-varying local behaviors from imperfect (noisy and incomplete) measurements in the internet of things (IoT) based distributed decision-making problems. We first show that the problem of finding the lowest order model for a multi-input single-output system is a cardinality (ℓ 0 ) optimization problem, known to be NP-hard.To solve the problem a simpler approach is proposed which uses the recently developed atomic norm concept and the modified Frank-Wolfe (mFW) algorithm is introduced. Further, the paper computes the minimum data-rate required for computing the models with imperfect measurements. The proposed approach is illustrated on a building heating, ventilation, and air-conditioning (HVAC) control system that aims at optimizing energy consumption in commercial buildings using IoT devices in a distributed manner. The HVAC control application requires recursive thermal dynamical model updates due to frequently changing conditions and non-linear dynamics. We show that the method proposed in this paper can approximate such complex dynamics on single-board computers interfaced to sensors using unreliable communication channels. Real-time experiments on HVAC systems and simulation studies are used to illustrate the proposed method.

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