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Minimum Information Exchange in Distributed Systems

Efficient representation of observed data has many applications in various domains of engineering and science. Having a good representation of data, downstream tasks such as classification, regression, and decision making become easier. Even though representing still datasets such as images is a living branch in machine learning, representation of dynamical systems has received less attention. One area where such representation is beneficial is distributed control systems. Distributed systems can be modeled as graphs consisting of nodes that exchange information. This exchange is often costly (e.g. when happening over a shared network) and thus needs to be minimized, while a predefined objective is still satisfied. In this work, we present a method to represent a dynamical system efficiently as a combination of state and local approximate model to fulfill a criterion similar to Minimum Description Length (MDL) principle. MDL is used in machine learning and statistics to state that the best explanation for data is one which yields the best compression. We empirically show the efficacy of the method for several dynamical systems and justify the logic behind the proposed criterion for model selection. Moreover, the method is applied to event-triggered state estimation, used in monitoring and control, and shown to yield a unified framework of previous approaches.