Abstract:
In this paper, we show through examples, how the existing definitions of information transfer, namely directed information and transfer entropy fail to capture true causa...Show MoreMetadata
Abstract:
In this paper, we show through examples, how the existing definitions of information transfer, namely directed information and transfer entropy fail to capture true causal interaction between states in control dynamical system. Furthermore, existing definitions are shown to be too weak to have any implication on two of the most fundamental concepts in system theory, namely controllability and observability. We propose a new definition of information transfer, based on the ideas from dynamical system theory, and show that this new definition can not only capture true causal interaction between states, but also have implication on system controllability and observability properties. In particular, we show that non-zero transfer of information from input-to-state and state-to-output implies structural controllability and observability properties of the control dynamical system respectively. Analytical expression for information transfer between state-to-state, input-to-state, state-to-output, and input-to-output are provided for linear system. There is a natural extension of our proposed definition to define information transfer over n time steps and average information transfer over infinite time step. We show that the average information transfer in feedback control system between plant output and input is equal to the entropy of the open loop dynamics thereby re-deriving the Bode fundamental limitation results using the proposed definition of transfer.
Published in: 2016 IEEE 55th Conference on Decision and Control (CDC)
Date of Conference: 12-14 December 2016
Date Added to IEEE Xplore: 29 December 2016
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