Causality preserving information transfer measure for control dynamical system

Sinha, Subhrajit; Vaidya, Umesh

doi:10.1109/cdc.2016.7799401

Cited by 22 publications

(45 citation statements)

References 17 publications

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“…In this section, we review the basics of information transfer in a dynamical system. For details, we refer the reader to [1], [2]. Consider the dynamical system z(t + 1) = F (z(t)) + ξ(t), where F = [F x F y ] , such that where x ∈ R |x| , y ∈ R |y| (here | · | denotes the dimension of {·}), z = (x , y ) , and Fx : R |x|+|y| → R |x| , Fy : R |x|+|y| → R |y| are assumed to be continuously differentiable and ξ(t) = (ξx(t) , ξy(t) ) is additive independent and identically distributed noise.…”

Section: Information Transfer In Dynamical Systemsmentioning

confidence: 99%

“…We have following definition of information transfer from x → y going from time step t to t + 1. Definition 1: [Information transfer] [1], [2] The information transfer from x to y for the dynamical system (1), as the system evolves from time t to time t+1 (denoted by [Tx→y]), is given by following formula…”

Section: Information Transfer In Dynamical Systemsmentioning

confidence: 99%

“…Financial support from the National Science Foundation grant ECCS-1150405 and CNS-1329915 is gratefully acknowledged. S. Sinha The main idea behind the definition of information transfer proposed in [23] is the concept of freezing part of the system dynamics and has similarity with the definition of information transfer proposed in [1], [2]. The concept of freezing elevates the problem associated with other information-based causality measure and captures the true causal structure [1].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On Data-Driven Computation of Information Transfer for Causal Inference in Discrete-Time Dynamical Systems

Sinha

Vaidya

2020

J Nonlinear Sci

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In this paper, we provide a novel approach to capture causal interaction in a dynamical system from time-series data. In [1], we have shown that the existing measures of information transfer, namely directed information, granger causality and transfer entropy fail to capture true causal interaction in dynamical system and proposed a new definition of information transfer that captures true causal interaction. The main contribution of this paper is to show that the proposed definition of information transfer in [1] [2] can be computed from time-series data. We use transfer operator theoretic framework involving Perron-Frobenius and Koopman operators for the data-driven approximation of the system dynamics and for the computation of information transfer. Several examples involving linear and nonlinear system dynamics are presented to verify the efficiency of the developed algorithm.

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Section: Information Transfer In Dynamical Systemsmentioning

confidence: 99%

Section: Information Transfer In Dynamical Systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On Data-Driven Computation of Information Transfer for Causal Inference in Discrete-Time Dynamical Systems

Sinha

Vaidya

2020

J Nonlinear Sci

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“…The information transfer thus defined, can be extended to define information transfer between the various signals in a control dynamical system, namely information transfer from input to state, input to output and state to output. For details see [15].…”

Section: Information Transfer Based Participation and Stability Amentioning

confidence: 99%

On Information Transfer-Based Characterization of Power System Stability

Sinha

Sharma

Vaidya

et al. 2019

IEEE Trans. Power Syst.

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In this paper, we present a novel approach to identify the generators and states responsible for the small-signal stability of power networks. To this end, the newly developed notion of information transfer between the states of a dynamical system is used. In particular, using the concept of information transfer, which characterizes influence between the various states and a linear combination of states of a dynamical system, we identify the generators and states which are responsible for causing instability of the power network. While characterizing influence from state to state, information transfer can also describe influence from state to modes thereby generalizing the well-known notion of participation factor while at the same time overcoming some of the limitations of the participation factor. The developed framework is applied to study the three bus system identifying various cause of instabilities in the system. The simulation study is extended to IEEE 39 bus system. arXiv:1809.07704v1 [cs.SY]

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“…For example, the directed information [25][26][27][28] and Schreiber's transfer entropy [29] are commonly applied to infer the causality structure and characterize the information transfer process. Moreover, referring to the idea from dynamical system theory, new information transfer measures are proposed to indicate the causality between states and control the systems [30][31][32].…”

Section: Related Work For Information Measures In Big Datamentioning

confidence: 99%

Recognizing Information Feature Variation: Message Importance Transfer Measure and Its Applications in Big Data

Sheng

Liu

Fan

2018

Entropy

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Information transfer that characterizes the information feature variation can have a crucial impact on big data analytics and processing. Actually, the measure for information transfer can reflect the system change from the statistics by using the variable distributions, similar to Kullback-Leibler (KL) divergence and Renyi divergence. Furthermore, to some degree, small probability events may carry the most important part of the total message in an information transfer of big data. Therefore, it is significant to propose an information transfer measure with respect to the message importance from the viewpoint of small probability events. In this paper, we present the message importance transfer measure (MITM) and analyze its performance and applications in three aspects. First, we discuss the robustness of MITM by using it to measuring information distance. Then, we present a message importance transfer capacity by resorting to the MITM and give an upper bound for the information transfer process with disturbance. Finally, we apply the MITM to discuss the queue length selection, which is the fundamental problem of caching operation on mobile edge computing.

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Causality preserving information transfer measure for control dynamical system

Cited by 22 publications

References 17 publications

On Data-Driven Computation of Information Transfer for Causal Inference in Discrete-Time Dynamical Systems

On Data-Driven Computation of Information Transfer for Causal Inference in Discrete-Time Dynamical Systems

On Information Transfer-Based Characterization of Power System Stability

Recognizing Information Feature Variation: Message Importance Transfer Measure and Its Applications in Big Data

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