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Research Papers

# On Timescale Separation in Networked Systems With Intermittent Communication

[+] Author and Article Information

Control Research Laboratory,
William E. Boeing Department of Aeronautics
and Astronautics,
University of Washington,
Seattle, WA 98195

Anshu Narang-Siddarth

Control Research Laboratory,
William E. Boeing Department of Aeronautics
and Astronautics,
University of Washington,
Seattle, WA 98195
e-mail: anshu@aa.washington.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received May 2, 2017; final manuscript received September 19, 2017; published online December 19, 2017. Assoc. Editor: Jongeun Choi.

J. Dyn. Sys., Meas., Control 140(5), 051011 (Dec 19, 2017) (9 pages) Paper No: DS-17-1234; doi: 10.1115/1.4038096 History: Received May 02, 2017; Revised September 19, 2017

## Abstract

This paper studies the multiple timescale behavior that is induced by dynamic coupling between continuous-time and discrete-time systems, and that arises naturally in distributed networked systems. An order reduction method is proposed that establishes a mathematically rigorous separation principle between the fast evolution of the continuous-time dynamics and the slow updates of the discrete-time dynamics. Quantitative conditions on the discrete update rate are then derived that ensure the stability of the coupled dynamics based on the behavior of the isolated systems. The results are illustrated for a distributed network of satellites whose attitudes evolve continuously while communicating intermittently over the network.

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## Figures

Fig. 1

Evolution of the coupled discrete-time network states x and continuous-time agent states y as the agents evolve toward their state-dependent equilibrium h(x, t) over each interval

Fig. 2

Distributed attitude consensus for a network of satellites with intermittent communication: (a) the set of reference attitudes updates distributively at time tk over a barbell graph and (b) each satellite's attitude evolves toward its reference attitude between discrete updates

Fig. 3

Comparison of reduced-order models and true evolution of one satellite's state as τ increases: (a) continuous evolution of the first MRP within a normalized interval and (b) discrete evolution of the first MRP reference commands

Fig. 4

Evolution of all 8 satellites' attitudes, showing instability for small τ: (a) τ=33  s=τ⋆ and (b) τ=10  s<τ⋆

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