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Research Papers

On Timescale Separation in Networked Systems With Intermittent Communication

[+] Author and Article Information
Armand Awad

Advanced Dynamics, Validation &
Control Research Laboratory,
William E. Boeing Department of Aeronautics
and Astronautics,
University of Washington,
Seattle, WA 98195
e-mail: awada@uw.edu

Anshu Narang-Siddarth

Advanced Dynamics, Validation &
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

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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References

Sedghi, B. , 2003, “ Control Design of Hybrid Systems Via Dehybridization,” Ph.D. thesis, Ecole Polytechnique Federale De Lausanne, Lausanne, Switzerland. https://infoscience.epfl.ch/record/28440/files/fulltext.pdf
Chung, S.-J. , Ahsun, U. , and Slotine, J.-J. E. , 2009, “ Application of Synchronization to Formation Flying Spacecraft: Lagrangian Approach,” J. Guid., Control, Dyn., 32(2), pp. 512–526. [CrossRef]
Li, Z. , Ren, W. , Liu, X. , and Fu, M. , 2013, “ Consensus of Multi-Agent Systems With General Linear and Lipschitz Nonlinear Dynamics Using Distributed Adaptive Protocols,” IEEE Trans. Autom. Control, 58(7), pp. 1786–1791. [CrossRef]
Naghshtabrizi, P. , Hespanha, J. P. , and Teel, A. R. , 2006, “ On the Robust Stability and Stabilization of Sampled-Data Systems: A Hybrid System Approach,” 45th IEEE Conference on Decision and Control (CDC), San Diego, CA, Dec. 13–15, pp. 4873–4878.
Jentzen, A. , Leber, F. , Schneisgen, D. , Berger, A. , and Siegmund, S. , 2010, “ An Improved Maximum Allowable Transfer Interval for Lp-Stability of Networked Control Systems,” IEEE Trans. Autom. Control, 55(1), pp. 179–184. [CrossRef]
Narang-Siddarth, A. , and Valasek, J. , 2014, Nonlinear Time Scale Systems in Standard and Nonstandard Forms, SIAM, Philadelphia, PA. [CrossRef]
Khalil, H. K. , 2001, Nonlinear Systems, 3rd ed., Prentice Hall, Upper Saddle River, NJ.
Awad, A. , Chapman, A. , Schoof, E. , Narang-Siddarth, A. , and Mesbahi, M. , 2015, “ Time-Scale Separation on Networks: Consensus, Tracking, and State-Dependent Interactions,” 54th IEEE Conference on Decision and Control (CDC), Osaka, Japan, Dec. 15–18, pp. 6172–6177.
Bouyekhf, R. , and El Moudni, A. , 1997, “ On Analysis of Discrete Singularly Perturbed Non-Linear Systems: Application to the Study of Stability Properties,” J. Franklin Inst., 334(2), pp. 199–212. [CrossRef]
Veliov, V. , 1997, “ A Generalization of the Tikhonov Theorem for Singularly Perturbed Differential Inclusions,” J. Dyn. Control Syst., 3(3), pp. 291–319. [CrossRef]
Bainov, D. , and Covachev, V. , 1994, Impulsive Differential Equations With a Small Parameter, World Scientific Publishing, Singapore. [CrossRef]
Chen, W. H. , Yuan, G. , and Zheng, W. X. , 2013, “ Robust Stability of Singularly Perturbed Impulsive Systems Under Nonlinear Perturbation,” IEEE Trans. Autom. Control, 58(1), pp. 168–174. [CrossRef]
Sanfelice, R. G. , and Teel, A. R. , 2011, “ On Singular Perturbations Due to Fast Actuators in Hybrid Control Systems,” Automatica, 47(4), pp. 692–701. [CrossRef]
Wang, W. , Teel, A. R. , and Nešić, D. , 2012, “ Analysis for a Class of Singularly Perturbed Hybrid Systems Via Averaging,” Automatica, 48(6), pp. 1057–1068. [CrossRef]
Siljak, D. D. , 1978, Large-Scale Dynamical Systems, Elsevier, New York.
Zečević, A. I. , and Šiljak, D. D. , 2008, “ Control Design With Arbitrary Information Structure Constraints,” Automatica, 44(10), pp. 2642–2647.
Sghaier Tlili, A. , 2017, “ Linear Matrix Inequality Robust Tracking Control Conditions for Nonlinear Disturbed Interconnected Systems,” ASME J. Dyn. Syst., Meas., Control, 139(6), p. 061002.
Haddad, W. M. , Chellaboina, V. S. , and Nersesov, S. G. , 2014, Impulsive and Hybrid Dynamical Systems: Stability, Dissipativity, and Control, Princeton University Press, Princeton, NJ.
Goebel, R. , Sanfelice, R. G. , and Teel, A. R. , 2009, “ Hybrid Dynamical Systems,” IEEE Control Syst., 29(2), pp. 28–93. [CrossRef]
Mesbahi, M. , and Egerstedt, M. , 2010, Graph Theoretic Methods in Multiagent Networks, Princeton University Press, Princeton, NJ. [CrossRef]
Schaub, H. , and Junkins, J. L. , 2003, Analytical Mechanics of Space Systems, AIAA, Reston, VA. [CrossRef]

Figures

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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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