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Research Papers

Thermodynamics-Based Control of Network Systems

[+] Author and Article Information
Jordan M. Berg

Professor
Fellow of ASME
Department of Mechanical Engineering
and Nano Tech Center,
Texas Tech University,
Lubbock, TX 79409
e-mail: jordan.berg@ttu.edu

D. H. S. Maithripala

Senior Lecturer
Department of Mechanical Engineering,
Faculty of Engineering,
University of Peradeniya,
KY-400200, Sri Lanka
e-mail: smaithri@pdn.ac.lk

Qing Hui

Assistant Professor
Member of ASME
Department of Mechanical Engineering,
Texas Tech University,
Lubbock, TX 79409
e-mail: qing.hui@ttu.edu

Wassim M. Haddad

Professor
School of Aerospace Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: wm.haddad@aerospace.gatech.edu

This version of the first law holds only when work performed by the system on the environment, and work done by the environment on the system, are assumed to be zero.

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the Journal of Dynamic Systems, Measurements, and Control. Manuscript received May 11, 2012; final manuscript received February 19, 2013; published online May 21, 2013. Assoc. Editor: Sergey Nersesov.

J. Dyn. Sys., Meas., Control 135(5), 051003 (May 21, 2013) (11 pages) Paper No: DS-12-1134; doi: 10.1115/1.4023845 History: Received May 11, 2012; Revised February 19, 2013

The zeroth and first laws of thermodynamics define the concepts of thermal equilibrium and thermal energy. The second law of thermodynamics determines whether a particular transfer of thermal energy can occur. Collectively, these fundamental laws of nature imply that a closed collection of thermodynamic subsystems will tend to thermal equilibrium. This paper generalizes the concepts of energy, entropy, and temperature to undirected and directed networks of single integrators, and demonstrates how thermodynamic principles can be applied to the design of distributed consensus control algorithms for networked dynamical systems.

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Figures

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Fig. 1

(a) Lyapunov stable nonisolated equilibrium point (hollow). The perturbed trajectory need not converge to a new equilibrium. (b) Semistable nonisolated equilibrium point (hollow). Semistability guarantees convergence of the perturbed trajectory to a nearby equilibrium point (filled), and is a stronger property than Lyapunov stability.

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Fig. 3

Simple four-subsystem network

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Fig. 4

(a)–(c) Response of Case 1 showing consensus reached with energy conserved and entropy strictly increasing. (a) Consensus variables xi. (b) Energy UX. (c) Entropy SX. (d)–(f) Response of Case 2 showing consensus reached with energy conserved and entropy strictly increasing. (d) Consensus variables (1/2)xi2. (e) Energy UX. (f) Entropy SX

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Fig. 2

The subset of feasible temperatures T(UX) corresponding to total system energy UX

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Fig. 5

Directed network of four agents without a simple complete strong cycle

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Fig. 6

Simulation of the controlled four agent network for different choices of subsystem energy function. (a) Ui=xi2/2. (b) Ui=xi. (c) Ui=exi.

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