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Complexity, robustness, self-organization, swarms, and system thermodynamics

Authors
Journal
Nonlinear Analysis Real World Applications
1468-1218
Publisher
Elsevier
Publication Date
Volume
10
Issue
1
Identifiers
DOI: 10.1016/j.nonrwa.2008.02.036
Keywords
  • System Complexity
  • Robustness
  • Swarms
  • Continuum Thermodynamics
  • Entropy
  • Boundary Control
  • Semistability
  • Consensus Control
  • Advection–Diffusion Equation
Disciplines
  • Mathematics
  • Physics

Abstract

Abstract In this paper, we develop a thermodynamic framework for addressing consensus problems for Eulerian swarm models. Specifically, we present a distributed boundary controller architecture involving the exchange of information between uniformly distributed swarms over an n -dimensional (not necessarily Euclidian) space that guarantees that the closed-loop system is consistent with basic thermodynamic principles. In addition, we establish the existence of a unique continuously differentiable entropy functional for all equilibrium and non-equilibrium states of our thermodynamically consistent dynamical system. Information consensus and semistability are shown using the well-known Sobolev embedding theorems and the notion of generalized (or weak) solutions. Finally, since the closed-loop system is guaranteed to satisfy basic thermodynamic principles, robustness to individual agent failures and unplanned individual agent behavior is automatically guaranteed.

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