Geometric Construction of Mixed Potentials

Hudon, Nicolas;Bao, J.;Ydstie, B. E.
(2013) IFAC Workshop on Thermodynamics Foundations of Mathematical Systems Theory (TFMST2013) — Location: Lyon, France (13.July.2013)

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  • Hudon, NicolasUCLouvain
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  • Bao, J.University of New South Wales, Australia
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  • Ydstie, B. E.Carnegie Mellon University
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Abstract
This paper presents an approach to construct mixed potentials, to be used as storage functions in the context of dissipative systems theory. The objective is to obtain, through a locally-defined geometric decomposition of a given drift vector field, a potential similar to the thermodynamically-defined availability function proposed in the literature. The mixed potential is obtained by homotopy integration of a differential one-form for the drift vector field which decomposes the system into an exact part (generated by a potential) and an anti-exact part (which is not directly generated by a potential). The key element in the proposed approach is the computation of an integrating factor for the anti-exact part of the dynamics.
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Hudon, N., Bao, J., & Ydstie, B. E. (2013). Geometric Construction of Mixed Potentials. Proceedings of TFMST2013. Published. IFAC Workshop on Thermodynamics Foundations of Mathematical Systems Theory (TFMST2013), Lyon, France. https://doi.org/10.3182/20130714-3-FR-4040.00016 (Original work published 2013)