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Entropy 2016, 18(3), 99; doi:10.3390/e18030099

System Entropy Measurement of Stochastic Partial Differential Systems

Lab of Control and Systems Biology, National Tsing Hua University, Hsinchu 30013, Taiwan
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Author to whom correspondence should be addressed.
Academic Editor: Kevin H. Knuth
Received: 24 December 2015 / Revised: 7 March 2016 / Accepted: 8 March 2016 / Published: 18 March 2016
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Abstract

System entropy describes the dispersal of a system’s energy and is an indication of the disorder of a physical system. Several system entropy measurement methods have been developed for dynamic systems. However, most real physical systems are always modeled using stochastic partial differential dynamic equations in the spatio-temporal domain. No efficient method currently exists that can calculate the system entropy of stochastic partial differential systems (SPDSs) in consideration of the effects of intrinsic random fluctuation and compartment diffusion. In this study, a novel indirect measurement method is proposed for calculating of system entropy of SPDSs using a Hamilton–Jacobi integral inequality (HJII)-constrained optimization method. In other words, we solve a nonlinear HJII-constrained optimization problem for measuring the system entropy of nonlinear stochastic partial differential systems (NSPDSs). To simplify the system entropy measurement of NSPDSs, the global linearization technique and finite difference scheme were employed to approximate the nonlinear stochastic spatial state space system. This allows the nonlinear HJII-constrained optimization problem for the system entropy measurement to be transformed to an equivalent linear matrix inequalities (LMIs)-constrained optimization problem, which can be easily solved using the MATLAB LMI-toolbox (MATLAB R2014a, version 8.3). Finally, several examples are presented to illustrate the system entropy measurement of SPDSs. View Full-Text
Keywords: entropy maximization principle; Hamilton–Jacobi integral inequality (HJII); linear matrix inequalities (LMIs); stochastic partial differential system (SPDS); system entropy entropy maximization principle; Hamilton–Jacobi integral inequality (HJII); linear matrix inequalities (LMIs); stochastic partial differential system (SPDS); system entropy
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Chen, B.-S.; Hsieh, C.-Y.; Ho, S.-J. System Entropy Measurement of Stochastic Partial Differential Systems. Entropy 2016, 18, 99.

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