System Entropy Measurement of Stochastic Partial Differential Systems
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 dyna...
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| Format: | Article |
| Language: | English |
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MDPI AG
2016-03-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/18/3/99 |
| _version_ | 1798034963473367040 |
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| author | Bor-Sen Chen Chao-Yi Hsieh Shih-Ju Ho |
| author_facet | Bor-Sen Chen Chao-Yi Hsieh Shih-Ju Ho |
| author_sort | Bor-Sen Chen |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T20:51:39Z |
| format | Article |
| id | doaj.art-17e0325673e348808b15da2233d72f16 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T20:51:39Z |
| publishDate | 2016-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-17e0325673e348808b15da2233d72f162022-12-22T04:03:49ZengMDPI AGEntropy1099-43002016-03-011839910.3390/e18030099e18030099System Entropy Measurement of Stochastic Partial Differential SystemsBor-Sen Chen0Chao-Yi Hsieh1Shih-Ju Ho2Lab of Control and Systems Biology, National Tsing Hua University, Hsinchu 30013, TaiwanLab of Control and Systems Biology, National Tsing Hua University, Hsinchu 30013, TaiwanLab of Control and Systems Biology, National Tsing Hua University, Hsinchu 30013, TaiwanSystem 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.http://www.mdpi.com/1099-4300/18/3/99entropy maximization principleHamilton–Jacobi integral inequality (HJII)linear matrix inequalities (LMIs)stochastic partial differential system (SPDS)system entropy |
| spellingShingle | Bor-Sen Chen Chao-Yi Hsieh Shih-Ju Ho System Entropy Measurement of Stochastic Partial Differential Systems Entropy entropy maximization principle Hamilton–Jacobi integral inequality (HJII) linear matrix inequalities (LMIs) stochastic partial differential system (SPDS) system entropy |
| title | System Entropy Measurement of Stochastic Partial Differential Systems |
| title_full | System Entropy Measurement of Stochastic Partial Differential Systems |
| title_fullStr | System Entropy Measurement of Stochastic Partial Differential Systems |
| title_full_unstemmed | System Entropy Measurement of Stochastic Partial Differential Systems |
| title_short | System Entropy Measurement of Stochastic Partial Differential Systems |
| title_sort | system entropy measurement of stochastic partial differential systems |
| topic | entropy maximization principle Hamilton–Jacobi integral inequality (HJII) linear matrix inequalities (LMIs) stochastic partial differential system (SPDS) system entropy |
| url | http://www.mdpi.com/1099-4300/18/3/99 |
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