Estimation of initial functions for systems with delays from discrete measurements
The work presents a gradient-based approach to estimation of initial functions of time delay elements appearing in models of dynamical systems. It is shown how to generate the gradient of the estimation objective function in the initial function space using adjoint sensitivity analysis. It is assume...
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| Format: | Article |
| Language: | English |
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AIMS Press
2017-01-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017011 |
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| _version_ | 1832590072135811072 |
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| author | Krzysztof Fujarewicz |
| author_facet | Krzysztof Fujarewicz |
| author_sort | Krzysztof Fujarewicz |
| collection | DOAJ |
| description | The work presents a gradient-based approach to estimation of initial functions of time delay elements appearing in models of dynamical systems. It is shown how to generate the gradient of the estimation objective function in the initial function space using adjoint sensitivity analysis. It is assumed that the system is continuous-time and described by ordinary differential equations with delays but the estimation is done based on discrete-time measurements of the signals appearing in the system. Results of gradient-based estimation of initial functions for exemplary models are presented and discussed. |
| format | Article |
| id | doaj-art-a6fd8f8551ef4a2498754c98ab5ced0a |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-a6fd8f8551ef4a2498754c98ab5ced0a2025-01-24T02:39:32ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-01-0114116517810.3934/mbe.2017011Estimation of initial functions for systems with delays from discrete measurementsKrzysztof Fujarewicz0Silesian University of Technology, Akademicka 16, 44-100 Gliwice, PolandThe work presents a gradient-based approach to estimation of initial functions of time delay elements appearing in models of dynamical systems. It is shown how to generate the gradient of the estimation objective function in the initial function space using adjoint sensitivity analysis. It is assumed that the system is continuous-time and described by ordinary differential equations with delays but the estimation is done based on discrete-time measurements of the signals appearing in the system. Results of gradient-based estimation of initial functions for exemplary models are presented and discussed.https://www.aimspress.com/article/doi/10.3934/mbe.2017011delay differential equationssystems with delaysinitial functionsparameter estimationadjoint sensitivity analysissampled systems |
| spellingShingle | Krzysztof Fujarewicz Estimation of initial functions for systems with delays from discrete measurements Mathematical Biosciences and Engineering delay differential equations systems with delays initial functions parameter estimation adjoint sensitivity analysis sampled systems |
| title | Estimation of initial functions for systems with delays from discrete measurements |
| title_full | Estimation of initial functions for systems with delays from discrete measurements |
| title_fullStr | Estimation of initial functions for systems with delays from discrete measurements |
| title_full_unstemmed | Estimation of initial functions for systems with delays from discrete measurements |
| title_short | Estimation of initial functions for systems with delays from discrete measurements |
| title_sort | estimation of initial functions for systems with delays from discrete measurements |
| topic | delay differential equations systems with delays initial functions parameter estimation adjoint sensitivity analysis sampled systems |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017011 |
| work_keys_str_mv | AT krzysztoffujarewicz estimationofinitialfunctionsforsystemswithdelaysfromdiscretemeasurements |