Distributionally robust parameter estimation for nonlinear fed-batch switched time-delay system with moment constraints of uncertain measured output data
In this paper, we investigated a nonlinear continuous-time switched time-delay (NCTSTD) system for glycerol fed-batch bioconversion to 1, 3-propanediol with unknown time-delay and system parameters. The measured output data was uncertain, while the first moment information about its distribution was...
Saved in:
| Main Authors: | , , , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2024-10-01
|
| Series: | Electronic Research Archive |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2024272 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832590742943432704 |
|---|---|
| author | Sida Lin Jinlong Yuan Zichao Liu Tao Zhou An Li Chuanye Gu Kuikui Gao Jun Xie |
| author_facet | Sida Lin Jinlong Yuan Zichao Liu Tao Zhou An Li Chuanye Gu Kuikui Gao Jun Xie |
| author_sort | Sida Lin |
| collection | DOAJ |
| description | In this paper, we investigated a nonlinear continuous-time switched time-delay (NCTSTD) system for glycerol fed-batch bioconversion to 1, 3-propanediol with unknown time-delay and system parameters. The measured output data was uncertain, while the first moment information about its distribution was available. Our goal was to identify these unknown quantities under the environment of uncertain measurement output data. A distributionally robust parameter estimation problem (i.e., a bi-level parameter estimation (BLPE) problem) subject to the NCTSTD system was presented, where the expectation of the discrepancy between the output of the NCTSTD system and the uncertain measured output data with respect to its probability distributions was included in the cost functional. By applying the duality theory, the BLPE problem was transformed into a single-level parameter estimation (SLPE) problem with non-smooth term approximated by a smoothing technique and its error analysis was given. Then, the gradients of the cost function of the SLPE problem were derived. A hybrid optimization algorithm was proposed for solving the SLPE problem. The paper concluded by presenting the simulation results. |
| format | Article |
| id | doaj-art-4f87173ba54545e6b8404c78a53da7cb |
| institution | Kabale University |
| issn | 2688-1594 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj-art-4f87173ba54545e6b8404c78a53da7cb2025-01-23T07:52:53ZengAIMS PressElectronic Research Archive2688-15942024-10-0132105889591310.3934/era.2024272Distributionally robust parameter estimation for nonlinear fed-batch switched time-delay system with moment constraints of uncertain measured output dataSida Lin0Jinlong Yuan1Zichao Liu2Tao Zhou3An Li4Chuanye Gu5Kuikui Gao6Jun Xie7School of Science, Dalian Maritime University, Dalian 116026, ChinaSchool of Science, Dalian Maritime University, Dalian 116026, ChinaSchool of Science, Dalian Maritime University, Dalian 116026, ChinaInstitute for Intelligent Systems Research and Innovation (IISRI), Deakin University, Geelong, VIC, 3217, AustraliaSchool of Mathematical Sciences, Xiamen University, Xiamen 361005, ChinaSchool of Management, Guangzhou University, Guangzhou 510006, ChinaAyata Inc., 2700 Post Oak Blvd, 21st Floor Houston, TX 77056, USATeaching and Research Office of Mathematics, Department of Basics, PLA Dalian Naval Academy, Dalian 116018, Liaoning, ChinaIn this paper, we investigated a nonlinear continuous-time switched time-delay (NCTSTD) system for glycerol fed-batch bioconversion to 1, 3-propanediol with unknown time-delay and system parameters. The measured output data was uncertain, while the first moment information about its distribution was available. Our goal was to identify these unknown quantities under the environment of uncertain measurement output data. A distributionally robust parameter estimation problem (i.e., a bi-level parameter estimation (BLPE) problem) subject to the NCTSTD system was presented, where the expectation of the discrepancy between the output of the NCTSTD system and the uncertain measured output data with respect to its probability distributions was included in the cost functional. By applying the duality theory, the BLPE problem was transformed into a single-level parameter estimation (SLPE) problem with non-smooth term approximated by a smoothing technique and its error analysis was given. Then, the gradients of the cost function of the SLPE problem were derived. A hybrid optimization algorithm was proposed for solving the SLPE problem. The paper concluded by presenting the simulation results.https://www.aimspress.com/article/doi/10.3934/era.2024272distributionally robust parameter estimationuncertain measured output datacontinuous-time switched time-delay systemerror analysishybrid algorithm |
| spellingShingle | Sida Lin Jinlong Yuan Zichao Liu Tao Zhou An Li Chuanye Gu Kuikui Gao Jun Xie Distributionally robust parameter estimation for nonlinear fed-batch switched time-delay system with moment constraints of uncertain measured output data Electronic Research Archive distributionally robust parameter estimation uncertain measured output data continuous-time switched time-delay system error analysis hybrid algorithm |
| title | Distributionally robust parameter estimation for nonlinear fed-batch switched time-delay system with moment constraints of uncertain measured output data |
| title_full | Distributionally robust parameter estimation for nonlinear fed-batch switched time-delay system with moment constraints of uncertain measured output data |
| title_fullStr | Distributionally robust parameter estimation for nonlinear fed-batch switched time-delay system with moment constraints of uncertain measured output data |
| title_full_unstemmed | Distributionally robust parameter estimation for nonlinear fed-batch switched time-delay system with moment constraints of uncertain measured output data |
| title_short | Distributionally robust parameter estimation for nonlinear fed-batch switched time-delay system with moment constraints of uncertain measured output data |
| title_sort | distributionally robust parameter estimation for nonlinear fed batch switched time delay system with moment constraints of uncertain measured output data |
| topic | distributionally robust parameter estimation uncertain measured output data continuous-time switched time-delay system error analysis hybrid algorithm |
| url | https://www.aimspress.com/article/doi/10.3934/era.2024272 |
| work_keys_str_mv | AT sidalin distributionallyrobustparameterestimationfornonlinearfedbatchswitchedtimedelaysystemwithmomentconstraintsofuncertainmeasuredoutputdata AT jinlongyuan distributionallyrobustparameterestimationfornonlinearfedbatchswitchedtimedelaysystemwithmomentconstraintsofuncertainmeasuredoutputdata AT zichaoliu distributionallyrobustparameterestimationfornonlinearfedbatchswitchedtimedelaysystemwithmomentconstraintsofuncertainmeasuredoutputdata AT taozhou distributionallyrobustparameterestimationfornonlinearfedbatchswitchedtimedelaysystemwithmomentconstraintsofuncertainmeasuredoutputdata AT anli distributionallyrobustparameterestimationfornonlinearfedbatchswitchedtimedelaysystemwithmomentconstraintsofuncertainmeasuredoutputdata AT chuanyegu distributionallyrobustparameterestimationfornonlinearfedbatchswitchedtimedelaysystemwithmomentconstraintsofuncertainmeasuredoutputdata AT kuikuigao distributionallyrobustparameterestimationfornonlinearfedbatchswitchedtimedelaysystemwithmomentconstraintsofuncertainmeasuredoutputdata AT junxie distributionallyrobustparameterestimationfornonlinearfedbatchswitchedtimedelaysystemwithmomentconstraintsofuncertainmeasuredoutputdata |