Distributed Parameter State Estimation for the Gray–Scott Reaction-Diffusion Model
A constructive approach is provided for the reconstruction of stationary and non-stationary patterns in the one-dimensional Gray-Scott model, utilizing measurements of the system state at a finite number of locations. Relations between the parameters of the model and the density of the sensor locati...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-10-01
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| Series: | Systems |
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| Online Access: | https://www.mdpi.com/2079-8954/9/4/71 |
| _version_ | 1797500319307923456 |
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| author | Petro Feketa Alexander Schaum Thomas Meurer |
| author_facet | Petro Feketa Alexander Schaum Thomas Meurer |
| author_sort | Petro Feketa |
| collection | DOAJ |
| description | A constructive approach is provided for the reconstruction of stationary and non-stationary patterns in the one-dimensional Gray-Scott model, utilizing measurements of the system state at a finite number of locations. Relations between the parameters of the model and the density of the sensor locations are derived that ensure the exponential convergence of the estimated state to the original one. The designed observer is capable of tracking a variety of complex spatiotemporal behaviors and self-replicating patterns. The theoretical findings are illustrated in particular numerical case studies. The results of the paper can be used for the synchronization analysis of the master–slave configuration of two identical Gray–Scott models coupled via a finite number of spatial points and can also be exploited for the purposes of feedback control applications in which the complete state information is required. |
| first_indexed | 2024-03-10T03:00:12Z |
| format | Article |
| id | doaj.art-9c8122ef6ed54a288238a4e82dda9262 |
| institution | Directory Open Access Journal |
| issn | 2079-8954 |
| language | English |
| last_indexed | 2024-03-10T03:00:12Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Systems |
| spelling | doaj.art-9c8122ef6ed54a288238a4e82dda92622023-11-23T10:47:29ZengMDPI AGSystems2079-89542021-10-01947110.3390/systems9040071Distributed Parameter State Estimation for the Gray–Scott Reaction-Diffusion ModelPetro Feketa0Alexander Schaum1Thomas Meurer2Automation and Control Group, Kiel University, 24143 Kiel, GermanyAutomation and Control Group, Kiel University, 24143 Kiel, GermanyAutomation and Control Group, Kiel University, 24143 Kiel, GermanyA constructive approach is provided for the reconstruction of stationary and non-stationary patterns in the one-dimensional Gray-Scott model, utilizing measurements of the system state at a finite number of locations. Relations between the parameters of the model and the density of the sensor locations are derived that ensure the exponential convergence of the estimated state to the original one. The designed observer is capable of tracking a variety of complex spatiotemporal behaviors and self-replicating patterns. The theoretical findings are illustrated in particular numerical case studies. The results of the paper can be used for the synchronization analysis of the master–slave configuration of two identical Gray–Scott models coupled via a finite number of spatial points and can also be exploited for the purposes of feedback control applications in which the complete state information is required.https://www.mdpi.com/2079-8954/9/4/71Gray–Scott modelobserver designpattern formationreaction diffusion equations |
| spellingShingle | Petro Feketa Alexander Schaum Thomas Meurer Distributed Parameter State Estimation for the Gray–Scott Reaction-Diffusion Model Systems Gray–Scott model observer design pattern formation reaction diffusion equations |
| title | Distributed Parameter State Estimation for the Gray–Scott Reaction-Diffusion Model |
| title_full | Distributed Parameter State Estimation for the Gray–Scott Reaction-Diffusion Model |
| title_fullStr | Distributed Parameter State Estimation for the Gray–Scott Reaction-Diffusion Model |
| title_full_unstemmed | Distributed Parameter State Estimation for the Gray–Scott Reaction-Diffusion Model |
| title_short | Distributed Parameter State Estimation for the Gray–Scott Reaction-Diffusion Model |
| title_sort | distributed parameter state estimation for the gray scott reaction diffusion model |
| topic | Gray–Scott model observer design pattern formation reaction diffusion equations |
| url | https://www.mdpi.com/2079-8954/9/4/71 |
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