Observability of Uncertain Nonlinear Systems Using Interval Analysis
In the field of control engineering, observability of uncertain nonlinear systems is often neglected and not examined. This is due to the complex analytical calculations required for the verification. Therefore, the aim of this work is to provide an algorithm which numerically analyzes the observabi...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-03-01
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| Series: | Algorithms |
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| Online Access: | https://www.mdpi.com/1999-4893/13/3/66 |
| _version_ | 1818940786347081728 |
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| author | Thomas Paradowski Sabine Lerch Michelle Damaszek Robert Dehnert Bernd Tibken |
| author_facet | Thomas Paradowski Sabine Lerch Michelle Damaszek Robert Dehnert Bernd Tibken |
| author_sort | Thomas Paradowski |
| collection | DOAJ |
| description | In the field of control engineering, observability of uncertain nonlinear systems is often neglected and not examined. This is due to the complex analytical calculations required for the verification. Therefore, the aim of this work is to provide an algorithm which numerically analyzes the observability of nonlinear systems described by finite-dimensional, continuous-time sets of ordinary differential equations. The algorithm is based on definitions for distinguishability and local observability using a rank check from which conditions are deduced. The only requirements are the uncertain model equations of the system. Further, the methodology verifies observability of nonlinear systems on a given state space. In case that the state space is not fully observable, the algorithm provides the observable set of states. In addition, the results obtained by the algorithm allows insight into why the remaining states cannot be distinguished. |
| first_indexed | 2024-12-20T06:45:10Z |
| format | Article |
| id | doaj.art-8b26efa4e0824fa1a5294fac20ebd07b |
| institution | Directory Open Access Journal |
| issn | 1999-4893 |
| language | English |
| last_indexed | 2024-12-20T06:45:10Z |
| publishDate | 2020-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj.art-8b26efa4e0824fa1a5294fac20ebd07b2022-12-21T19:49:44ZengMDPI AGAlgorithms1999-48932020-03-011336610.3390/a13030066a13030066Observability of Uncertain Nonlinear Systems Using Interval AnalysisThomas Paradowski0Sabine Lerch1Michelle Damaszek2Robert Dehnert3Bernd Tibken4Chair of Automation and Control Theory, Bergische Universität Wuppertal, 42119 Wuppertal, GermanyChair of Automation and Control Theory, Bergische Universität Wuppertal, 42119 Wuppertal, GermanyChair of Automation and Control Theory, Bergische Universität Wuppertal, 42119 Wuppertal, GermanyChair of Automation and Control Theory, Bergische Universität Wuppertal, 42119 Wuppertal, GermanyChair of Automation and Control Theory, Bergische Universität Wuppertal, 42119 Wuppertal, GermanyIn the field of control engineering, observability of uncertain nonlinear systems is often neglected and not examined. This is due to the complex analytical calculations required for the verification. Therefore, the aim of this work is to provide an algorithm which numerically analyzes the observability of nonlinear systems described by finite-dimensional, continuous-time sets of ordinary differential equations. The algorithm is based on definitions for distinguishability and local observability using a rank check from which conditions are deduced. The only requirements are the uncertain model equations of the system. Further, the methodology verifies observability of nonlinear systems on a given state space. In case that the state space is not fully observable, the algorithm provides the observable set of states. In addition, the results obtained by the algorithm allows insight into why the remaining states cannot be distinguished.https://www.mdpi.com/1999-4893/13/3/66observabilityuncertain nonlinear systemsinterval analysis |
| spellingShingle | Thomas Paradowski Sabine Lerch Michelle Damaszek Robert Dehnert Bernd Tibken Observability of Uncertain Nonlinear Systems Using Interval Analysis Algorithms observability uncertain nonlinear systems interval analysis |
| title | Observability of Uncertain Nonlinear Systems Using Interval Analysis |
| title_full | Observability of Uncertain Nonlinear Systems Using Interval Analysis |
| title_fullStr | Observability of Uncertain Nonlinear Systems Using Interval Analysis |
| title_full_unstemmed | Observability of Uncertain Nonlinear Systems Using Interval Analysis |
| title_short | Observability of Uncertain Nonlinear Systems Using Interval Analysis |
| title_sort | observability of uncertain nonlinear systems using interval analysis |
| topic | observability uncertain nonlinear systems interval analysis |
| url | https://www.mdpi.com/1999-4893/13/3/66 |
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