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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2410.20637 |
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| _version_ | 1866914993110253568 |
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| author | Raptis, Ioannis |
| author_facet | Raptis, Ioannis |
| contents | This paper explores the observability and estimation capability of dynamical systems using predominantly relative measurements of the system's state-space variables, with minimal to no reliance on absolute measurements of these variables. We concentrate on linear time-invariant systems, in which the observation matrix serves as the algebraic representation of a graph object. This graph object encapsulates the availability of relative measurements. Utilizing algebraic graph theory and abstract linear algebra (geometric) tools, we establish a link between the structure of the graph of relative measurements and the system-theoretic observability subspace of linear systems. Special emphasis is given to multi-agent networked systems whose dynamics are governed by the linear consensus protocol. We demonstrate the importance of absolute information and its placement to the system's dynamics in achieving full-state estimation. Finally, the analysis shifts to the synthesis of a distributed observer with relative measurements for single integrator dynamics, exemplifying the relevance of the preceding analytical findings. We support our theoretical analysis with numerical simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20637 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Observability of Linear Time-Invariant Systems with Relative Measurements: A Geometric Approach Raptis, Ioannis Systems and Control This paper explores the observability and estimation capability of dynamical systems using predominantly relative measurements of the system's state-space variables, with minimal to no reliance on absolute measurements of these variables. We concentrate on linear time-invariant systems, in which the observation matrix serves as the algebraic representation of a graph object. This graph object encapsulates the availability of relative measurements. Utilizing algebraic graph theory and abstract linear algebra (geometric) tools, we establish a link between the structure of the graph of relative measurements and the system-theoretic observability subspace of linear systems. Special emphasis is given to multi-agent networked systems whose dynamics are governed by the linear consensus protocol. We demonstrate the importance of absolute information and its placement to the system's dynamics in achieving full-state estimation. Finally, the analysis shifts to the synthesis of a distributed observer with relative measurements for single integrator dynamics, exemplifying the relevance of the preceding analytical findings. We support our theoretical analysis with numerical simulations. |
| title | Observability of Linear Time-Invariant Systems with Relative Measurements: A Geometric Approach |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2410.20637 |