On the Output Redundancy of LTI Systems: A Geometric Approach with Application to Privacy
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910620966715392 |
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| author | Yang, Guitao Gallo, Alexander J. Barboni, Angelo Ferrari, Riccardo M. G. Serrani, Andrea Parisini, Thomas |
| author_facet | Yang, Guitao Gallo, Alexander J. Barboni, Angelo Ferrari, Riccardo M. G. Serrani, Andrea Parisini, Thomas |
| contents | This paper examines the properties of output-redundant systems, that is, systems possessing a larger number of outputs than inputs, through the lenses of the geometric approach of Wonham et al. We begin by formulating a simple output allocation synthesis problem, which involves ``concealing" input information from a malicious eavesdropper having access to the system output, while still allowing for a legitimate user to reconstruct it. It is shown that the solvability of this problem requires the availability of a redundant set of outputs. This very problem is instrumental to unveiling the fundamental geometric properties of output-redundant systems, which form the basis for our subsequent constructions and results. As a direct application, we demonstrate how output allocation can be employed to effectively protect the information of input information from certain output eavesdroppers with guaranteed results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17705 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Output Redundancy of LTI Systems: A Geometric Approach with Application to Privacy Yang, Guitao Gallo, Alexander J. Barboni, Angelo Ferrari, Riccardo M. G. Serrani, Andrea Parisini, Thomas Systems and Control This paper examines the properties of output-redundant systems, that is, systems possessing a larger number of outputs than inputs, through the lenses of the geometric approach of Wonham et al. We begin by formulating a simple output allocation synthesis problem, which involves ``concealing" input information from a malicious eavesdropper having access to the system output, while still allowing for a legitimate user to reconstruct it. It is shown that the solvability of this problem requires the availability of a redundant set of outputs. This very problem is instrumental to unveiling the fundamental geometric properties of output-redundant systems, which form the basis for our subsequent constructions and results. As a direct application, we demonstrate how output allocation can be employed to effectively protect the information of input information from certain output eavesdroppers with guaranteed results. |
| title | On the Output Redundancy of LTI Systems: A Geometric Approach with Application to Privacy |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2409.17705 |