Signal reconstruction under finite-rate measurements: Finite-horizon navigation application
In this paper, we study finite-length signal reconstruction over a finite-rate noiseless channel. We allow the class of signals to belong to a bounded ellipsoid and derive a universal lower bound on a worst-case reconstruction error. We then compute upper bounds on the error that arise from differen...
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Institute of Electrical and Electronics Engineers
2010
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| Online Access: | http://hdl.handle.net/1721.1/60299 https://orcid.org/0000-0002-1470-2148 |
| _version_ | 1811084877414531072 |
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| author | Sarma, Sridevi V. Dahleh, Munther A. |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Sarma, Sridevi V. Dahleh, Munther A. |
| author_sort | Sarma, Sridevi V. |
| collection | MIT |
| description | In this paper, we study finite-length signal reconstruction over a finite-rate noiseless channel. We allow the class of signals to belong to a bounded ellipsoid and derive a universal lower bound on a worst-case reconstruction error. We then compute upper bounds on the error that arise from different coding schemes and under different causality assumptions. We then map our general reconstruction problem into an important control problem in which the plant and controller are local to each other, but are together driven by a remote reference signal that is transmitted through a finite-rate noiseless channel. The problem is to navigate the state of the remote system from a nonzero initial condition to as close to the origin as possible in finite-time. Our analysis enables us to quantify the tradeoff between time horizon and performance accuracy which is not well-studied in the area of control with limited information as most works address infinite-horizon control objectives (eg. stability, disturbance rejection). |
| first_indexed | 2024-09-23T12:58:55Z |
| format | Article |
| id | mit-1721.1/60299 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T12:58:55Z |
| publishDate | 2010 |
| publisher | Institute of Electrical and Electronics Engineers |
| record_format | dspace |
| spelling | mit-1721.1/602992022-09-28T11:18:18Z Signal reconstruction under finite-rate measurements: Finite-horizon navigation application Sarma, Sridevi V. Dahleh, Munther A. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Dahleh, Munther A. Dahleh, Munther A. Sarma, Sridevi V. In this paper, we study finite-length signal reconstruction over a finite-rate noiseless channel. We allow the class of signals to belong to a bounded ellipsoid and derive a universal lower bound on a worst-case reconstruction error. We then compute upper bounds on the error that arise from different coding schemes and under different causality assumptions. We then map our general reconstruction problem into an important control problem in which the plant and controller are local to each other, but are together driven by a remote reference signal that is transmitted through a finite-rate noiseless channel. The problem is to navigate the state of the remote system from a nonzero initial condition to as close to the origin as possible in finite-time. Our analysis enables us to quantify the tradeoff between time horizon and performance accuracy which is not well-studied in the area of control with limited information as most works address infinite-horizon control objectives (eg. stability, disturbance rejection). Burroughs Wellcome Fund (CASI) L'Oréal-UNESCO For Women in Science 2010-12-17T15:38:27Z 2010-12-17T15:38:27Z 2009-10 2009-08 Article http://purl.org/eprint/type/ConferencePaper 978-89-956056-2-2 INSPEC Accession Number: 10904273 http://hdl.handle.net/1721.1/60299 Sarma, S.V. and M.A. Dahleh. “Signal reconstruction under finite-rate measurements: Finite-horizon navigation application.” Asian Control Conference, 2009. ASCC 2009. 7th. 2009. 459-464. ©2009 IEEE. https://orcid.org/0000-0002-1470-2148 en_US Proceedings of the 7th Asian Control Conference, 2009. ASCC 2009 Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Institute of Electrical and Electronics Engineers IEEE |
| spellingShingle | Sarma, Sridevi V. Dahleh, Munther A. Signal reconstruction under finite-rate measurements: Finite-horizon navigation application |
| title | Signal reconstruction under finite-rate measurements: Finite-horizon navigation application |
| title_full | Signal reconstruction under finite-rate measurements: Finite-horizon navigation application |
| title_fullStr | Signal reconstruction under finite-rate measurements: Finite-horizon navigation application |
| title_full_unstemmed | Signal reconstruction under finite-rate measurements: Finite-horizon navigation application |
| title_short | Signal reconstruction under finite-rate measurements: Finite-horizon navigation application |
| title_sort | signal reconstruction under finite rate measurements finite horizon navigation application |
| url | http://hdl.handle.net/1721.1/60299 https://orcid.org/0000-0002-1470-2148 |
| work_keys_str_mv | AT sarmasrideviv signalreconstructionunderfiniteratemeasurementsfinitehorizonnavigationapplication AT dahlehmunthera signalreconstructionunderfiniteratemeasurementsfinitehorizonnavigationapplication |