Sensitivity Analysis of Limit-Cycle Oscillating Hybrid Systems
A theory is developed for local, first-order sensitivity analysis of limit-cycle oscillating hybrid systems, which are dynamical systems exhibiting both continuous-state and discrete-state dynamics whose state trajectories are closed, isolated, and time-periodic. Methods for the computation of initi...
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| Format: | Article |
| Language: | en_US |
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Society for Industrial and Applied Mathematics
2011
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| Online Access: | http://hdl.handle.net/1721.1/67305 https://orcid.org/0000-0003-2895-9443 |
| _version_ | 1826193680773414912 |
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| author | Khan, Kamil A. Saxena, Vibhu Barton, Paul I. |
| author2 | Massachusetts Institute of Technology. Department of Chemical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Chemical Engineering Khan, Kamil A. Saxena, Vibhu Barton, Paul I. |
| author_sort | Khan, Kamil A. |
| collection | MIT |
| description | A theory is developed for local, first-order sensitivity analysis of limit-cycle oscillating hybrid systems, which are dynamical systems exhibiting both continuous-state and discrete-state dynamics whose state trajectories are closed, isolated, and time-periodic. Methods for the computation of initial-condition sensitivities and parametric sensitivities are developed to account exactly for any jumps in the sensitivities at discrete transitions and to exploit the time-periodicity of the system. It is shown that the initial-condition sensitivities of any limit-cycle oscillating hybrid system can be represented as the sum of a time-decaying component and a time-periodic component so that they become periodic in the long-time limit. A method is developed for decomposition of the parametric sensitivities into three parts, characterizing the influence of parameter changes on period, state variable amplitudes, and relative phases, respectively. The computation of parametric sensitivities of period, amplitudes, and different types of phases is also described. The methods developed in this work are applied to particular models for illustration, including models exhibiting state variable jumps. |
| first_indexed | 2024-09-23T09:43:00Z |
| format | Article |
| id | mit-1721.1/67305 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T09:43:00Z |
| publishDate | 2011 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | mit-1721.1/673052022-09-26T13:18:54Z Sensitivity Analysis of Limit-Cycle Oscillating Hybrid Systems Khan, Kamil A. Saxena, Vibhu Barton, Paul I. Massachusetts Institute of Technology. Department of Chemical Engineering Barton, Paul I. Barton, Paul I. Khan, Kamil A. Saxena, Vibhu A theory is developed for local, first-order sensitivity analysis of limit-cycle oscillating hybrid systems, which are dynamical systems exhibiting both continuous-state and discrete-state dynamics whose state trajectories are closed, isolated, and time-periodic. Methods for the computation of initial-condition sensitivities and parametric sensitivities are developed to account exactly for any jumps in the sensitivities at discrete transitions and to exploit the time-periodicity of the system. It is shown that the initial-condition sensitivities of any limit-cycle oscillating hybrid system can be represented as the sum of a time-decaying component and a time-periodic component so that they become periodic in the long-time limit. A method is developed for decomposition of the parametric sensitivities into three parts, characterizing the influence of parameter changes on period, state variable amplitudes, and relative phases, respectively. The computation of parametric sensitivities of period, amplitudes, and different types of phases is also described. The methods developed in this work are applied to particular models for illustration, including models exhibiting state variable jumps. 2011-11-29T19:10:18Z 2011-11-29T19:10:18Z 2011-07 2010-08 Article http://purl.org/eprint/type/JournalArticle 1064-8275 1095-7197 http://hdl.handle.net/1721.1/67305 Khan, Kamil A., Vibhu P. Saxena, and Paul I. Barton. “Sensitivity Analysis of Limit-Cycle Oscillating Hybrid Systems.” SIAM Journal on Scientific Computing 33 (2011): 1475. © 2011 Society for Industrial and Applied Mathematics. https://orcid.org/0000-0003-2895-9443 en_US http://dx.doi.org/10.1137/100804632 SIAM Journal on Scientific Computing 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 Society for Industrial and Applied Mathematics SIAM |
| spellingShingle | Khan, Kamil A. Saxena, Vibhu Barton, Paul I. Sensitivity Analysis of Limit-Cycle Oscillating Hybrid Systems |
| title | Sensitivity Analysis of Limit-Cycle Oscillating Hybrid Systems |
| title_full | Sensitivity Analysis of Limit-Cycle Oscillating Hybrid Systems |
| title_fullStr | Sensitivity Analysis of Limit-Cycle Oscillating Hybrid Systems |
| title_full_unstemmed | Sensitivity Analysis of Limit-Cycle Oscillating Hybrid Systems |
| title_short | Sensitivity Analysis of Limit-Cycle Oscillating Hybrid Systems |
| title_sort | sensitivity analysis of limit cycle oscillating hybrid systems |
| url | http://hdl.handle.net/1721.1/67305 https://orcid.org/0000-0003-2895-9443 |
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