Time-scale separation based design of biomolecular feedback controllers
© 2019 IEEE. Time-scale separation is a powerful property that can be used to simplify control systems design. In this work, we consider the problem of designing biomolecular feedback controllers that provide tracking of slowly varying references and rejection of slowly varying disturbances for nonl...
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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IEEE
2021
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| Online Access: | https://hdl.handle.net/1721.1/137975 |
| _version_ | 1811096617574465536 |
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| author | Grunberg, Theodore W. Del Vecchio, Domitilla |
| 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 Grunberg, Theodore W. Del Vecchio, Domitilla |
| author_sort | Grunberg, Theodore W. |
| collection | MIT |
| description | © 2019 IEEE. Time-scale separation is a powerful property that can be used to simplify control systems design. In this work, we consider the problem of designing biomolecular feedback controllers that provide tracking of slowly varying references and rejection of slowly varying disturbances for nonlinear systems. We propose a design methodology that uses timescale separation to accommodate physical constraints on the implementation of integral control in cellular systems. The main result of this paper gives sufficient conditions under which controllers designed using our time-scale separation methodology have desired asymptotic performance when the reference and disturbance are constant or slowly varying. Our analysis is based on construction of Lyapunov functions for a class of singularly perturbed systems that are dependent on an additional parameter that perturbs the system regularly. When the exogenous inputs are slowly varying, this approach allows us to bound the system trajectories by a function of the regularly perturbing parameter. This bound decays to zero as the parameter's value increases, while an inner-estimate of the region of attraction stays unchanged as this parameter is varied. These results cannot be derived using standard singular perturbation results. We apply our results to an application demonstrating a physically realizable parameter tuning that controls performance. |
| first_indexed | 2024-09-23T16:46:33Z |
| format | Article |
| id | mit-1721.1/137975 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T16:46:33Z |
| publishDate | 2021 |
| publisher | IEEE |
| record_format | dspace |
| spelling | mit-1721.1/1379752022-10-03T08:13:03Z Time-scale separation based design of biomolecular feedback controllers Grunberg, Theodore W. Del Vecchio, Domitilla Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology. Department of Mechanical Engineering © 2019 IEEE. Time-scale separation is a powerful property that can be used to simplify control systems design. In this work, we consider the problem of designing biomolecular feedback controllers that provide tracking of slowly varying references and rejection of slowly varying disturbances for nonlinear systems. We propose a design methodology that uses timescale separation to accommodate physical constraints on the implementation of integral control in cellular systems. The main result of this paper gives sufficient conditions under which controllers designed using our time-scale separation methodology have desired asymptotic performance when the reference and disturbance are constant or slowly varying. Our analysis is based on construction of Lyapunov functions for a class of singularly perturbed systems that are dependent on an additional parameter that perturbs the system regularly. When the exogenous inputs are slowly varying, this approach allows us to bound the system trajectories by a function of the regularly perturbing parameter. This bound decays to zero as the parameter's value increases, while an inner-estimate of the region of attraction stays unchanged as this parameter is varied. These results cannot be derived using standard singular perturbation results. We apply our results to an application demonstrating a physically realizable parameter tuning that controls performance. 2021-11-09T16:52:48Z 2021-11-09T16:52:48Z 2019-12 2020-07-08T15:02:53Z Article http://purl.org/eprint/type/ConferencePaper https://hdl.handle.net/1721.1/137975 Grunberg, Theodore W. and Del Vecchio, Domitilla. 2019. "Time-scale separation based design of biomolecular feedback controllers." Proceedings of the IEEE Conference on Decision and Control, 2019-December. en 10.1109/cdc40024.2019.9029355 Proceedings of the IEEE Conference on Decision and Control Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf IEEE MIT web domain |
| spellingShingle | Grunberg, Theodore W. Del Vecchio, Domitilla Time-scale separation based design of biomolecular feedback controllers |
| title | Time-scale separation based design of biomolecular feedback controllers |
| title_full | Time-scale separation based design of biomolecular feedback controllers |
| title_fullStr | Time-scale separation based design of biomolecular feedback controllers |
| title_full_unstemmed | Time-scale separation based design of biomolecular feedback controllers |
| title_short | Time-scale separation based design of biomolecular feedback controllers |
| title_sort | time scale separation based design of biomolecular feedback controllers |
| url | https://hdl.handle.net/1721.1/137975 |
| work_keys_str_mv | AT grunbergtheodorew timescaleseparationbaseddesignofbiomolecularfeedbackcontrollers AT delvecchiodomitilla timescaleseparationbaseddesignofbiomolecularfeedbackcontrollers |