Time-scale separation based design of biomolecular feedback controllers (extended version)
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | en_US |
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2019
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| Online Access: | http://hdl.handle.net/1721.1/120973 |
| _version_ | 1826205315180265472 |
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| author | Grunberg, Theodore W. Del Vecchio, Domitilla |
| author_facet | Grunberg, Theodore W. Del Vecchio, Domitilla |
| author_sort | Grunberg, Theodore W. |
| collection | MIT |
| description | 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 time-scale 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 | 2024-09-23T13:11:04Z |
| format | Article |
| id | mit-1721.1/120973 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T13:11:04Z |
| publishDate | 2019 |
| record_format | dspace |
| spelling | mit-1721.1/1209732019-04-12T22:37:29Z Time-scale separation based design of biomolecular feedback controllers (extended version) Grunberg, Theodore W. Del Vecchio, Domitilla biomolecular feedback control singular perturbation Lyapunov functions synthetic biology 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 time-scale 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. This work was supported in part by the National Science Foundation through grant NSF-CMMI 1727189. 2019-03-15T02:06:15Z 2019-03-15T02:06:15Z 2019-03-14 Article http://hdl.handle.net/1721.1/120973 en_US application/pdf |
| spellingShingle | biomolecular feedback control singular perturbation Lyapunov functions synthetic biology Grunberg, Theodore W. Del Vecchio, Domitilla Time-scale separation based design of biomolecular feedback controllers (extended version) |
| title | Time-scale separation based design of biomolecular feedback controllers (extended version) |
| title_full | Time-scale separation based design of biomolecular feedback controllers (extended version) |
| title_fullStr | Time-scale separation based design of biomolecular feedback controllers (extended version) |
| title_full_unstemmed | Time-scale separation based design of biomolecular feedback controllers (extended version) |
| title_short | Time-scale separation based design of biomolecular feedback controllers (extended version) |
| title_sort | time scale separation based design of biomolecular feedback controllers extended version |
| topic | biomolecular feedback control singular perturbation Lyapunov functions synthetic biology |
| url | http://hdl.handle.net/1721.1/120973 |
| work_keys_str_mv | AT grunbergtheodorew timescaleseparationbaseddesignofbiomolecularfeedbackcontrollersextendedversion AT delvecchiodomitilla timescaleseparationbaseddesignofbiomolecularfeedbackcontrollersextendedversion |