Shaping Pulses to Control Bistable Systems: Analysis, Computation and Counterexamples
File(s)shaping-final.pdf (791.76 KB)
Accepted version
Author(s)
Sootla, A
Oyarzun, DA
Angeli, D
Stan, GB
Type
Journal Article
Abstract
In this paper we study how to shape temporal pulses to switch a bistable system between its stable steady states. Our motivation for
pulse-based control comes from applications in synthetic biology, where it is generally difficult to implement real-time feedback control
systems due to technical limitations in sensors and actuators. We show that for monotone bistable systems, the estimation of the set of
all pulses that switch the system reduces to the computation of one non-increasing curve. We provide an efficient algorithm to compute
this curve and illustrate the results with a genetic bistable system commonly used in synthetic biology. We also extend these results to
models with parametric uncertainty and provide a number of examples and counterexamples that demonstrate the power and limitations
of the current theory. In order to show the full potential of the framework, we consider the problem of inducing oscillations in a monotone
biochemical system using a combination of temporal pulses and event-based control. Our results provide an insight into the dynamics of
bistable systems under external inputs and open up numerous directions for future investigation.
pulse-based control comes from applications in synthetic biology, where it is generally difficult to implement real-time feedback control
systems due to technical limitations in sensors and actuators. We show that for monotone bistable systems, the estimation of the set of
all pulses that switch the system reduces to the computation of one non-increasing curve. We provide an efficient algorithm to compute
this curve and illustrate the results with a genetic bistable system commonly used in synthetic biology. We also extend these results to
models with parametric uncertainty and provide a number of examples and counterexamples that demonstrate the power and limitations
of the current theory. In order to show the full potential of the framework, we consider the problem of inducing oscillations in a monotone
biochemical system using a combination of temporal pulses and event-based control. Our results provide an insight into the dynamics of
bistable systems under external inputs and open up numerous directions for future investigation.
Date Issued
2016-01-01
Date Acceptance
2015-10-05
Citation
Automatica, 2016, 63, pp.254-264
ISSN
1873-2836
Publisher
Elsevier
Start Page
254
End Page
264
Journal / Book Title
Automatica
Volume
63
Copyright Statement
© 2015, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Grant Number
EP/J014214/1
EP/M002187/1
Subjects
Industrial Engineering & Automation
01 Mathematical Sciences
09 Engineering
08 Information And Computing Sciences
Publication Status
Published
Date Publish Online
2015-11-11