4.7 Article

Shaping pulses to control bistable systems: Analysis, computation and counterexamples

Journal

AUTOMATICA
Volume 63, Issue -, Pages 254-264

Publisher

PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.automatica.2015.10.037

Keywords

Monotone systems; Near-monotone systems; Toggle switch; Control by pulses; Open-loop control; Event-based control

Funding

  1. EPSRC [EP/G036004/1, EP/J014214/1]
  2. F.R.S.-FNRS Fellowship
  3. ICL
  4. EPRSC [EP/M002187/1]
  5. EPSRC [EP/M002187/1, EP/K020617/1] Funding Source: UKRI
  6. Engineering and Physical Sciences Research Council [EP/K020617/1, EP/G036004/1, EP/M002187/1, EP/J014214/1] Funding Source: researchfish

Ask authors/readers for more resources

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. (C) 2015 Elsevier Ltd. All rights reserved.

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