Shaping Pulses to Control Bistable Monotone Systems Using Koopman Operator

Aivar Sootla, Alexandre Mauroy, Jorge Goncalves

Research output: Contribution in Book/Catalog/Report/Conference proceedingConference contribution

Abstract

In this paper, we further develop a recently proposed control method to switch a bistable system between its steady states using temporal pulses. The motivation for using pulses comes from biomedical and biological applications (e.g. synthetic biology), where it is generally difficult to build feedback control systems due to technical limitations in sensing and actuation. The original framework was derived for monotone systems and all the extensions relied on monotone systems theory. In contrast, we introduce the concept of switching function which is related to eigenfunctions of the so-called Koopman operator subject to a fixed control pulse. Using the level sets of the switching function we can (i) compute the set of all pulses that drive the system toward the steady state in a synchronous way and (ii) estimate the time needed by the flow to reach an epsilon neighborhood of the target steady state. Additionally, we show that for monotone systems the switching function is also monotone in some sense, a property that can yield efficient algorithms to compute it. This observation recovers and further extends the results of the original framework, which we illustrate on numerical examples inspired by biological applications.

Original languageEnglish
Title of host publicationProceedings of the 10th IFAC Symposium on Nonlinear Control Systems (NOLCOS)
Pages698-703
Number of pages6
Volume49
Edition18
DOIs
Publication statusPublished - 2016
Externally publishedYes

Publication series

NameIFAC-PapersOnLine
PublisherIFAC Secretariat

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Switching functions
Pulse shaping
System theory
Eigenvalues and eigenfunctions
Feedback control
Switches
Control systems

Cite this

Sootla, A., Mauroy, A., & Goncalves, J. (2016). Shaping Pulses to Control Bistable Monotone Systems Using Koopman Operator. In Proceedings of the 10th IFAC Symposium on Nonlinear Control Systems (NOLCOS) (18 ed., Vol. 49, pp. 698-703). (IFAC-PapersOnLine). https://doi.org/10.1016/j.ifacol.2016.10.247
Sootla, Aivar ; Mauroy, Alexandre ; Goncalves, Jorge. / Shaping Pulses to Control Bistable Monotone Systems Using Koopman Operator. Proceedings of the 10th IFAC Symposium on Nonlinear Control Systems (NOLCOS). Vol. 49 18. ed. 2016. pp. 698-703 (IFAC-PapersOnLine).
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Sootla, A, Mauroy, A & Goncalves, J 2016, Shaping Pulses to Control Bistable Monotone Systems Using Koopman Operator. in Proceedings of the 10th IFAC Symposium on Nonlinear Control Systems (NOLCOS). 18 edn, vol. 49, IFAC-PapersOnLine, pp. 698-703. https://doi.org/10.1016/j.ifacol.2016.10.247

Shaping Pulses to Control Bistable Monotone Systems Using Koopman Operator. / Sootla, Aivar; Mauroy, Alexandre; Goncalves, Jorge.

Proceedings of the 10th IFAC Symposium on Nonlinear Control Systems (NOLCOS). Vol. 49 18. ed. 2016. p. 698-703 (IFAC-PapersOnLine).

Research output: Contribution in Book/Catalog/Report/Conference proceedingConference contribution

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Sootla A, Mauroy A, Goncalves J. Shaping Pulses to Control Bistable Monotone Systems Using Koopman Operator. In Proceedings of the 10th IFAC Symposium on Nonlinear Control Systems (NOLCOS). 18 ed. Vol. 49. 2016. p. 698-703. (IFAC-PapersOnLine). https://doi.org/10.1016/j.ifacol.2016.10.247