Reference : Shaping Pulses to Control Bistable Monotone Systems Using Koopman Operator |

Scientific congresses, symposiums and conference proceedings : Paper published in a book | |||

Physical, chemical, mathematical & earth Sciences : Mathematics Engineering, computing & technology : Multidisciplinary, general & others | |||

Systems Biomedicine | |||

http://hdl.handle.net/10993/28490 | |||

Shaping Pulses to Control Bistable Monotone Systems Using Koopman Operator | |

English | |

Sootla, Aivar [Université de Liège - ULg] | |

Mauroy, Alexandre [University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB) > >] | |

Goncalves, Jorge [University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB) > >] | |

Aug-2016 | |

10th IFAC Symposium on Nonlinear Control Systems | |

710-715 | |

Yes | |

No | |

International | |

10th IFAC Symposium on Nonlinear Control Systems | |

from 23-08-2016 to 25-08-2016 | |

Monterey | |

USA | |

[en] 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 di cult 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 xed 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 ow 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 e cient 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. | |

http://hdl.handle.net/10993/28490 |

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