Article (Scientific journals)
An Optimal Control Formulation of Pulse-Based Control Using Koopman Operator
Sootla, Aivar; Mauroy, Alexandre; Ernst, Damien
2018In Automatica, 91, p. 217-224
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Keywords :
Monotone Systems; Koopman Operator; Isostables; Generalized Repressilator; Genetic Toggle Switch
Abstract :
[en] In many applications, and in systems/synthetic biology in particular, it is desirable to compute control policies that force the trajectory of a bistable system from one equilibrium (the initial point) to another equilibrium (the target point), or in other words to solve the switching problem. It was recently shown that, for monotone bistable systems, this problem admits easyto-implement open-loop solutions in terms of temporal pulses (i.e., step functions of fixed length and fixed magnitude). In this paper, we develop this idea further and formulate a problem of convergence to an equilibrium from an arbitrary initial point. We show that this problem can be solved using a static optimization problem in the case of monotone systems. Changing the initial point to an arbitrary state allows to build closed-loop, event-based or open-loop policies for the switching/convergence problems. In our derivations we exploit the Koopman operator, which offers a linear infinite-dimensional representation of an autonomous nonlinear system. One of the main advantages of using the Koopman operator is the powerful computational tools developed for this framework. Besides the presence of numerical solutions, the switching/convergence problem can also serve as a building block for solving more complicated control problems and can potentially be applied to non-monotone systems. We illustrate this argument on the problem of synchronizing cardiac cells by defibrillation. Potentially, our approach can be extended to problems with different parametrizations of control signals since the only fundamental limitation is the finite time application of the control signal.
Disciplines :
Computer science
Author, co-author :
Sootla, Aivar
Mauroy, Alexandre
Ernst, Damien  ;  Université de Liège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Smart grids
Language :
English
Title :
An Optimal Control Formulation of Pulse-Based Control Using Koopman Operator
Publication date :
May 2018
Journal title :
Automatica
ISSN :
0005-1098
Publisher :
Pergamon Press - An Imprint of Elsevier Science, Oxford, United Kingdom
Volume :
91
Pages :
217-224
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBi :
since 04 August 2017

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