Name
Abstract | ||
|---|---|---|
In many applications, and in systems/synthetic biology, in particular, it is desirable to solve the switching problem, i.e., to compute control policies that force the trajectory of a bistable system from one equilibrium (the initial point) to another equilibrium (the target point). It was recently shown that for monotone bistable systems, this problem admits easy-to-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 the convergence problem can be solved using a static optimization problem in the case of monotone systems. Changing the initial point to an arbitrary state allows building 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 and powerful computational tools for their analysis. Our solutions to the switching/convergence problems can serve as building blocks for other control problems and can potentially be applied to non-monotone systems. We illustrate this argument on the problem of synchronizing cardiac cells by defibrillation. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1016/j.automatica.2018.01.036 | Automatica |
Keywords | DocType | Volume |
Monotone systems,Koopman operator,Isostables,Generalized repressilator,Genetic toggle switch | Journal | 91 |
Issue | ISSN | Citations |
1 | 0005-1098 | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Aivar Sootla | 1 | 38 | 11.17 |
| Alexandre Mauroy | 2 | 59 | 8.21 |
| Damien Ernst | 3 | 730 | 56.74 |