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Motor systems show an overall robustness, but because they are highly nonlinear, understanding how they achieve robustness is difficult. In many rhythmic systems, robustness against perturbations involves response of both the shape and the timing of
Externí odkaz:
http://arxiv.org/abs/2205.08339
Autor:
Bonnet, Benoît, Frankowska, Hélène
Publikováno v:
Journal de Math\'ematiques Pures et Appliqu\'eees, Published online (2021)
In this article, we investigate some of the fine properties of the value function associated to an optimal control problem in the Wasserstein space of probability measures. Building on new interpolation and linearisation formulas for non-local flows,
Externí odkaz:
http://arxiv.org/abs/2108.02609
Autor:
Bonnet, Benoît, Frankowska, Hélène
In this article, we derive first-order necessary optimality conditions for a constrained optimal control problem formulated in the Wasserstein space of probability measures. To this end, we introduce a new notion of localised metric subdifferential f
Externí odkaz:
http://arxiv.org/abs/2101.10668
Optimal control problems reflecting the finding of effective quarantine strategies are considered for two control SEIR~type models describing the spread of the COVID-19 virus in the human population. The properties of the corresponding optimal contro
Externí odkaz:
http://arxiv.org/abs/2004.10614
Autor:
Bonnet, Benoît, Rossi, Francesco
In this article, we provide sufficient conditions under which the controlled vector fields solution of optimal control problems formulated on continuity equations are Lipschitz regular in space. Our approach involves a novel combination of mean-field
Externí odkaz:
http://arxiv.org/abs/1908.04183
Autor:
Agrachev, Andrei, Sarychev, Andrey
We study the controlled dynamics of the {\it ensembles of points} of a Riemannian manifold $M$. Parameterized ensemble of points of $M$ is the image of a continuous map $\gamma:\Theta \to M$, where $\Theta$ is a compact set of parameters. The dynamic
Externí odkaz:
http://arxiv.org/abs/1907.00905
When dynamical systems that produce rhythmic behaviors operate within hard limits, they may exhibit limit cycles with sliding components, that is, closed isolated periodic orbits that make and break contact with a constraint surface. Examples include
Externí odkaz:
http://arxiv.org/abs/1906.04387
Ensemble Kalman inversion is a parallelizable methodology for solving inverse or parameter estimation problems. Although it is based on ideas from Kalman filtering, it may be viewed as a derivative-free optimization method. In its most basic form it
Externí odkaz:
http://arxiv.org/abs/1901.10382
In this paper, we justify by the use of Enumerative Combinatorics, that the results obtained in \cite{Alarcon1}, where is analysed the complex dynamics of an epidemic model to identify the nodes that contribute the most to the propagation process and
Externí odkaz:
http://arxiv.org/abs/1811.08280
Autor:
Bonnet, Benoît
Publikováno v:
ESAIM COCV 25 (52) 2019
In this paper, we prove a Pontryagin Maximum Principle for constrained optimal control problems in the Wasserstein space of probability measures. The dynamics, is described by a transport equation with non-local velocities and is subject to end-point
Externí odkaz:
http://arxiv.org/abs/1810.13117