Benoît Bonnet
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View article: Set-Valued Koopman Theory for Control Systems
Set-Valued Koopman Theory for Control Systems Open
International audience
View article: Exponential Consensus Formation in Time-Varying Multiagent Systems via Compactification Methods
Exponential Consensus Formation in Time-Varying Multiagent Systems via Compactification Methods Open
In this article, we establish exponential contraction results for the diameter and variance of general first-order multiagent systems. Our approach is based on compactification techniques, and works under rather mild assumptions. Namely, w…
View article: On the Viability and Invariance of Proper Sets under Continuity Inclusions in Wasserstein Spaces
On the Viability and Invariance of Proper Sets under Continuity Inclusions in Wasserstein Spaces Open
International audience
View article: Set-Valued Koopman Theory for Control Systems
Set-Valued Koopman Theory for Control Systems Open
In this paper, we introduce a new notion of Koopman operator which faithfully encodes the dynamics of controlled systems by leveraging the tools of set-valued analysis. In this context, we propose generalisations of the Liouville and Perro…
View article: First-Order Pontryagin Maximum Principle for Risk-Averse Stochastic Optimal Control Problems
First-Order Pontryagin Maximum Principle for Risk-Averse Stochastic Optimal Control Problems Open
International audience
View article: On the Viability and Invariance of Proper Sets under Continuity Inclusions in Wasserstein Spaces
On the Viability and Invariance of Proper Sets under Continuity Inclusions in Wasserstein Spaces Open
In this article, we derive conditions for the existence of solutions to state-constrained continuity inclusions in Wasserstein spaces whose right-hand sides may be discontinuous in time. These latter are based on a fine investigation of th…
View article: Carathéodory Theory and A Priori Estimates for Continuity Inclusions in the Space of Probability Measures
Carathéodory Theory and A Priori Estimates for Continuity Inclusions in the Space of Probability Measures Open
In this article, we extend the foundations of the theory of differential inclusions in the space of compactly supported probability measures, introduced recently by the authors, to the setting of general Wasserstein spaces. In this context…
View article: Viability and Exponentially Stable Trajectories for Differential Inclusions in Wasserstein Spaces
Viability and Exponentially Stable Trajectories for Differential Inclusions in Wasserstein Spaces Open
International audience
View article: Adversarial images with downscaling
Adversarial images with downscaling Open
Most works on adversarial attacks consider small images whose size already fits the model. This paper explores attacking large images on classifiers with different input sizes. Downscaling is a necessary first step to adapt the size of the…
View article: Viability and Exponentially Stable Trajectories for Differential Inclusions in Wasserstein Spaces
Viability and Exponentially Stable Trajectories for Differential Inclusions in Wasserstein Spaces Open
In this article, we prove a general viability theorem for continuity inclusions in Wasserstein spaces, and provide an application thereof to the existence of exponentially stable trajectories obtained via the second method of Lyapunov.
View article: Consensus formation in first-order graphon models with time-varying topologies
Consensus formation in first-order graphon models with time-varying topologies Open
In this paper, we investigate the asymptotic formation of consensus for several classes of time-dependent cooperative graphon dynamics. After motivating the use of this type of macroscopic models to describe multi-agent systems, we adapt t…
View article: First-Order Pontryagin Maximum Principle for Risk-Averse Stochastic Optimal Control Problems
First-Order Pontryagin Maximum Principle for Risk-Averse Stochastic Optimal Control Problems Open
In this paper, we derive first-order Pontryagin optimality conditions for risk-averse stochastic optimal control problems subject to final time inequality constraints, and whose costs are general, possibly non-smooth finite coherent risk m…
View article: On the Properties of the Value Function Associated to a Mean-Field Optimal Control Problem of Bolza Type
On the Properties of the Value Function Associated to a Mean-Field Optimal Control Problem of Bolza Type Open
In this paper, we obtain several structural results for the value function associated to a mean-field optimal control problem of Bolza type in the space of measures. After establishing the sensitivity relations bridging between the costate…
View article: A Measure Theoretical Approach to the Mean-field Maximum Principle for Training NeurODEs
A Measure Theoretical Approach to the Mean-field Maximum Principle for Training NeurODEs Open
In this paper we consider a measure-theoretical formulation of the training of NeurODEs in the form of a mean-field optimal control with $L^2$-regularization of the control. We derive first order optimality conditions for the NeurODE train…
View article: Necessary Optimality Conditions for Optimal Control Problems in\n Wasserstein Spaces
Necessary Optimality Conditions for Optimal Control Problems in\n Wasserstein Spaces Open
In this article, we derive first-order necessary optimality conditions for a\nconstrained optimal control problem formulated in the Wasserstein space of\nprobability measures. To this end, we introduce a new notion of localised\nmetric sub…
View article: Intrinsic Lipschitz Regularity of Mean-Field Optimal Controls
Intrinsic Lipschitz Regularity of Mean-Field Optimal Controls Open
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…
View article: Mean-Field Optimal Control of Continuity Equations and Differential Inclusions
Mean-Field Optimal Control of Continuity Equations and Differential Inclusions Open
In this article, we propose a new unifying framework for the investigation of multi-agent control problems in the mean-field setting. Our approach is based on a new definition of differential inclusions for continuity equations formulated …
View article: Adversarial Images through Stega Glasses
Adversarial Images through Stega Glasses Open
This paper explores the connection between steganography and adversarial images. On the one hand, ste-ganalysis helps in detecting adversarial perturbations. On the other hand, steganography helps in forging adversarial perturbations that …
View article: Mean-Field Optimal Control of Continuity Equations and Differential\n Inclusions
Mean-Field Optimal Control of Continuity Equations and Differential\n Inclusions Open
In this article, we propose a new unifying framework for the investigation of\nmulti-agent control problems in the mean-field setting. Our approach is based\non a new definition of differential inclusions for continuity equations\nformulat…
View article: Differential Inclusions in Wasserstein Spaces: The Cauchy-Lipschitz\n Framework
Differential Inclusions in Wasserstein Spaces: The Cauchy-Lipschitz\n Framework Open
In this article, we propose a general framework for the study of differential\ninclusions in the Wasserstein space of probability measures. Based on earlier\ngeometric insights on the structure of continuity equations, we define\nsolutions…