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20072025
most citedStochastic gradient descent on Riemannian manifolds

359 citations

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math.OC2024

Variational Dynamic Programming for Stochastic Optimal Control

Marc Lambert, Francis Bach, Silvère Bonnabel

We consider the problem of stochastic optimal control, where the state-feedback control policies take the form of a probability distribution and where a penalty on the entropy is a…

math.OC2019★ 1 cited

Small-time stabilization of nonholonomic or underactuated mechanical systems: the unicycle and the slider examples

Brigitte d'Andréa-Novel, Jean-Michel Coron, Wilfrid Perruquetti

This paper concerns the small-time stabilization of some classes of mechanical systems which are not stabilizable by means of at least continuous state feedback laws. This is the c…

math.OC2018

Modelling the Time-dependent VRP through Open Data

Augustin Lombard, Simon Tamayo, Frédéric Fontane

This paper presents an open data approach to model and solve the vehicle routing problem with time-dependent travel times (TDVRP). The proposed model is based on a multi-layer matr…

math.OC2017★ 16 cited

Controllability of the 1D Schrödinger equation using flatness

Philippe Martin, Lionel Rosier, Pierre Rouchon

We derive in a direct way the exact controllability of the 1D free Schrödinger equation with Dirichlet boundary control. We use the so-called flatness approach, which consists in p…

math.OC2016★ 12 cited

Some remarks on wheeled autonomous vehicles and the evolution of their control design

Brigitte d'Andréa-Novel, Lghani Menhour, Michel Fliess +1

Recent investigations on the longitudinal and lateral control of wheeled autonomous vehicles are reported. Flatness-based techniques are first introduced via a simplified model. It…

math.OC2011★ 359 cited

Stochastic gradient descent on Riemannian manifolds

Silvere Bonnabel

Stochastic gradient descent is a simple approach to find the local minima of a cost function whose evaluations are corrupted by noise. In this paper, we develop a procedure extendi…