Deterministic optimal control on Riemannian manifolds under probability knowledge of the initial condition - ENSTA Paris - École nationale supérieure de techniques avancées Paris
Preprints, Working Papers, ... Year : 2022

Deterministic optimal control on Riemannian manifolds under probability knowledge of the initial condition

Frédéric Jean
Othmane Jerhaoui

Abstract

In this article, we study an optimal control problem on a compact Riemannian manifold M with imperfect information on the initial state of the system. The lack of information is modelled by a Borel probability measure along which the initial state is distributed. The state space of this problem is the space of Borel probability measures over M. We define a notion of viscosity in this space by taking as test functions a subset of the set of functions that can be written as a difference of two semi-convex functions. With this choice of test functions, we extend the notion of viscosity solution to Hamilton-Jacobi-Bellman equations in Wasserstein space, we also establish that the value function of the control problem with imperfect information is the unique viscosity solution of a Hamilton-Jacobi-Bellman equation in the space of Borel probability measures.
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Dates and versions

hal-03564787 , version 1 (10-02-2022)
hal-03564787 , version 2 (14-09-2022)

Identifiers

  • HAL Id : hal-03564787 , version 1

Cite

Frédéric Jean, Othmane Jerhaoui, Hasnaa Zidani. Deterministic optimal control on Riemannian manifolds under probability knowledge of the initial condition. 2022. ⟨hal-03564787v1⟩
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