Pré-Publication, Document De Travail Année : 2025

Constrained non-linear estimation and links with stochastic filtering

Résumé

This article studies the problem of estimating the state variable of non-smooth subdifferential dynamics constrained in a bounded convex domain given some real-time observation. On the one hand, we show that the value function of the estimation problem is a viscosity solution of a Hamilton Jacobi Bellman equation whose sub and super solutions have different Neumann type boundary conditions. This intricacy arises from the non-reversibility in time of the non-smooth dynamics, and hinders the derivation of a comparison principle and the uniqueness of the solution in general. Nonetheless, we identify conditions on the drift (including zero drift) coefficient in the non-smooth dynamics that make such a derivation possible. On the other hand, we show in a general situation that the value function appears in the small noise limit of the corresponding stochastic filtering problem by establishing a large deviation result. We also give quantitative approximation results when replacing the non-smooth dynamics with a smooth penalised one.
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Dates et versions

hal-04925307 , version 1 (02-02-2025)

Identifiants

  • HAL Id : hal-04925307 , version 1

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Louis-Pierre Chaintron, Laurent Mertz, Philippe Moireau, Hasnaa Zidani. Constrained non-linear estimation and links with stochastic filtering. 2025. ⟨hal-04925307⟩
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