A Mayer optimal control problem on Wasserstein spaces over Riemannian manifolds. Issue 16 (2022)

• Record Type: Journal Article
• Authors: Jean, F.; Jerhaoui, O.; Zidani, H.
• Is Part Of: IFAC-PapersOnLine. Volume 55:Issue 16(2022)
• Page Start: 44
• Page End: 49
• Publication Date: 2022
• Subjects: Optimal Control -- Viscosity solutions -- Hamilton Jacobi Bellman equation -- Wasserstein spaces -- Multi-agent systems; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2022.08.079
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: This paper concerns an optimal control problem on the space of probability measures over a compact Riemannian manifold. The motivation behind it is to model certain situations where the central planner of a deterministic controlled system has only a probabilistic knowledge of the initial condition. The lack of information here is very specific. In particular, we show that the value function verifies a dynamic programming principle and we prove that it is the unique viscosity solution to a suitable Hamilton Jacobi Bellman equation. The notion of viscosity is defined using test functions that are directionally differentiable in the space of probability measures.