Compatibility of state constraints and dynamics for multiagent control systems
Abstract
This study concerns the problem of compatibility of state constraints with a multiagent control system. Such a system deals with a number of agents so large that only a statistical description is available. For this reason, the state variable is described by a probability measure on $${\mathbb {R}}^d$$ R d representing the density of the agents and evolving according to the so-called continuity equation which is an equation stated in the Wasserstein space of probability measures. The aim of the paper is to provide a necessary and sufficient condition for a given constraint (a closed subset of the Wasserstein space) to be compatible with the controlled continuity equation. This new condition is characterized in a viscosity sense as follows: the distance function to the constraint set is a viscosity supersolution of a suitable Hamilton–Jacobi–Bellman equation stated on the Wasserstein space. As a byproduct and key ingredient of our approach, we obtain a new comparison theorem for evolutionary Hamilton–Jacobi equations in the Wasserstein space.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jun 14, 2021
- Source ID
- 10.1007/s00028-021-00724-z
Entities
People
- Antonio Marigonda
- Giulia Cavagnari
- Marc Quincampoix
Organizations
- Air Force Office of Scientific Research
- David and Lucile Packard Foundation
- Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni
- National Institutes of Health