Optimal Control of Nonlocal Continuity Equations: Numerical Solution

• Type: Article in International Scientific Journal
• Date: 2023

Authors

Chertovskih, R (Author) FEUP; Pogodaev, N (Author) Other; Staritsyn, M (Author) FEUP

Journal

Title: Applied Mathematics and Optimization

Vol. 88

ISSN: 0095-4616

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 0 Citations

Scopus - 0 Citations

Scientific classification

CORDIS: Physical sciences

FOS: Natural sciences

Other information

Authenticus ID: P-00Z-5GM

DOI: 10.1007/s00245-023-10062-w

Abstract (EN): The paper addresses an optimal ensemble control problem for nonlocal continuity equations on the space of probability measures. We admit the general nonlinear cost functional, and an option to directly control the nonlocal terms of the driving vector field. For this problem, we design a descent method based on Pontryagin's maximum principle (PMP). To this end, we derive a new form of PMP with a decoupled Hamiltonian system. Specifically, we extract the adjoint system of linear nonlocal balance laws on the space of signed measures and prove its well-posedness. As an implementation of the designed descent method, we propose an indirect deterministic numeric algorithm with backtracking. We prove the convergence of the algorithm and illustrate its modus operandi by treating a simple case involving a Kuramoto-type model of a population of interacting oscillators.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 37