On the viability and invariance of proper sets under continuity inclusions in wasserstein spaces

B Bonnet-Weill, H Frankowska - SIAM Journal on Mathematical Analysis, 2024 - SIAM
In this article, we derive conditions for the existence of solutions to state-constrained
continuity inclusions in Wasserstein spaces whose right-hand sides may be discontinuous in …

[HTML][HTML] Sixty Years of the Maximum Principle in Optimal Control: Historical Roots and Content Classification

R Chertovskih, VM Ribeiro, R Gonçalves, AP Aguiar - Symmetry, 2024 - mdpi.com
This study examines the scientific production focused on the Maximum Principle between
1962 and 2021. Results indicate a consistent increase in the absolute number of …

Trajectory stabilization of nonlocal continuity equations by localized controls

N Pogodaev, F Rossi - arXiv preprint arXiv:2403.02837, 2024 - arxiv.org
We discuss stabilization around trajectories of the continuity equation with nonlocal vector
fields, where the control is localized, ie, it acts on a fixed subset of the configuration space …

A Convergence result of a continuous model of deep learning via\L {} ojasiewicz--Simon inequality

N Isobe - arXiv preprint arXiv:2311.15365, 2023 - arxiv.org
This study focuses on a Wasserstein-type gradient flow, which represents an optimization
process of a continuous model of a Deep Neural Network (DNN). First, we establish the …

Optimal control of distributed ensembles with application to Bloch equations

R Chertovskih, N Pogodaev… - IEEE Control Systems …, 2023 - ieeexplore.ieee.org
Motivated by the problem of designing robust composite pulses for Bloch equations in the
presence of natural perturbations, we study an abstract optimal ensemble control problem in …

Optimal Control of Diffusion Processes: Infinite-Order Variational Analysis and Numerical Solution

R Chertovskih, N Pogodaev… - IEEE Control Systems …, 2024 - ieeexplore.ieee.org
We tackle a nonlinear optimal control problem for a stochastic differential equation in
Euclidean space and its state-linear counterpart for the Fokker-Planck-Kolmogorov equation …

Stabilization via localized controls in nonlocal models of crowd dynamics

N Pogodaev, F Rossi - arXiv preprint arXiv:2403.03580, 2024 - arxiv.org
We consider a control system driven by a nonlocal continuity equation. Admissible controls
are Lipschitz vector fields acting inside a fixed open set. We demonstrate that small …

[PDF][PDF] Sixty Years of the Maximum Principle in Optimal Control: Historical Roots and Content Classification. Symmetry 2024, 16, 1398

R Chertovskih, VM Ribeiro, R Gonçalves, AP Aguiar - 2024 - researchgate.net
This study examines the scientific production focused on the Maximum Principle between
1962 and 2021. Results indicate a consistent increase in the absolute number of …

An Enhanced Newton-Kantorovich Technique for Nonlinear Problem-solvers to Optimal Control Convergence

RA Isewid - Al-Qadisiyah Journal of Pure Science, 2024 - qjps.researchcommons.org
The aforementioned study aims to tackle the shortcomings of current methods to solve
Banach space-valued problems in nonlinear functional modeling using the Newton …