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The objective of this paper is to weaken the Lipschitz condition to a monotonicity condition and to study the corresponding Pontryagin stochastic maximum principle (SMP) for a mean-field optimal control problem under monotonicity…

Optimization and Control · Mathematics 2025-03-18 Bowen He , Juan Li , Zhanxin Li

This paper is mainly concerned with the solutions to both forward and backward mean-field stochastic partial differential equation and the corresponding optimal control problem for mean-field stochastic partial differential equation. We…

Optimization and Control · Mathematics 2016-10-11 Maoning Tang , Qingxin Meng

This paper considers a mean field game model inspired by crowd motion where agents want to leave a given bounded domain through a part of its boundary in minimal time. Each agent is free to move in any direction, but their maximal speed is…

Optimization and Control · Mathematics 2022-02-21 Guilherme Mazanti , Filippo Santambrogio

We consider distributed-order non-local fractional optimal control problems with controls taking values on a closed set and prove a strong necessary optimality condition of Pontryagin type. The possibility that admissible controls are…

Optimization and Control · Mathematics 2021-08-10 Faical Ndairou , Delfim F. M. Torres

We consider optimal control problems, where the control appears in the main part of the operator. We derive the Pontryagin maximum principle as a necessary optimality condition. The proof uses the concept of topological derivatives. In…

Optimization and Control · Mathematics 2024-08-01 Daniel Wachsmuth

We establish a variety of results extending the well-known Pontryagin maximum principle of optimal control to discrete-time optimal control problems posed on smooth manifolds. These results are organized around a new theorem on critical and…

Optimization and Control · Mathematics 2017-07-14 Robert Kipka , Rohit Gupta

We derive a first order optimality condition for a class of agent-based systems, as well as for their mean-field counterpart. A relevant difficulty of our analysis is that the state equation is formulated on possibly infinite-dimensional…

Analysis of PDEs · Mathematics 2025-03-05 Stefano Almi , Riccardo Durastanti , Francesco Solombrino

In this work, we propose and study a new approach to formulate the optimal control problem of second-order differential equations, with a particular interest in those derived from force-controlled Lagrangian systems. The formulation results…

The fundamental theorem of the theory of optimal control, the Pontryagin maximum principle (PMP), is extended to the setting of almost Lie (AL) algebroids, geometrical objects generalizing Lie algebroids. This formulation of the PMP yields,…

Optimization and Control · Mathematics 2013-06-13 Janusz Grabowski , Michal Jozwikowski

The famous proof of the Pontryagin maximum principle for control problems on a finite horizon bases on the needle variation technique, as well as the separability concept of cones created by disturbances of the trajectories. In this…

Optimization and Control · Mathematics 2018-07-05 Nico Tauchnitz

In this article we derive a strong version of the Pontryagin Maximum Principle for general nonlinear optimal control problems on time scales in finite dimension. The final time can be fixed or not, and in the case of general boundary…

Optimization and Control · Mathematics 2013-02-15 Loïc Bourdin , Emmanuel Trélat

In this work, we systematically investigate mean field games and mean field type control problems with multiple populations using a coupled system of forward-backward stochastic differential equations of McKean-Vlasov type stemming from…

Probability · Mathematics 2020-11-03 Masaaki Fujii

We consider deterministic mean field games in which the agents control their acceleration and are constrained to remain in a domain of R n. We study relaxed equilibria in the Lagrangian setting; they are described by a probability measure…

Analysis of PDEs · Mathematics 2021-11-04 Yves Achdou , Paola Mannucci , Claudio Marchi , Nicoletta Tchou

We study the time-optimal robust control of a two-level quantum system subjected to field inhomogeneities. We apply the Pontryagin Maximum Principle and we introduce a reduced space onto which the optimal dynamics is projected down. This…

Quantum Physics · Physics 2025-09-03 O. Fresse-Colson , S. Guérin , Xi Chen , D. Sugny

A geometric approach to time-dependent optimal control problems is proposed. This formulation is based on the Skinner and Rusk formalism for Lagrangian and Hamiltonian systems. The corresponding unified formalism developed for optimal…

We consider an optimal control problem for a system of local continuity equations on a space of probability measures. Such systems can be viewed as macroscopic models of ensembles of non-interacting particles or homotypic individuals,…

Optimization and Control · Mathematics 2021-10-07 Maxim Staritsyn , Nikolay Pogodaev , Roman Chertovskih , Fernando Lobo Pereira

Controllability maximization problem under sparsity constraints is a node selection problem that selects inputs that are effective for control in order to minimize the energy to control for desired state. In this paper we discuss the…

Optimization and Control · Mathematics 2022-03-25 Tomofumi Ohtsuka , Takuya Ikeda , Kenji Kashima

In this paper, we prove a Pontryagin Maximum Principle for constrained optimal control problems in the Wasserstein space of probability measures. The dynamics, is described by a transport equation with non-local velocities and is subject to…

Optimization and Control · Mathematics 2019-10-22 Benoît Bonnet

In this paper, we derive a version of the Pontryagin maximum principle for general finite-dimensional nonlinear optimal sampled-data control problems. Our framework is actually much more general, and we treat optimal control problems for…

Optimization and Control · Mathematics 2015-12-09 Loïc Bourdin , Emmanuel Trélat

We consider nonsmooth optimal control problems subject to a linear elliptic partial differential equation with homogeneous Dirichlet boundary conditions. It is well-known that local solutions satisfy the celebrated Pontryagin maximum…

Optimization and Control · Mathematics 2024-06-28 Daniel Wachsmuth