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Motivated by the applications, a class of optimal control problems is investigated, where the goal is to influence the behavior of a given population through another controlled one interacting with the first. Diffusive terms accounting for…

Optimization and Control · Mathematics 2023-03-10 Stefano Almi , Marco Morandotti , Francesco Solombrino

We consider an optimal control problem constrained by a parabolic partial differential equation (PDE) with Robin boundary conditions. We use a well-posed space-time variational formulation in Lebesgue--Bochner spaces with minimal…

Numerical Analysis · Mathematics 2022-12-06 Nina Beranek , M. Alexander Reinhold , Karsten Urban

The first-order optimality conditions for a generic nonlinear optimization problem are generated as part of the terminal transversality conditions of an optimal control problem. It is shown that the Lagrangian of the optimization problem is…

Optimization and Control · Mathematics 2022-03-17 I. M. Ross

In this note, we develop the first-order theory of optimal control problems with box constraints on the control. We emphasize the precise modification of Pontryagin's maximum principle when the admissible control set is compact, the…

Optimization and Control · Mathematics 2026-04-08 Louis Shuo Wang

The study is devoted to mathematical modeling and optimal control design of longitudinal motions of a rectilinear elastic rod. The control inputs are a force, which is normal to the cross section and distributed piecewise constantly along…

Optimization and Control · Mathematics 2022-07-22 Georgy Kostin , Alexander Gavrikov

This paper firstly presents the necessary and sufficient conditions for a kind of discrete-time robust stochastic optimal control problem with convex control domains. As it is an "inf sup problem", the classical variational method is…

Optimization and Control · Mathematics 2025-08-26 Wei He

We study the problem of optimally managing an inventory with unknown demand trend. Our formulation leads to a stochastic control problem under partial observation, in which a Brownian motion with non-observable drift can be singularly…

Optimization and Control · Mathematics 2022-11-28 Salvatore Federico , Giorgio Ferrari , Neofytos Rodosthenous

We generalize the Lagrangian-Hamiltonian formalism of Skinner and Rusk to higher order field theories on fiber bundles. As a byproduct we solve the long standing problem of defining, in a coordinate free manner, a Hamiltonian formalism for…

Differential Geometry · Mathematics 2010-05-07 L. Vitagliano

Numerical methods that preserve geometric invariants of the system, such as energy, momentum or the symplectic form, are called geometric integrators. In this paper we present a method to construct symplectic-momentum integrators for…

Numerical Analysis · Mathematics 2014-11-07 Leonardo Colombo , Sebastián Ferraro , David Martín de Diego

It has been shown recently that optimal control problems with the dynamical constraint given by a second order system admit a regular Lagrangian formulation. This implies that the optimality conditions can be obtained in a new form based on…

The present paper extends the classical second-order variational problem of Herglotz type to the more general context of the Euclidean sphere S^n following variational and optimal control approaches. The relation between the Hamiltonian…

Differential Geometry · Mathematics 2018-11-13 L. Machado , L. Abrunheiro , N. Martins

In this paper we study, from a variational and geometrical point of view, second-order variational problems on Lie groupoids and the construction of variational integrators for optimal control problems. First, we develop variational…

Dynamical Systems · Mathematics 2015-06-30 Leonardo Colombo , David Martin de Diego

In this paper we develop a geometric approach to higher order mechanics on graded bundles in both, the Lagrangian and Hamiltonian formalism, via the recently discovered weighted algebroids. We present the corresponding Tulczyjew triple for…

Mathematical Physics · Physics 2015-12-18 Andrew James Bruce , Katarzyna Grabowska , Janusz Grabowski

This article develops variational integrators for a class of underactuated mechanical systems using the theory of discrete mechanics. Further, a discrete optimal control problem is formulated for the considered class of systems and…

Systems and Control · Computer Science 2018-11-16 Siddharth H. Nair , Ravi N. Banavar

We investigate symmetry reduction of optimal control problems for left-invariant control systems on Lie groups, with partial symmetry breaking cost functions. Our approach emphasizes the role of variational principles and considers a…

Optimization and Control · Mathematics 2017-01-25 Anthony Bloch , Leonardo Colombo , Rohit Gupta , Tomoki Ohsawa

An interesting family of geometric integrators for Lagrangian systems can be defined using discretizations of the Hamilton's principle of critical action. This family of geometric integrators is called variational integrators. In this…

Mathematical Physics · Physics 2015-06-16 Leonardo Colombo , David Martín de Diego , Marcela Zuccalli

The paper concerns the study and applications of a new class of optimal control problems governed by a perturbed sweeping process of the hysteresis type with control functions acting in both play-and-stop operator and additive…

Optimization and Control · Mathematics 2015-12-01 Tan H. Cao , Boris S. Mordukhovich

This paper aims to establish second order necessary conditions for optimal control in quantum stochastic systems. We employ a variational approach, analogous to methods in classical stochastic control, to analyze systems governed by quantum…

Optimization and Control · Mathematics 2026-03-17 Penghui Wang , Shan Wang

We consider control-constrained linear-quadratic optimal control problems on evolving surfaces. In order to formulate well-posed problems, we prove existence and uniqueness of weak solutions for the state equation, in the sense of…

Optimization and Control · Mathematics 2015-03-19 Morten Vierling

We study a multiscale stochastic optimal control problem subject to state constraints on the slow variable. To address this class of problems, we develop a rigorous theoretical framework based on singular perturbation analysis, tailored to…

Optimization and Control · Mathematics 2025-08-12 Anderson O. Calixto , Bernardo Freitas Paulo da Costa , Glauco Valle