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We consider the Cauchy problem for non-autonomous forms inducing elliptic operators in divergence form with Dirichlet, Neumann, or mixed boundary conditions on an open subset $\Omega$ $\subseteq$ R n. We obtain maximal regularity in L 2…

Functional Analysis · Mathematics 2019-12-06 Pascal Auscher , Moritz Egert

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…

We consider optimal control of the scalar wave equation where the control enters as a coefficient in the principal part. Adding a total variation penalty allows showing existence of optimal controls, which requires continuity results for…

Optimization and Control · Mathematics 2021-09-28 Christian Clason , Karl Kunisch , Philip Trautmann

We consider a pathwise stochastic optimal control problem and study the associated (not necessarily adapted) Hamilton-Jacobi-Bellman stochastic partial differential equation. We show that the value process is the unique solution of this…

Probability · Mathematics 2023-11-02 Neeraj Bhauryal , Ana Bela Cruzeiro , Carlos Oliveira

Optimal control problems without control costs in general do not possess solutions due to the lack of coercivity. However, unilateral constraints together with the assumption of existence of strictly positive solutions of a pre-adjoint…

Optimization and Control · Mathematics 2017-02-27 Christian Clason , Anton Schiela

A geometric derivation of numerical integrators for optimal control problems is proposed. It is based in the classical technique of generating functions adapted to the special features of optimal control problems.

Optimization and Control · Mathematics 2025-10-20 M. de Leon , D. Martin de Diego , A. Santamaria-Merino

This paper introduces and analyses a continuous optimization approach to solve optimal control problems involving ordinary differential equations (ODEs) and tracking type objectives. Our aim is to determine control or input functions, and…

Optimization and Control · Mathematics 2024-05-09 Vicky Holfeld , Michael Burger , Claudia Schillings

An optimal control problem for the linear wave equation with control cost chosen as the BV semi-norm in time is analyzed. This formulation enhances piecewise constant optimal controls and penalizes the number of jumps. Existence of optimal…

Optimization and Control · Mathematics 2018-09-11 Sebastian Engel , Karl Kunisch

In this work we study an optimal control problem subject to the instationary Navier-Stokes equations, where the control enters via an inhomogeneous Neumann/Do-Nothing boundary condition. Despite the Navier-Stokes equations with these…

Optimization and Control · Mathematics 2026-05-20 Boris Vexler , Jakob Wagner

We use a computer algebra system to compute, in an efficient way, optimal control variational symmetries up to a gauge term. The symmetries are then used to obtain families of Noether's first integrals, possibly in the presence of…

Optimization and Control · Mathematics 2007-10-14 Paulo D. F. Gouveia , Delfim F. M. Torres , Eugenio A. M. Rocha

We consider an optimal control problem governed by a class of boundary value problem with the spectral Dirichlet fractional Laplacian. Some sufficient condition for the existence of optimal processes is stated. The proof of the main result…

Analysis of PDEs · Mathematics 2017-12-29 Dorota Bors

In this article we study an optimal control problem subject to the Fokker-Planck equation \[ \partial_t \rho - \nu \Delta \rho - {\rm div } \big(\rho B[u]\big) = 0. \] The control variable $u$ is time-dependent and possibly…

Analysis of PDEs · Mathematics 2021-01-19 M. Soledad Aronna , Fredi Tröltzsch

In this paper we study and solve an optimal control problem motivated by applications in quantum and classical physics. Although apparently simple, this optimal control problem is not easy to solve and we resort to various elaborated…

Optimization and Control · Mathematics 2025-07-18 Arnaud Lazarus , Emmanuel Trélat

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 well-posedness of a class of optimal control problems is analysed, where the state equation couples a nonlinear degenerate Fokker-Planck equation with a system of Ordinary Differential Equations (ODEs). Such problems naturally arise as…

Optimization and Control · Mathematics 2024-11-01 Francesca Anceschi , Giacomo Ascione , Daniele Castorina , Francesco Solombrino

This paper concerns optimal control problems for a class of sweeping processes governed by discontinuous unbounded differential inclusions that are described via normal cone mappings to controlled moving sets. Largely motivated by…

Optimization and Control · Mathematics 2018-05-01 Nguyen D. Hoang , Boris S. Mordukhovich

A tracking type optimal control problem for a nonlinear and nonlocal kinetic Fokker-Planck equation which arises as the mean field limit of an interacting particle systems that is subject to distance dependent random fluctuations is…

Optimization and Control · Mathematics 2025-01-08 Tobias Breiten , Karl Kunisch

In this paper we study vakonomic dynamics on contact systems with nonlinear constraints. In order to obtain the dynamics, we consider a space of admisible paths, which are the ones tangent to a given submanifold. Then, we find the critical…

Mathematical Physics · Physics 2021-06-07 Manuel de León , Manuel Lainz , Miguel C. Muñoz-Lecanda

We develop a unified geometric framework for dissipative mechanical systems based on uniform $q$-contact manifolds, which provide an extended phase space equipped with multiple contact $1$-forms. Within this setting, we construct both…

Mathematical Physics · Physics 2026-04-09 Melvin Leok , Cristina Sardón , Xuefeng Zhao

Optimal Dirichlet boundary control for a fractional/normal evolution with a final observation is considered. The unique existence of the solution and the first-order optimality condition of the optimal control problem are derived. The…

Numerical Analysis · Mathematics 2020-07-20 Qin Zhou , Binjie Li