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We consider an abstract framework for the numerical solution of optimal control problems (OCPs) subject to partial differential equations (PDEs). Examples include not only the distributed control of elliptic PDEs such as the Poisson…

Numerical Analysis · Mathematics 2025-05-27 Ulrich Langer , Richard Löscher , Olaf Steinbach , Huidong Yang

Model predictive control is a powerful framework for enabling optimal control of constrained systems. However, for systems that are described by high-dimensional state spaces this framework can be too computationally demanding for real-time…

Systems and Control · Electrical Eng. & Systems 2020-08-24 Joseph Lorenzetti , Marco Pavone

In this chapter, we are concerned with inverse optimal control problems, i.e., optimization models which are used to identify parameters in optimal control problems from given measurements. Here, we focus on linear-quadratic optimal control…

Optimization and Control · Mathematics 2023-11-27 Stephan Dempe , Markus Friedemann , Felix Harder , Patrick Mehlitz , Gerd Wachsmuth

In this paper we study the conditioning of optimal control problems constrained by linear parabolic equations with Neumann boundary conditions. While we concentrate on a given end-time target function the results hold also when the target…

Numerical Analysis · Mathematics 2025-03-24 Luise Blank

Model Predictive Control (MPC) is a well-established approach to solve infinite horizon optimal control problems. Since optimization over an infinite time horizon is generally infeasible, MPC determines a suboptimal feedback control by…

Optimization and Control · Mathematics 2022-10-26 Saskia Dietze , Martin A. Grepl

A finite element analysis of a Dirichlet boundary control problem governed by the linear parabolic equation is presented in this article. The Dirichlet control is considered in a closed and convex subset of the energy space $H^1(\Omega…

Numerical Analysis · Mathematics 2021-11-04 Thirupathi Gudi , Gouranga Mallik , Ramesh Ch. Sau

This paper considers the problem of determining an optimal control action based on observed data. We formulate the problem assuming that the system can be modelled by a nonlinear state-space model, but where the model parameters, state and…

Optimization and Control · Mathematics 2021-07-02 Johannes N. Hendriks , James R. Z. Holdsworth , Adrian G. Wills , Thomas B. Schon , Brett Ninness

We derive a framework to compute optimal controls for problems with states in the space of probability measures. Since many optimal control problems constrained by a system of ordinary differential equations (ODE) modelling interacting…

Optimization and Control · Mathematics 2020-09-23 Martin Burger , René Pinnau , Claudia Totzeck , Oliver Tse

We consider a one dimensional elliptic distributed optimal control problem with pointwise constraints on the derivative of the state. By exploiting the variational inequality satisfied by the derivative of the optimal state, we obtain…

Numerical Analysis · Mathematics 2021-06-18 Susanne C. Brenner , Li-yeng Sung , Winnifried Wollner

In this paper we discuss optimality conditions for abstract optimization problems over complex spaces. We then apply these results to optimal control problems with a semigroup structure. As an application we detail the case when the state…

Optimization and Control · Mathematics 2019-01-15 M. Soledad Aronna , Frédéric Bonnans , Axel Kröner

We study a control problem governed by a semilinear parabolic equation with pointwise control and state constraints imposed at every point of the space-time cylinder. We obtain second order sufficient optimality conditions for local…

Optimization and Control · Mathematics 2024-03-04 Eduardo Casas , Mariano Mateos , Arnd Rösch

In this work, we will investigate the question of optimal control for bilinear systems with constrained endpoint. The optimal control will be characterized through a set of unconstrained minimization problems that approximate the former.…

Optimization and Control · Mathematics 2021-07-28 Soufiane Yahyaoui , Lahoussine Lafhim , Mohamed Ouzahra

Infinite horizon open loop optimal control problems for semilinear parabolic equations are investigated. The controls are subject to a cost-functional which promotes sparsity in time. The focus is put on deriving first order optimality…

Optimization and Control · Mathematics 2021-12-14 Eduardo Casas , Karl Kunisch

This paper studies multiobjective optimal control problems in the continuous-time framework when the space of states and the space of controls are infinite-dimensional and with lighter smoothness assumptions than the usual ones. The paper…

Optimization and Control · Mathematics 2022-07-04 Naila Hayek , Hasan Yilmaz

This paper is dedicated to the analysis of infinite horizon optimal control problems subject to semilinear parabolic equations with constraints on the controls and discounted cost functionals. The discount factors on the cost and the state…

Optimization and Control · Mathematics 2026-04-24 Eduardo Casas , Karl Kunisch

An optimal control problem driven by an ordinary differential equation under continuous state constraints is considered in this study. From an operational point of view, we introduce a discrete state constraints optimal control problem and…

Optimization and Control · Mathematics 2018-12-04 Shuzhen Yang

We study a control problem where the state equation is a nonlinear partial differential equation of the calculus of variation in a bounded domain, perturbed by noise. We allow the control to act on the boundary and set stochastic boundary…

Probability · Mathematics 2025-11-26 Stefano Bonaccorsi , Adrian Zalinescu

We consider both discrete and continuous control problems constrained by a fixed budget of some resource, which may be renewed upon entering a preferred subset of the state space. In the discrete case, we consider both deterministic and…

Optimization and Control · Mathematics 2014-09-30 Ryo Takei , Weiyan Chen , Zachary Clawson , Slav Kirov , Alexander Vladimirsky

Infinite-dimensional linear conic formulations are described for nonlinear optimal control problems. The primal linear problem consists of finding occupation measures supported on optimal relaxed controlled trajectories, whereas the dual…

Optimization and Control · Mathematics 2014-07-08 Didier Henrion , Edouard Pauwels

We consider a distributed optimal control problem subject to a parabolic evolution equation as constraint. The control will be considered in the energy norm of the anisotropic Sobolev space $[H_{0;,0}^{1,1/2}(Q)]^\ast$, such that the state…

Numerical Analysis · Mathematics 2025-02-14 Richard Löscher , Michael Reichelt , Olaf Steinbach