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Computationally efficient nonlinear model predictive control relies on elaborate discrete-time optimal control problem (OCP) formulations trading off accuracy with respect to the continuous-time problem and associated computational burden.…

Optimization and Control · Mathematics 2024-08-15 Jonathan Frey , Katrin Baumgärtner , Gianluca Frison , Moritz Diehl

PDE-constrained optimal control problems require regularisation to ensure well-posedness, introducing small perturbations that make the solutions challenging to approximate accurately. We propose a finite element approach that couples both…

Numerical Analysis · Mathematics 2025-03-17 Jenny Power , Tristan Pryer

Probabilistic solvers for ordinary differential equations (ODEs) provide efficient quantification of numerical uncertainty associated with simulation of dynamical systems. Their convergence rates have been established by a growing body of…

Machine Learning · Statistics 2020-12-21 Nicholas Krämer , Philipp Hennig

Many robotics tasks, such as path planning or trajectory optimization, are formulated as optimal control problems (OCPs). The key to obtaining high performance lies in the design of the OCP's objective function. In practice, the objective…

Systems and Control · Electrical Eng. & Systems 2025-04-02 Trevor Barron , Xiaojing Zhang

Optimal Control (OC) is the process of determining control and state trajectories for a dynamic system, over a period of time, in order to optimize a given performance index. With the increasing of variables and complexity, OC problems can…

Optimization and Control · Mathematics 2014-09-02 Helena Sofia Rodrigues , M. Teresa T. Monteiro , Delfim F. M. Torres

This paper studies an optimal control problem governed by a semilinear elliptic equation, in which the control acts in a multiplicative or bilinear way as the reaction coefficient of the equation. We focus on the numerical discretization of…

Optimization and Control · Mathematics 2025-06-25 Eduardo Casas , Konstantinos Chrysafinos , Mariano Mateos

This paper studies an optimal control problem for continuous-time stochastic systems subject to reachability objectives specified in a subclass of metric interval temporal logic specifications, a temporal logic with real-time constraints.…

Systems and Control · Computer Science 2015-04-21 Jie Fu , Ufuk Topcu

We consider a control-constrained optimal control problem subject to time-harmonic Maxwell's equations; the control variable belongs to a finite-dimensional set and enters the state equation as a coefficient. We derive existence of optimal…

Numerical Analysis · Mathematics 2024-05-10 Francisco Fuica , Felipe Lepe , Pablo Venegas

In this paper, we study probabilistic numerical methods based on optimal quantization algorithms for computing the solution to optimal multiple switching problems with regime-dependent state process. We first consider a discrete-time…

Probability · Mathematics 2012-02-14 Paul Gassiat , Idris Kharroubi , Huyên Pham

Dynamical systems with a distributed yet interconnected structure, like multi-rigid-body robots or large-scale multi-agent systems, introduce valuable sparsity into the system dynamics that can be exploited in an optimal control setting for…

Robotics · Computer Science 2021-04-08 Roshan Pradhan , Shuo Yang , Frank Dellaert , Howie Choset , Matthew Travers

We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a control function. The robust formulation of the…

Numerical Analysis · Mathematics 2019-10-23 Philipp A. Guth , Vesa Kaarnioja , Frances Y. Kuo , Claudia Schillings , Ian H. Sloan

Time delays are ubiquitous in industry, and they must be accounted for when designing control strategies. However, numerical optimal control (NOC) of delay differential equations (DDEs) is challenging because it requires specialized…

Optimization and Control · Mathematics 2024-10-22 Tobias K. S. Ritschel , Søren Stange

Method-of-lines discretizations are demanding test problems for stiff integration methods. However, for PDE problems with known analytic solution the presence of space discretization errors or the need to use codes to compute reference…

Numerical Analysis · Mathematics 2023-05-24 Jens Lang , Bernhard A. Schmitt

In this paper, we propose an efficient implementation of deep policy gradient method (PGM) for optimal control problems in continuous time. The proposed method has the ability to manage the allocation of computational resources, number of…

Optimization and Control · Mathematics 2025-02-25 Arash Fahim , Md. Arafatur Rahman

In this paper we investigate a priori error estimates for the space-time Galerkin finite element discretization of a simplified semilinear gradient enhanced damage model. The model equations are of a special structure as the state equation…

Optimization and Control · Mathematics 2020-04-14 Marita Holtmannspötter , Arnd Rösch

This paper develops a probabilistic numerical method for solution of partial differential equations (PDEs) and studies application of that method to PDE-constrained inverse problems. This approach enables the solution of challenging inverse…

Methodology · Statistics 2017-07-12 Jon Cockayne , Chris Oates , Tim Sullivan , Mark Girolami

Optimal control of stochastic nonlinear dynamical systems is a major challenge in the domain of robot learning. Given the intractability of the global control problem, state-of-the-art algorithms focus on approximate sequential optimization…

Machine Learning · Computer Science 2020-04-23 Joe Watson , Hany Abdulsamad , Jan Peters

A research frontier has emerged in scientific computation, wherein numerical error is regarded as a source of epistemic uncertainty that can be modelled. This raises several statistical challenges, including the design of statistical…

Machine Learning · Statistics 2017-10-19 François-Xavier Briol , Chris. J. Oates , Mark Girolami , Michael A. Osborne , Dino Sejdinovic

In this article a special class of nonlinear optimal control problems involving a bilinear term in the boundary condition is studied. These kind of problems arise for instance in the identification of an unknown space-dependent Robin…

Numerical Analysis · Mathematics 2024-12-20 Max Winkler

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