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Related papers: Error estimates for a bilinear optimal control pro…

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Optimal control of bilinear systems has been a well-studied subject in the areas of mathematical and computational optimal control. However, effective methods for solving emerging optimal control problems involving an ensemble of…

Optimization and Control · Mathematics 2016-12-02 Shuo Wang , Jr-Shin Li

This paper studies convergence properties of inexact iterative solution schemes for bilevel optimization problems. Bilevel optimization problems emerge in control-aware design optimization, where the system design parameters are optimized…

Optimization and Control · Mathematics 2024-03-26 Torbjørn Cunis Ilya Kolmanovsky

This work is motivated by the need to study the impact of data uncertainties and material imperfections on the solution to optimal control problems constrained by partial differential equations. We consider a pathwise optimal control…

Optimization and Control · Mathematics 2016-03-01 Ahmad Ahmad Ali , Elisabeth Ullmann , Michael Hinze

We consider an elliptic optimal control problem where the objective functional contains evaluations of the state at a finite number of points. In particular, we use a fidelity term that encourages the state to take certain values at these…

Numerical Analysis · Mathematics 2014-11-19 C. Brett , A. S. Dedner , C. M. Elliott

In this paper, we present and analyze an interior penalty discontinuous Galerkin method for the distributed elliptic optimal control problems. It is based on a reconstructed discontinuous approximation which admits arbitrarily high-order…

Numerical Analysis · Mathematics 2026-01-05 Ruo Li , Haoyang Liu , Jun Yin

We propose a randomized a posteriori error estimator for reduced order approximations of parametrized (partial) differential equations. The error estimator has several important properties: the effectivity is close to unity with prescribed…

Numerical Analysis · Mathematics 2019-04-02 Kathrin Smetana , Olivier Zahm , Anthony T Patera

This work deals with optimal control problems as a strategy to drive bifurcating solution of nonlinear parametrized partial differential equations towards a desired branch. Indeed, for these governing equations, multiple solution…

Numerical Analysis · Mathematics 2023-08-08 Federico Pichi , Maria Strazzullo , Francesco Ballarin , Gianluigi Rozza

We propose a new a posteriori error estimator for mixed finite element discretizations of the curl-curl problem. This estimator relies on a Prager--Synge inequality, and therefore leads to fully guaranteed constant-free upper bounds on the…

Numerical Analysis · Mathematics 2023-08-07 T. Chaumont-Frelet

In this paper, error estimates are presented for a certain class of optimal control problems with elliptic PDE-constraints. It is assumed that in the cost functional the state is measured in terms of the energy norm generated by the state…

Numerical Analysis · Mathematics 2014-10-31 Olli Mali

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

This paper studies the problem of steering a linear time-invariant system subject to state and input constraints towards a goal location that may be inferred only through partial observations. We assume mixed-observable settings, where the…

Optimization and Control · Mathematics 2022-11-22 Ugo Rosolia , Yuxiao Chen , Shreyansh Daftry , Masahiro Ono , Yisong Yue , Aaron D. Ames

In this paper we study the mixed virtual element approximation to an elliptic optimal control problem with boundary observations. The objective functional of this type of optimal control problem contains the outward normal derivatives of…

Numerical Analysis · Mathematics 2023-12-19 Minghui Yang , Zhaojie Zhou

We present a method for the numerical approximation of distributed optimal control problems constrained by parabolic partial differential equations. We complement the first-order optimality condition by a recently developed space-time…

Numerical Analysis · Mathematics 2022-08-23 Thomas Führer , Michael Karkulik

We introduce a family of hybrid discretisations for the numerical approximation of optimal control problems governed by the equations of immiscible displacement in porous media. The proposed schemes are based on mixed and discontinuous…

Numerical Analysis · Mathematics 2019-05-02 S. Kumar , R. Ruiz Baier , R. Sandilya

Though switched dynamical systems have shown great utility in modeling a variety of physical phenomena, the construction of an optimal control of such systems has proven difficult since it demands some type of optimal mode scheduling. In…

Optimization and Control · Mathematics 2014-02-04 Ramanarayan Vasudevan , Humberto Gonzalez , Ruzena Bajcsy , S. Shankar Sastry

The aim of this paper is to obtain a posteriori error bounds of optimal order in time and space for the linear second-order wave equation discretized by the Newmark scheme in time and the finite element method in space. Error estimates are…

Numerical Analysis · Mathematics 2017-09-22 Olga Gorynina , Alexei Lozinski , Marco Picasso

We develop a Monte-Carlo based numerical method for solving discrete-time stochastic optimal control problems with inventory. These are optimal control problems in which the control affects only a deterministically evolving inventory…

Optimization and Control · Mathematics 2018-02-05 Alessandro Balata , Jan Palczewski

We present the conditions under which the time-optimal control problem for a nonlinear non-autonomous linearizable system can be solved by the method of successive approximations, at each step of which a power Markov moment min-problem is…

Optimization and Control · Mathematics 2022-03-17 Katerina V. Sklyar , Svetlana Yu. Ignatovich

This papers shows the convergence of optimal control problems where the constraint function is discretised by a particle method. In particular, we investigate the viscous Burgers equation in the whole space $\mathbb R$ by using…

Optimization and Control · Mathematics 2013-10-01 Jan Marburger , Rene Pinnau

In this paper we study the a posteriori bounds for a conforming piecewise linear finite element approximation of the Signorini problem. We prove new rigorous a posteriori estimates of residual type in $L^{p}$, for $p \in (4,\infty)$ in two…

Numerical Analysis · Mathematics 2024-04-02 Ben S. Ashby , Tristan Pryer