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Appropriate time discretization is crucial for real-time applications of numerical optimal control, such as nonlinear model predictive control. However, if the discretization error strongly depends on the applied control input, meeting…

Optimization and Control · Mathematics 2024-09-17 Amon Lahr , Filip Tronarp , Nathanael Bosch , Jonathan Schmidt , Philipp Hennig , Melanie N. Zeilinger

In this study, we introduce numerical methods for discretizing continuous-time linear-quadratic optimal control problems (LQ-OCPs). The discretization of continuous-time LQ-OCPs is formulated into differential equation systems, and we can…

This study focuses on the numerical discretization methods for the continuous-time discounted linear-quadratic optimal control problem (LQ-OCP) with time delays. By assuming piecewise constant inputs, we formulate the discrete system…

Optimization and Control · Mathematics 2024-07-29 Zhanhao Zhang , Steen Hørsholt , John Bagterp Jørgensen

This paper presents the numerical discretization methods of the continuous-time linear-quadratic optimal control problems (LQ-OCPs) with time delays. We describe the weight matrices of the LQ-OCPs as differential equations systems, allowing…

Systems and Control · Electrical Eng. & Systems 2024-04-15 Zhanhao Zhang , Steen Hørsholt , John Bagterp Jørgensen

For linear-quadratic optimal control problems (OCPs) governed by elliptic and parabolic partial differential equations (PDEs), we investigate the impact of perturbations on optimal solutions. Local perturbations may occur, e.g., due to…

Optimization and Control · Mathematics 2024-10-08 Simone Göttlich , Manuel Schaller , Karl Worthmann

In this work, we present numerical analysis for a distributed optimal control problem, with box constraint on the control, governed by a subdiffusion equation which involves a fractional derivative of order $\alpha\in(0,1)$ in time. The…

Numerical Analysis · Mathematics 2017-12-22 Bangti Jin , Buyang Li , Zhi Zhou

A new method for the optimal solutions is proposed. Originating from the continuous-time dynamics stability theory in the control field, the optimal solution is anticipated to be obtained in an asymptotically evolving way. By introducing a…

Systems and Control · Computer Science 2017-04-11 Sheng Zhang , En-Mi Yong , Wei-Qi Qian , Kai-Feng He

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

The derivation of second-order ordinary differential equations (ODEs) as continuous-time limits of optimization algorithms has been shown to be an effective tool for the analysis of these algorithms. Additionally, discretizing…

Optimization and Control · Mathematics 2019-08-29 Rachel Walker , Emily Zhang

Optimal control problems with oscillations (chattering controls) and concentrations (impulsive controls) can have integral performance criteria such that concentration of the control signal occurs at a discontinuity of the state signal.…

Optimization and Control · Mathematics 2019-01-29 Didier Henrion , Martin Kru{ž}ík , Tillmann Weisser

A parametric constrained convex optimal control problem, where the initial state is perturbed and the linear state equation contains a noise, is considered in this paper. Formulas for computing the subdifferential and the singular…

Optimization and Control · Mathematics 2017-07-14 Duong Thi Viet An , Jen-Chih Yao , Nguyen Dong Yen

The first order optimality conditions of optimal control problems (OCPs) can be regarded as boundary value problems for Hamiltonian systems. Variational or symplectic discretisation methods are classically known for their excellent long…

Optimization and Control · Mathematics 2021-11-24 Christian Offen , Sina Ober-Blöbaum

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

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

We propose an {\em implementable} numerical scheme for the discretization of linear-quadratic optimal control problems involving SDEs in higher dimensions with {\em control constraint}. For time discretization, we employ the implicit Euler…

Analysis of PDEs · Mathematics 2024-12-12 Abhishek Chaudhary

This work discusses the finite element discretization of an optimal control problem for the linear wave equation with time-dependent controls of bounded variation. The main focus lies on the convergence analysis of the discretization…

Optimization and Control · Mathematics 2019-07-26 Sebastian Engel , Philip Trautmann , Boris Vexler

Optimal control problems naturally arise in many scientific applications where one wishes to steer a dynamical system from a certain initial state $\mathbf{x}_0$ to a desired target state $\mathbf{x}^*$ in finite time $T$. Recent advances…

Machine Learning · Computer Science 2022-09-20 Lucas Böttcher , Thomas Asikis

In this paper we consider an optimal control problem (OCP) for the coupled system of a nonlinear monotone Dirichlet problem with matrix- valued non-smooth controls in coefficients and a nonlinear equation of Ham- merstein type. Since…

Optimization and Control · Mathematics 2017-02-28 Olha P. Kupenko , Rosanna Manzo

Limitations of the delayed feedback control and of its extended versions have been fully treated in the literature. The oscillating delayed feedback control appears as a promising scheme to overcome this problem. In this work, two methods…

Dynamical Systems · Mathematics 2018-05-25 Verónica E. Pastor , Graciela González

We study an optimal control problem in which both the objective function and the dynamic constraint contain an uncertain parameter. Since the distribution of this uncertain parameter is not exactly known, the objective function is taken as…

Optimization and Control · Mathematics 2016-11-29 Jianxiong Ye , Lei Wang , Changzhi Wu , Jie Sun , Kok Lay Teo , Xiangyu Wang
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