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We consider a nonlinear ordinary differential equation and want to control its behavior so that it reaches a target by minimizing a cost function. Our approach is to use hybrid systems to solve this problem: the complex dynamic is replaced…

Optimization and Control · Mathematics 2008-01-07 Jean-Guillaume Luc Dumas , Aude Rondepierre

Semi-lagrangian schemes for discretization of the dynamic programming principle are based on a time discretization projected on a state-space grid. The use of a structured grid makes this approach not feasible for high-dimensional problems…

Numerical Analysis · Mathematics 2023-06-09 Alessandro Alla , Hugo Oliveira , Gabriele Santin

Piecewise constant control approximation provides a practical framework for designing numerical schemes of continuous-time control problems. We analyze the accuracy of such approximations for extended mean field control (MFC) problems,…

Optimization and Control · Mathematics 2025-09-03 Christoph Reisinger , Wolfgang Stockinger , Maria Olympia Tsianni , Yufei Zhang

The paper addresses an optimal control problem for a perturbed sweeping process of the rate-independent hysteresis type described by a controlled "play and stop" operator with separately controlled perturbations. This problem can be reduced…

Optimization and Control · Mathematics 2015-12-01 Tan H. Cao , Boris S. Mordukhovich

In this work, we investigate the optimal control problem for continuous-time Markov decision processes with the random impact of the environment. We provide conditions to show the existence of optimal controls under finite-horizon criteria.…

Optimization and Control · Mathematics 2020-06-23 Jinghai Shao , Kun Zhao

This paper considers an optimal impulse control problem of dynamical systems generated by a flow. The performance criteria are total costs over the infinite time horizon. Apart from the main performance to be minimized, there are multiple…

Optimization and Control · Mathematics 2020-10-27 Alexey Piunovskiy , Yi Zhang

We study an explicit mirror-descent method for finite-horizon deterministic optimal control problems. The method is motivated by Pontryagin's maximum principle: at each iteration, one solves the state and adjoint equations and updates the…

Optimization and Control · Mathematics 2026-05-05 Ye Feng , Jianfeng Lu

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

This paper is concerned with the problem of Model Predictive Control and Rolling Horizon Control of discrete-time systems subject to possibly unbounded random noise inputs, while satisfying hard bounds on the control inputs. We use a…

Optimization and Control · Mathematics 2010-09-08 Peter Hokayem , Debasish Chatterjee , John Lygeros

This work presents an algorithmic scheme for solving the infinite-time constrained linear quadratic regulation problem. We employ an accelerated version of a popular proximal gradient scheme, commonly known as the Forward-Backward Splitting…

Optimization and Control · Mathematics 2015-01-20 Giorgos Stathopoulos , Milan Korda , Colin N. Jones

This paper is concerned with the distributed control and stabilization problems for linear discrete-time large scale systems with imposed constraints. The main contributions of this paper are: Firstly, by using the maximum principle…

Optimization and Control · Mathematics 2018-01-03 Qingyuan Qi , Huanshui Zhang , Peijun Ju

This paper presents and proves an equation for the time horizon of symmetric trajectories with zero boundary conditions and bounded derivatives of arbitrary order. This equation holds regardless of the number of phases comprising the…

Optimization and Control · Mathematics 2026-02-05 Rico Zöllner

The paper is devoted to the study of a new class of optimal control problems for nonsmooth dynamical systems governed by nonconvex discontinuous differential inclusions of the sweeping type with involving variable time into optimization. We…

Optimization and Control · Mathematics 2025-03-05 Tan H. Cao , Boris S. Mordukhovich , Dao Nguyen , Trang Nguyen , Nguyen N. Thieu

This paper addresses the optimal covariance steering problem for stochastic discrete-time linear systems subject to probabilistic state and control constraints. A method is presented for efficiently attaining the exact solution of the…

Systems and Control · Electrical Eng. & Systems 2023-10-06 George Rapakoulias , Panagiotis Tsiotras

We consider optimal control problems for partial differential equations where the controls take binary values but vary over the time horizon, they can thus be seen as dynamic switches. The switching patterns may be subject to combinatorial…

Optimization and Control · Mathematics 2024-04-04 Christoph Buchheim , Alexandra Grütering , Christian Meyer

Motivated by the design of fast reinforcement learning algorithms, we study the diffusive limit of a class of pure jump ergodic stochastic control problems. We show that, whenever the intensity of jumps is large enough, the approximation…

Optimization and Control · Mathematics 2022-10-03 Marc Abeille , Bruno Bouchard , Lorenzo Croissant

This paper investigates the infinite horizon optimal control problem (OCP) for space applications characterized by nonlinear dynamics. The proposed approach divides the problem into a finite horizon OCP with a regularized terminal cost,…

Optimization and Control · Mathematics 2025-10-13 Abhijeet , Mohamed Naveed Gul Mohamed , Aayushman Sharma , Suman Chakravorty

This paper is an attempt to remedy the problem of slow convergence for first-order numerical algorithms by proposing an adaptive conditioning heuristic. First, we propose a parallelizable numerical algorithm that is capable of solving…

Optimization and Control · Mathematics 2021-03-02 Muhammad Adil , Sasan Tavakkol , Ramtin Madani

The paper is concerned with space-time IgA approximations of parabolic initial-boundary value problems. We deduce guaranteed and fully computable error bounds adapted to special features of IgA approximations and investigate their…

Numerical Analysis · Mathematics 2018-02-20 Ulrich Langer , Svetlana Matculevich , Sergey Repin

In this paper we summarize our results in infinite horizon optimal control. We present optimality conditions for weak local minimizer in the framework of weighted functions. Moreover we formulate the Pontryagin Maximum Principle for strong…

Optimization and Control · Mathematics 2018-07-05 Nico Tauchnitz