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In this paper we discuss the use of implicit Runge-Kutta schemes for the time discretization of optimal control problems with evolution equations. The specialty of the considered discretizations is that the discretizations schemes for the…

Numerical Analysis · Mathematics 2013-11-05 Thomas G. Flaig

Iterative linear quadratic regulator (iLQR) has gained wide popularity in addressing trajectory optimization problems with nonlinear system models. However, as a model-based shooting method, it relies heavily on an accurate system model to…

Machine Learning · Computer Science 2022-09-16 Zilong Cheng , Yulin Li , Kai Chen , Jun Ma , Tong Heng Lee

Optimal control theory is usually formulated as an indirect method requiring the solution of a two-point boundary value problem. Practically, the solution is obtained by iterative forward and backward propagation of quantum wavepackets.…

Quantum Physics · Physics 2020-10-09 Alejandro R. Ramos Ramos , Oliver Kühn

- In this paper we introduce a new method to solve fixed-delay optimal control problems which exploits numerical homotopy procedures. It is known that solving this kind of problems via indirect methods is complex and computationally…

Optimization and Control · Mathematics 2017-03-16 Riccardo Bonalli , Bruno Hérissé , Emmanuel Trélat

Mechanical systems are usually modeled by second-order Ordinary Differential Equations (ODE) which take the form $\ddot{q} = f(t, q, \dot{q})$. While simulation methods tailored to these equations have been studied, using them in direct…

Optimization and Control · Mathematics 2023-04-26 Léo Simpson , Armin Nurkanović , Moritz Diehl

High order spatial discretizations with monotonicity properties are often desirable for the solution of hyperbolic PDEs. These methods can advantageously be coupled with high order strong stability preserving time discretizations. The…

Numerical Analysis · Mathematics 2014-03-27 Sigal Gottlieb , Zachary J. Grant , Daniel Higgs

This thesis presents new mathematical algorithms for the numerical solution of a mathematical problem class called \emph{dynamic optimization problems}. These are mathematical optimization problems, i.e., problems in which numbers are…

Optimization and Control · Mathematics 2022-08-22 Martin Peter Neuenhofen

The problem of resource allocation of nonlinear networked control systems is investigated, where, unlike the well discussed case of triggering for stability, the objective is optimal triggering. An approximate dynamic programming approach…

Systems and Control · Computer Science 2014-12-19 Ali Heydari

This paper introduces and analyses a continuous optimization approach to solve optimal control problems involving ordinary differential equations (ODEs) and tracking type objectives. Our aim is to determine control or input functions, and…

Optimization and Control · Mathematics 2024-05-09 Vicky Holfeld , Michael Burger , Claudia Schillings

We deal with optimal approximation of solutions of ODEs under local Lipschitz condition and inexact discrete information about the right-hand side functions. We show that the randomized two-stage Runge-Kutta scheme is the optimal method…

Numerical Analysis · Mathematics 2021-03-23 Tomasz Bochacik , Maciej Goćwin , Paweł M. Morkisz , Paweł Przybyłowicz

In this article we study optimal control problems for systems that are affine in one part of the control variable. Finitely many equality and inequality constraints on the initial and final values of the state are considered. We investigate…

Optimization and Control · Mathematics 2019-01-15 M. Soledad Aronna

A variety of optimal control, estimation, system identification and design problems can be formulated as functional optimization problems with differential equality and inequality constraints. Since these problems are infinite-dimensional…

We address the design and synthesis of optimal control strategies for high-dimensional stochastic dynamical systems. Such systems may be deterministic nonlinear systems evolving from random initial states, or systems driven by random…

Numerical Analysis · Mathematics 2020-08-26 Panos Lambrianides , Qi Gong , Daniele Venturi

Conceptual framework is laid out of a deterministic program capable of obtaining optimum solutions with or without constraints for any reasonably behaved analytical system. Recipe implementable as a well-behaved Runge-Kutta procedure is…

Optimization and Control · Mathematics 2015-11-24 Yu-Chiu Chao

We deal with a control-affine problem with scalar control subject to bounds, a scalar state constraint and endpoint constraints of equality type. For the numerical solution of this problem, we propose a shooting algorithm and provide a…

Optimization and Control · Mathematics 2023-06-21 M. S. Aronna , F. Bonnans , B. S. Goh

Recent low-thrust space missions have highlighted the importance of designing trajectories that are robust against uncertainties. In its complete form, this process is formulated as a nonlinear constrained stochastic optimal control…

Optimization and Control · Mathematics 2022-02-25 Naoya Ozaki , Stefano Campagnola , Ryu Funase

A practical and new Runge--Kutta numerical scheme for stochastic differential equations is explored. Numerical examples demonstrate the strong convergence of the method. The first order strong convergence is then proved using Ito integrals…

Numerical Analysis · Mathematics 2012-10-04 A. J. Roberts

Optimal sampled-data control of a nonlinear system is considered with the stable-manifold approach and extensive use of numerical techniques. The idea is to notice the Hamiltonian system associated with the considered optimal control…

Systems and Control · Electrical Eng. & Systems 2021-12-30 Yasuaki Oishi , Noboru Sakamoto

This article addresses the problem of data-driven numerical optimal control for unknown nonlinear systems. In our scenario, we suppose to have the possibility of performing multiple experiments (or simulations) on the system. Experiments…

Systems and Control · Electrical Eng. & Systems 2025-06-19 Marco Borghesi , Lorenzo Sforni , Giuseppe Notarstefano

Optimal control problems can be solved via a one-shot (single) optimization or a sequence of optimization using dynamic programming (DP). However, the computation of their global optima often faces NP-hardness, and thus only locally optimal…

Optimization and Control · Mathematics 2024-09-04 Jihun Kim , Yuhao Ding , Yingjie Bi , Javad Lavaei