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This paper details a methodology to transcribe an optimal control problem into a nonlinear program for generation of the trajectories that optimize a given functional by approximating only the highest order derivatives of a given system's…

Optimization and Control · Mathematics 2025-09-09 Thomas L. Ahrens , Ian M. Down , Manoranjan Majji

Optimization under the symplecticity constraint is an approach for solving various problems in quantum physics and scientific computing. Building on the results that this optimization problem can be transformed into an unconstrained problem…

Optimization and Control · Mathematics 2024-06-21 Bin Gao , Nguyen Thanh Son , Tatjana Stykel

A geometric derivation of numerical integrators for nonholonomic systems and optimal control problems is obtained. It is based in the classical technique of generating functions adapted to the special features of nonholonomic systems and…

Mathematical Physics · Physics 2016-09-07 M. de Leon , D. Martin de Diego , A. Santamaria Merino

This paper develops a distributed model predictive control (DMPC) strategy for a class of discrete-time linear systems with consideration of globally coupled constraints. The DMPC under study is based on the dual problem concerning all…

Optimization and Control · Mathematics 2019-07-25 Yanxu Su , Yang Shi , Changyin Sun

In this paper we study, from a variational and geometrical point of view, second-order variational problems on Lie groupoids and the construction of variational integrators for optimal control problems. First, we develop variational…

Dynamical Systems · Mathematics 2015-06-30 Leonardo Colombo , David Martin de Diego

A new method is proposed for integrating the equations of motion of an elastic filament. In the standard finite-difference and finite-element formulations the continuum equations of motion are discretized in space and time, but it is then…

Computational Physics · Physics 2009-11-13 Anthony JC Ladd , Gaurav Misra

A time optimal attitude control problem is studied for the dynamics of a rigid body. The objective is to minimize the time to rotate the rigid body to a desired attitude and angular velocity while subject to constraints on the control…

Optimization and Control · Mathematics 2007-09-19 Taeyoung Lee , Melvin Leok , N. Harris McClamroch

In this article, we generalize the theory of discrete Lagrangian mechanics and variational integrators in two principal directions. First, we show that Lagrangian submanifolds of symplectic groupoids give rise to discrete dynamical systems,…

Symplectic Geometry · Mathematics 2015-11-04 Juan Carlos Marrero , David Martín de Diego , Ari Stern

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

This work investigates an elliptic optimal control problem defined on uncertain domains and discretized by a fictitious domain finite element method and cut elements. Key ingredients of the study are to manage cases considering the usually…

Numerical Analysis · Mathematics 2022-04-06 Aikaterini Aretaki , Efthymios N. Karatzas

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

In this work, we present composite Bernstein polynomials as a direct collocation method for approximating optimal control problems. An analysis of the convergence properties of composite Bernstein polynomials is provided, and beneficial…

Optimization and Control · Mathematics 2024-07-26 Gage MacLin , Venanzio Cichella , Andrew Patterson , Michael Acheson , Irene Gregory

We present a geometric algorithm for obtaining consistent solutions to systems of partial differential equations, mainly arising from singular covariant first-order classical field theories. This algorithm gives an intrinsic description of…

Mathematical Physics · Physics 2015-12-15 M. de Leon , J. Marin-Solano , J. C. Marrero , M. C. Munoz-Lecanda , N. Roman-Roy

This paper addresses the time-optimal control problem for a class of control systems which includes controlled mechanical systems with possible dissipation terms. The Lie algebras associated with such mechanical systems enjoy certain…

Optimization and Control · Mathematics 2007-05-23 M. Chyba , N. E. Leonard , E. D. Sontag

The paper is devoted to deriving necessary optimality conditions in a general optimal control problem for dynamical systems governed by controlled sweeping processes with hard-constrained control actions entering both polyhedral moving sets…

Optimization and Control · Mathematics 2021-03-17 Tan H. Cao , Giovanni Colombo , Boris S. Mordukhovich , Dao Nguyen

Nonequilibrium statistical models of point vortex systems are constructed using an optimal closure method, and these models are employed to approximate the relaxation toward equilibrium of systems governed by the two-dimensional Euler…

Fluid Dynamics · Physics 2018-12-26 Jonathan Maack , Bruce Turkington

We consider optimal control problems for discrete-time random dynamical systems, finding unique perturbations that provoke maximal responses of statistical properties of the system. We treat systems whose transfer operator has an $L^2$…

Dynamical Systems · Mathematics 2022-09-21 Fadi Antown , Gary Froyland , Stefano Galatolo

Optimal control theory is a powerful tool for improving figures of merit in quantum information tasks. Finding the solution to any optimal control problem via numerical optimization depends crucially on the choice of the optimization…

Li, Chen, Tai & E. (J. Machine Learning Research, 2018) have proposed a regularization of the forward-backward sweep iteration for solving the Pontryagin maximum principle in optimal control problems. The authors prove the global…

Numerical Analysis · Mathematics 2020-08-21 Xin Liu , Jason Frank

Inspired by applications in optimal control of semilinear elliptic partial differential equations and physics-integrated imaging, differential equation constrained optimization problems with constituents that are only accessible through…

Optimization and Control · Mathematics 2020-08-26 Guozhi Dong , Michael Hintermueller , Kostas Papafitsoros