Discrete adjoint method for variational integration of constrained ODEs and its application to optimal control of geometrically exact beam dynamics

IF 2.6 2区 工程技术 Q2 MECHANICS Multibody System Dynamics Pub Date : 2023-10-06 DOI:10.1007/s11044-023-09934-4
Matthias Schubert, Rodrigo T. Sato Martín de Almagro, Karin Nachbagauer, Sina Ober-Blöbaum, Sigrid Leyendecker
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Abstract

Abstract Direct methods for the simulation of optimal control problems apply a specific discretization to the dynamics of the problem, and the discrete adjoint method is suitable to calculate corresponding conditions to approximate an optimal solution. While the benefits of structure preserving or geometric methods have been known for decades, their exploration in the context of optimal control problems is a relatively recent field of research. In this work, the discrete adjoint method is derived for variational integrators yielding structure preserving approximations of the dynamics firstly in the ODE case and secondly for the case in which the dynamics is subject to holonomic constraints. The convergence rates are illustrated by numerical examples. Thirdly, the discrete adjoint method is applied to geometrically exact beam dynamics, represented by a holonomically constrained PDE.

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约束微分方程变分积分的离散伴随法及其在几何精确梁动力学最优控制中的应用
直接模拟最优控制问题的方法是对问题的动力学特性进行特定的离散化处理,而离散伴随法适合于计算近似最优解的相应条件。虽然结构保存或几何方法的好处已经知道了几十年,但它们在最优控制问题背景下的探索是一个相对较新的研究领域。本文推导了变分积分器的离散伴随方法,首先在ODE情况下给出了保持结构的动力学近似,其次在动力学受完整约束的情况下给出了保持结构的动力学近似。通过数值算例说明了算法的收敛速度。第三,将离散伴随方法应用于几何精确梁动力学,用完整约束偏微分方程表示。
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来源期刊
CiteScore
6.00
自引率
17.60%
发文量
46
审稿时长
12 months
期刊介绍: The journal Multibody System Dynamics treats theoretical and computational methods in rigid and flexible multibody systems, their application, and the experimental procedures used to validate the theoretical foundations. The research reported addresses computational and experimental aspects and their application to classical and emerging fields in science and technology. Both development and application aspects of multibody dynamics are relevant, in particular in the fields of control, optimization, real-time simulation, parallel computation, workspace and path planning, reliability, and durability. The journal also publishes articles covering application fields such as vehicle dynamics, aerospace technology, robotics and mechatronics, machine dynamics, crashworthiness, biomechanics, artificial intelligence, and system identification if they involve or contribute to the field of Multibody System Dynamics.
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