The Discrete Hamiltonian-Based Adjoint Method for Some Optimization Problems in Multibody Dynamics

Paweł Maciąg , Paweł Malczyk , Janusz Frączek

Abstract

The determination of various parameters or control input signals satisfying particular performance criteria is often addressed with optimization techniques where one aims at minimizing certain quantity, which may be implicitly dependent on the dynamic response of a system. Such an approach requires an efficient and reliable method of gradient calculation. The adjoint method is an effective procedure specifically designed for such calculations. This paper presents a discrete Hamiltonian--based adjoint method which allows one to find the gradient of the performance index in multibody systems' optimization. Hamilton's equations of motion are discretized by means of trapezoidal rule and incorporated into a discrete system of adjoint equations. Explicit formula for the gradient of the cost functional is derived and exploited in an exemplary optimal control problem.
Author Paweł Maciąg (FPAE / IAAM)
Paweł Maciąg,,
- The Institute of Aeronautics and Applied Mechanics
, Paweł Malczyk (FPAE / IAAM)
Paweł Malczyk,,
- The Institute of Aeronautics and Applied Mechanics
, Janusz Frączek (FPAE / IAAM)
Janusz Frączek,,
- The Institute of Aeronautics and Applied Mechanics
Pages359-366
Publication size in sheets0.5
Article number43
Book Kecskeméthy Andrés, Flores Francisco Geu (eds.): Multibody Dynamics 2019 - Proceedings of the 9th ECCOMAS Thematic Conference on Multibody Dynamics, Computational Methods in Applied Sciences, 2020, Springer International Publishing, ISBN 978-3-030-23131-6, [978-3-030-23132-3], 545 p., DOI:10.1007/978-3-030-23132-3
ASJC Classification2208 Electrical and Electronic Engineering; 2605 Computational Mathematics; 1507 Fluid Flow and Transfer Processes; 1706 Computer Science Applications; 2204 Biomedical Engineering; 2611 Modelling and Simulation; 2205 Civil and Structural Engineering
Abstract in original languageThe determination of various parameters or control input signals satisfying particular performance criteria is often addressed with optimization techniques where one aims at minimizing certain quantity, which may be implicitly dependent on the dynamic response of a system. Such an approach requires an efficient and reliable method of gradient calculation. The adjoint method is an effective procedure specifically designed for such calculations. This paper presents a discrete Hamiltonian--based adjoint method which allows one to find the gradient of the performance index in multibody systems' optimization. Hamilton's equations of motion are discretized by means of trapezoidal rule and incorporated into a discrete system of adjoint equations. Explicit formula for the gradient of the cost functional is derived and exploited in an exemplary optimal control problem.
DOIDOI:10.1007/978-3-030-23132-3_43
URL https://link.springer.com/chapter/10.1007/978-3-030-23132-3_43
Languageen angielski
Score (nominal)20
Score sourcepublisherList
ScoreMinisterial score = 20.0, 25-10-2019, ChapterFromConference
Publication indicators Scopus Citations = 0; Scopus SNIP (Source Normalised Impact per Paper): 2016 = 0.253
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