{"title":"Generalized Gaussian smoothing homotopy method for solving nonlinear optimal control problems","authors":"Binfeng Pan, Yunting Ran, Mengxin Zhao","doi":"10.1016/j.actaastro.2024.12.051","DOIUrl":null,"url":null,"abstract":"This paper introduces an innovative generalized Gaussian smoothing homotopy method for solving nonlinear optimal control problems using the indirect method. Compared to the original smoothing homotopy methods, this approach leverages a multivariate Gaussian function to smooth both state and costate variables, extending the convolution process beyond the time domain to all unknown variables. By utilizing the separability property of the Gaussian kernel, the multivariate convolution is decomposed into univariate convolutions along each dimension, allowing independent and efficient computation. Additionally, the Gauss–Chebyshev quadrature technique is employed to approximate these univariate convolutions, further reducing computational complexity. The convergence of the method is demonstrated through challenging numerical examples, showcasing its superiority over Gaussian smoothing homotopy method.","PeriodicalId":44971,"journal":{"name":"Acta Astronautica","volume":"9 1","pages":""},"PeriodicalIF":3.1000,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Astronautica","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1016/j.actaastro.2024.12.051","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, AEROSPACE","Score":null,"Total":0}
引用次数: 0
Abstract
This paper introduces an innovative generalized Gaussian smoothing homotopy method for solving nonlinear optimal control problems using the indirect method. Compared to the original smoothing homotopy methods, this approach leverages a multivariate Gaussian function to smooth both state and costate variables, extending the convolution process beyond the time domain to all unknown variables. By utilizing the separability property of the Gaussian kernel, the multivariate convolution is decomposed into univariate convolutions along each dimension, allowing independent and efficient computation. Additionally, the Gauss–Chebyshev quadrature technique is employed to approximate these univariate convolutions, further reducing computational complexity. The convergence of the method is demonstrated through challenging numerical examples, showcasing its superiority over Gaussian smoothing homotopy method.
期刊介绍：
Acta Astronautica is sponsored by the International Academy of Astronautics. Content is based on original contributions in all fields of basic, engineering, life and social space sciences and of space technology related to:
The peaceful scientific exploration of space,
Its exploitation for human welfare and progress,
Conception, design, development and operation of space-borne and Earth-based systems,
In addition to regular issues, the journal publishes selected proceedings of the annual International Astronautical Congress (IAC), transactions of the IAA and special issues on topics of current interest, such as microgravity, space station technology, geostationary orbits, and space economics. Other subject areas include satellite technology, space transportation and communications, space energy, power and propulsion, astrodynamics, extraterrestrial intelligence and Earth observations.
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