A TFC-based homotopy continuation algorithm with application to dynamics and control problems
نویسندگان
چکیده
A method for solving zero-finding problems is developed by tracking homotopy paths, which define connecting channels between an auxiliary problem and the objective problem. Current algorithms' success highly relies on empirical knowledge, due to manually, inherently selected paths. This work introduces a based Theory of Functional Connections (TFC). The TFC-based implicitly defines infinite from most promising ones are selected. two-layer continuation algorithm devised, where first layer tracks path monotonously varying parameter, while second recovers possible failures resorting TFC representation function. Compared pseudo-arclength methods, proposed retains simplicity direct allowing flexible switching. Numerical simulations illustrate effectiveness presented method.
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2022
ISSN: ['0377-0427', '1879-1778', '0771-050X']
DOI: https://doi.org/10.1016/j.cam.2021.113777