{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/expanding-the-class-of-quadratic-control","title":"Expanding the Class of Quadratic Control-Lyapunov Functions for Low-Thrust Trajectory Optimization","arxiv_id":"2408.14412","date":"2024-08-26","proceeding":null,"authors":["Nicholas P. Nurre","Saeid Tafazzol","Ehsan Taheri"],"abstract":"Control laws derived from Control-Lyapunov Functions (CLFs) offer an efficient way for generating near-optimal many-revolution low-thrust trajectories. A common approach to constructing CLFs is to consider the family of quadratic functions using a diagonal weighting matrix. In this paper, we explore the advantages of using a larger family of quadratic functions. More specifically, we consider positive-definite weighting matrices with non-zero off-diagonal elements (hereafter referred to as \"full\" matrices). We propose a novel eigendecomposition method for parameterizing $N$-dimensional weighting matrices that is easy to implement and guarantees positive-definiteness of the weighting matrices. We use particle swarm optimization, which is a stochastic optimization algorithm, to optimize the parameters and generate near-optimal minimum-time low-thrust trajectories. Solutions obtained using a full positive-definite matrix are compared to the results from the (standard) diagonal weighting matrix for a number of benchmark problems. Results demonstrate that improvements in optimality are achieved, especially for maneuvers with large changes in orbital elements.","url_abs":"https://arxiv.org/abs/2408.14412v2","url_pdf":"https://arxiv.org/pdf/2408.14412v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"expanding-the-class-of-quadratic-control","repo_url":"https://github.com/saeidtafazzol/positive_definite_parameterization","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}