{"ID":2892735,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.14455","arxiv_id":"2507.14455","title":"Koopman Operator Based Time-Delay Embeddings and State History Augmented LQR for Periodic Hybrid Systems: Bouncing Pendulum and Bipedal Walking","abstract":"Time-delay embedding is a technique that uses snapshots of state history over time to build a linear state space model of a nonlinear smooth system. We demonstrate that periodic non-smooth or hybrid system can also be modeled as a linear state space system using this approach as long as its behavior is consistent in modes and timings. We extend time-delay embeddings to generate a linear model of two periodic hybrid systems: the bouncing pendulum and the simplest walker with control inputs. This leads to a state history augmented linear quadratic regulator (LQR) which uses current and past state history for feedback control. Example code can be found at https://github.com/Chun-MingYang/koopman-timeDelay-lqr.git","short_abstract":"Time-delay embedding is a technique that uses snapshots of state history over time to build a linear state space model of a nonlinear smooth system. We demonstrate that periodic non-smooth or hybrid system can also be modeled as a linear state space system using this approach as long as its behavior is consistent in mo...","url_abs":"https://arxiv.org/abs/2507.14455","url_pdf":"https://arxiv.org/pdf/2507.14455v2","authors":"[\"Chun-Ming Yang\",\"Pranav A. Bhounsule\"]","published":"2025-07-19T03:00:52Z","proceeding":"cs.RO","tasks":"[\"cs.RO\"]","methods":"[]","has_code":false,"code_links":[{"ID":612013,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_id":2892735,"paper_url":"https://arxiv.org/abs/2507.14455","paper_title":"Koopman Operator Based Time-Delay Embeddings and State History Augmented LQR for Periodic Hybrid Systems: Bouncing Pendulum and Bipedal Walking","repo_url":"https://github.com/Chun-MingYang/koopman-timeDelay-lqr.git","is_official":false,"mentioned_in_paper":false,"mentioned_in_github":true,"github_stars":0}]}