{"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/controlled-synchronization-of-coupled","title":"Controlled Synchronization of Coupled Pendulums by Koopman Model Predictive Control","arxiv_id":"2212.13783","date":"2022-12-28","proceeding":null,"authors":["Loi Do","Milan Korda","Zdeněk Hurák"],"abstract":"We propose and experimentally demonstrate a feedback control method that allows synchronizing the motion of a chain of several coupled nonlinear oscillators actuated through one end of the chain. The chain considered in this work is a one-dimensional array of pendulums pivoting around a single axis and interacting with adjacent pendulums through torsion springs; the array is actuated using a single torque motor attached to one of the two boundary pendulums. This represents a mechanical realization of the Frenkel-Kontorova model { a spatially discrete version of a sine-Gordon equation describing (nonlinear) waves. The main challenges of controlling these systems are: high order (the number of pendulums can be high), nonlinear dynamics, and (as we set the problem here) only one actuator. The presented problem of synchronization of motion is a special case of the problem of reference tracking, where all pendulums reach a common point or a trajectory. In particular, we demonstrate synchronization to a stable equilibrium (all pendulums downward), unstable equilibrium (all pendulums upward), and a periodic orbit (all pendulums revolving). We use the Koopman Model Predictive Control (KMPC) that constructs a linear predictor of the nonlinear system in a higher-dimensional lifted space and uses the predictor within a classical linear MPC, thereby maintaining low computational cost that allows for a real-time implementation, while taking into account the complex nonlinear dynamics.","url_abs":"https://arxiv.org/abs/2212.13783v1","url_pdf":"https://arxiv.org/pdf/2212.13783v1.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":"controlled-synchronization-of-coupled","repo_url":"https://github.com/aa4cc/koompanmpc-for-synchronization","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}