{"ID":2855738,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.12456","arxiv_id":"2510.12456","title":"Micro-Macro Backstepping Control of Large-Scale Hyperbolic Systems (Extended Version)","abstract":"We introduce a control design and analysis framework for micro-macro, boundary control of large-scale, $n+m$ hyperbolic PDE systems. Specifically, we develop feedback laws for stabilization of hyperbolic systems at the micro level (i.e., of the large-scale system) that employ a) measurements obtained from the $n+m$ system (i.e., at micro level) and kernels constructed based on an $\\infty+\\infty$ continuum system counterpart (i.e., at macro level), or b) kernels and measurements both stemming from a continuum counterpart, or c) averaged-continuum kernels/measurements. We also address (d)) stabilization of the continuum (macro) system, employing continuum kernels and measurements. Towards addressing d) we derive in a constructive manner an $\\infty+\\infty$ continuum approximation of $n+m$ hyperbolic systems and establish that its solutions approximate, for large $n$ and $m$, the solutions of the $n+m$ system. We then construct a feedback law for stabilization of the $\\infty+\\infty$ system via introduction of a continuum-PDE backstepping transformation. We establish well-posedness of the resulting 4-D kernel equations and prove closed-loop stability via construction of a novel Lyapunov functional. Furthermore, under control configuration a) we establish that the closed-loop system is exponentially stable provided that $n$ and $m$ are large, by proving that the exact, stabilizing $n+m$ control kernels can be accurately approximated by the continuum kernels. While under control configurations b) and c), we establish closed-loop stability capitalizing on the established solutions' and kernels' approximation properties via employment of infinite-dimensional ISS arguments. We provide two numerical simulation examples to illustrate the effectiveness and potential limitations of our design approach.","short_abstract":"We introduce a control design and analysis framework for micro-macro, boundary control of large-scale, $n+m$ hyperbolic PDE systems. Specifically, we develop feedback laws for stabilization of hyperbolic systems at the micro level (i.e., of the large-scale system) that employ a) measurements obtained from the $n+m$ sys...","url_abs":"https://arxiv.org/abs/2510.12456","url_pdf":"https://arxiv.org/pdf/2510.12456v1","authors":"[\"Jukka-Pekka Humaloja\",\"Nikolaos Bekiaris-Liberis\"]","published":"2025-10-14T12:43:02Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"eess.SY\"]","methods":"[]","has_code":false}