Continuum approximation-based power series and closed-form solutions to large-scale backstepping kernels equationsContinuum approximation-based power series and closed-form solutions to large-scale backstepping kernels equations Πλήρης Δημοσίευση σε Συνέδριο Conference Full Paper 2025-08-252025enWe provide two methods for computation of continuum backstepping kernels that arise in control of continua (ensembles) of linear hyperbolic PDEs and which can approximate backstepping kernels arising in control of a large-scale, PDE system counterpart (with computational complexity that does not grow with the number of state components of the largescale system). In the first method, we provide explicit formulae for the solution to the continuum kernels PDEs, employing a (triple) power series representation of the continuum kernel and establishing its convergence properties. In the second method, we identify a class of systems for which the solution to the continuum (and hence, also an approximate solution to the respective large-scale) kernel equations can be constructed in closed form. We also present numerical examples to illustrate computational efficiency/accuracy of the approaches, as well as to validate the stabilization properties of the approximate control kernels, constructed based on the continuum.Funded by the European Union (ERC, C-NORA, 101088147). Views and opinions expressed are however those of the authors only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them. http://creativecommons.org/licenses/by-nc-nd/4.0/American Control ConferenceHumaloja_et_al_ACC_2025_preprint.pdfChania [Greece]Library of TUC2025-08-22application/pdf313.1 kB10.23919/ACC63710.2025.11107727free Humaloja Jukka-Pekka Gabriel Humaloja Jukka-Pekka-Gabriel Bekiaris-Liberis Nikolaos Μπεκιαρης-Λυμπερης Νικολαος Institute of Electrical and Electronics Engineers Backstepping kernels computation Large-scale hyperbolic systems PDE continua