{"ID":2879595,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.16801","arxiv_id":"2508.16801","title":"Stabilization of Parabolic Time-Varying PDEs using Certified Reduced-Order Receding Horizon Control","abstract":"We address the stabilization of linear, time-varying parabolic PDEs using finite-dimensional receding horizon controls (RHCs) derived from reduced-order models (ROMs). We first prove exponential stability and suboptimality of the continuous-time full-order model (FOM) RHC scheme in Hilbert spaces. A Galerkin model reduction is then introduced, along with a rigorous a posteriori error analysis for the associated finite-horizon optimal control problems. This results in a ROM-based RHC algorithm that adaptively constructs reduced-order controls, ensuring exponential stability of the FOM closed-loop state and providing computable performance bounds with respect to the infinite-horizon FOM control problem. Numerical experiments with a non-smooth cost functional involving the squared l1-norm confirm the methods effectiveness, even for exponentially unstable systems.","short_abstract":"We address the stabilization of linear, time-varying parabolic PDEs using finite-dimensional receding horizon controls (RHCs) derived from reduced-order models (ROMs). We first prove exponential stability and suboptimality of the continuous-time full-order model (FOM) RHC scheme in Hilbert spaces. A Galerkin model redu...","url_abs":"https://arxiv.org/abs/2508.16801","url_pdf":"https://arxiv.org/pdf/2508.16801v2","authors":"[\"Behzad Azmi\",\"Michael Kartmann\",\"Stefan Volkwein\"]","published":"2025-08-22T21:07:24Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"math.NA\"]","methods":"[]","has_code":false}