OS Numerical Optimization: Reduced Order Model Predictive Control for Parametrized Partial Differential Equations
Time
Tuesday, 9. July 2024
15:15 - 16:45
Location
F426
Organizer
B. Azmi & S. Volkwein
Speaker:
Prof. Martin Grepl, Ph.D.
On 9th July 2024 at 15:15, Prof. Martin Grepl, Ph.D. from the Institut für Geometrie und Praktische Mathematik (RWTH Aachen) will give a talk.
Abstract: Model Predictive Control (MPC) is a well established approach to solve infinite horizon optimal control problems. Since optimization over an infinite time horizon is, in general, infeasible, the method determines a suboptimal feedback control by repeatedly solving finite time optimal control problems.
In this talk, we consider systems governed by parametrized parabolic partial differential equations and employ the reduced basis method (RB) as a low-dimensional surrogate model for the finite time optimal control problem. The reduced order optimal control serves as the feedback control for the MPC of the original large-scale system. Based on rigorous and efficiently computable a posteriori error bounds we are able to guarantee asymptotic stability of the closed-loop system using the RB-MPC approach. We also propose an adaptive strategy to choose the optimal horizon length of the finite time optimal control problem. Finally, we consider an extension to nonlinear problems based on the Schlögl model. Numerical results are presented for the linear and nonlinear case to validate our approach.