Data-Driven Model-Order Reduction for Model Predictive Control

Abstract

In this thesis, quadratic optimal control problems for linear parabolic partial differen- tial equations (PDEs) with time-dependent coefficient functions are considered. After showing the existence and uniqueness of the solution, necessary and sufficient first order optimality conditions are derived. By applying a finite element (FE) discretization, the first-order optimality system can be represented as a linear time-variant (LTV) coupled dynamical system, which encompasses both the state equation and the dual equation. This leads us into the area of dynamical systems. Model predictive control (MPC) is applied to solve the problem over the long-time horizon. To speedup the computational time three data-driven model-order reduction (MOR) techniques are applied: Proper or- thogonal decomposition (POD), empirical gramians and extended dynamic mode decom- position (EDMD). Furthermore, an a-posteriori error analysis is conducted to guarantee the accuracy of the reduced model during the MPC. Numerical simulations illustrate the advantages and disadvantages of the various MOR techniques.