POD-Based Multiobjective Optimal Control of Time-Variant Heat Phenomena

Abstract

In the present paper, a multiobjective optimal control problem governed by a heat equation with time-dependent convection term and bilateral control constraints is considered. For computing Pareto optimal points and approximating the Pareto front, the reference point method is applied. As this method transforms the multiobjective optimal control problem into a series of scalar optimization problems, the method of proper orthogonal decomposition (POD) is introduced as an approach for model-order reduction. New strategies for efficiently updating the POD basis in the optimization process are proposed and tested numerically.

2 Model order reduction by proper orthogonal decomposition

“…Alternatively, the POD basis length could be chosen in alignment with the POD projection error (2.10) with the expected spatial and/or temporal discretization error; compare, e. g., [39,Theorem 5.1]. Let us also refer, e. g., to the recent paper [12], where different adaptive POD basis extension techniques are discussed. Table 2.1 summarizes how to choose ℓ c and ℓ w in order to capture a desired amount of information.…”

Model Order Reduction by Proper Orthogonal Decomposition

“…[39,Theorem 5.1]. Let us also refer, e.g., to the recent paper [12], where different adaptive POD basis extension techniques are discussed. Table 1 summarizes how to choose c and w in order to capture a desired amount of information.…”