A balanced truncation-based strategy for optimal control of evolution problems

Abstract

In this paper we present a balanced truncation based strategy for the numerical solution of optimal control problems governed by nonlinear evolution partial differential equations. The idea consists in utilizing a balanced truncation model reduction method for the efficient solution of the semidiscretized adjoint system, while the nonlinear state equations are fully solved. Our strategy is analyzed as a descent method in function spaces and global convergence results are presented. In combination with a Broyden-Fletcher-Goldfarb-Shanno update also superlinear convergence is verified. Numerical examples are given to illustrate the behaviour of the proposed method for different problems.

DOI: 10.1080/10556788.2010.526756

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@article{Reyes2011ABT, title={A balanced truncation-based strategy for optimal control of evolution problems}, author={Juan Carlos de los Reyes and Tatjana Stykel}, journal={Optimization Methods and Software}, year={2011}, volume={26}, pages={671-692} }