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

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 semi-discretized adjoint system, while the nonlinear state equations are fully solved. Our strategy is analysed 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.

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