Model Reduction of Controlled Fokker-Planck and Liouville-von Neumann Equations

Spectrum of system matrix A upon dimension reduction. From left to right: Balanced truncation, singular perturbation, H2-optimal model reduction.

Peter Benner, Tobias Breiten, Carsten Hartmann, and Burkhard Schmidt

Model reduction methods for bilinear control systems are compared by means of practical examples of Liouville-von Neumann and Fokker-Planck type. Methods based on balancing generalized system Gramians and on minimizing an H2-type cost functional are considered. The focus is on the numerical implementation and a thorough comparison of the methods. Structure and stability preservation are investigated, and the competitiveness of the approaches is shown for practically relevant, large-scale examples.

J. Comp. Dyn. 7 (1), 1-33 (2020)

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