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Balanced truncation model reduction for systems with inhomogeneous initial conditions. (English) Zbl 1216.93018

Summary: We present a rigorous approach to extend Balanced Truncation Model Reduction (BTMR) to systems with inhomogeneous initial conditions. We provide an estimate for the error between the input-output maps of the original and of the reduced initial value system, and finally we illustrate numerically the superiority of our approach over the naive application of BTMR. When BTMR is applied to linear time invariant systems with inhomogeneous initial conditions, it is crucial that the initial data are well represented by the subspaces generated by BTMR. This requirement is often ignored or it is avoided by making the restrictive assumption that the initial data are zero. To ensure that the initial data are well represented by the BTMR subspaces, we add auxiliary inputs determined by the initial data.

MSC:

93B05 Controllability
93B07 Observability
93C15 Control/observation systems governed by ordinary differential equations
93B11 System structure simplification

Software:

Gmsh
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Full Text: DOI

References:

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