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Preprint 6-2006

Systematic Discretization of Input-Output Maps of Linear Infinite-Dimensional Systems

Source file is available as :   Portable Document Format (PDF)

Author(s) : Michael Schmidt

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 6-2006

MSC 2000

93C20 Systems governed by partial differential equations
35B37 PDE in connection with control problems

Abstract :
Many model reduction techniques take a semi-discretization of the original PDE model as starting point and aim then at an accurate approximation of its input/output map. In this contribution, we discuss the direct discretization of the i/o map of the original infinite-dimensional system. First, the input and output signals are discretized in space and time, second, the system dynamics are approximated in form of the underlying evolution operator, leading to an approximated i/o map with matrix representation. The discretization framework, corresponding error estimations, a SVD-based system reduction method and a numerical application in and optimization problem are presented for a general class of linear time-invariant systems and illustrated for a heat control system.

Keywords : input-output map, discretization, infinite-dimensional control system, model reduction, optimization

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