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🆕 Date Issued:
2008-08-21
🗄 Date Available:2022-05-11
Research Paper

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Systematic discretization of input-output maps of linear infinite dimensional systems (revised)

Schmidt, Michael

Inst. Mathematik

Many model reduction techniques take a semi-discretization of a 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 infinite-dimensional system for a general class of linear time-invariant systems with distributed inputs and outputs. First, the input and output signals are discretized in space and time, resulting in the matrix representation of an approximated i/o-map. In a generalized sense, the matrix contains the Markov parameters of a corresponding time-discrete multi-input-multi-output system. Second, the system dynamics is approximated in form of the underlying evolution operator, in order to calculate the matrix representation numerically. The discretization framework, corresponding error estimates, a SVD-based system reduction method and a numerical application in an optimization problem are presented, and illustrated for a heat control system.
input-output mapdiscretizationinfinite-dimensional control systemtime-discrete MIMO systemmodel reductionoptimizationfeedback control
References
10.14279/depositonce-1600
Is Version Of
10.14279/depositonce-15654
  • This preprint is a completely revised version of Preprint 2006-06. For more details see the dissertation thesis of the author published in 2007.
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