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An approximation of an infinite-dimensional system by a finite-dimensional analog is required for numerical simulation and/or for a practical implementation of control/estimation algorithms in a digital device. This chapter develops a method of consistent discretization for homogeneous evolution equationsEvolution equation in separable Hilbert spacesHilbert space and proposes a special modification of the Galerkin method allowing the dilation symmetry of an infinite-dimensional system to be preserved in its finite-dimensional counterpart.

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Discretization of Infinite-Dimensional Homogeneous Systems

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  • 发表日期：

    2025年

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  • Andrey Polyakov

摘要

An approximation of an infinite-dimensional system by a finite-dimensional analog is required for numerical simulation and/or for a practical implementation of control/estimation algorithms in a digital device. This chapter develops a method of consistent discretization for homogeneous evolution equationsEvolution equation in separable Hilbert spacesHilbert space and proposes a special modification of the Galerkin method allowing the dilation symmetry of an infinite-dimensional system to be preserved in its finite-dimensional counterpart.