Balanced Reduction of Nonlinear Control Systems in Reproducing Kernel Hilbert Space

Details Balanced Reduction of Nonlinear Control Systems in Reproducing Kernel Hilbert Space Balanced Reduction of Nonlinear Control Systems in Reproducing Kernel Hilbert Space

2010-11-12

arxiv.org/abs/1011.2952v1

Proc. 48th Annual Allerton Conference on Communication, Control, and Computing, 2010, pp. 294 - 301

Mathematics

Optimization and Control

Scientific paper

We introduce a novel data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves linearly when lifted into a high (or infinite) dimensional feature space where balanced truncation may be carried out implicitly. This leads to a nonlinear reduction map which can be combined with a representation of the system belonging to a reproducing kernel Hilbert space to give a closed, reduced order dynamical system which captures the essential input-output characteristics of the original model. Empirical simulations illustrating the approach are also provided.

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