Empirical balanced truncation of nonlinear systems

Details Empirical balanced truncation of nonlinear systems Empirical balanced truncation of nonlinear systems

2006-06-18

arxiv.org/abs/math/0606430v1

Journal of Nonlinear Science, vol. 14 (2004) pp. 405-414

Mathematics

Optimization and Control

LaTeX, 11 pages, 2 figures

Scientific paper

10.1007/s00332-004-0617-5

Novel constructions of empirical controllability and observability gramians for nonlinear systems for subsequent use in a balanced truncation style of model reduction are proposed. The new gramians are based on a generalisation of the fundamental solution for a Linear Time-Varying system. Relationships between the given gramians for nonlinear systems and the standard gramians for both Linear Time-Invariant and Linear Time-Varying systems are established as well as relationships to prior constructions proposed for empirical gramians. Application of the new gramians is illustrated through a sample test-system.

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