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On an Invariance Principle for the Solution Space of the Differential Riccati Equation
Author(s) -
Behr Maximilian,
Benner Peter,
Heiland Jan
Publication year - 2018
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201800031
Subject(s) - riccati equation , algebraic riccati equation , mathematics , krylov subspace , subspace topology , projection (relational algebra) , differential equation , linear quadratic regulator , mathematical analysis , optimal control , linear subspace , space (punctuation) , pure mathematics , computer science , mathematical optimization , linear system , algorithm , operating system
The differential Riccati equation appears in different fields of applied mathematics like control theory and systems theory. For large‐scale systems the numerical solution comes with a large amount of storage requirements. This motivates the use of Krylov subspace and projection based methods [1–3]. In the present paper we apply an invariance theorem for ODEs to the differential Riccati Equation. We show that the solution is contained in a Krylov like subspace and extend our results to certain time‐varying cases.
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