Realizations of nonlinear systems and abstract transitive Lie algebras

DOI10.1090/S0273-0979-1980-14760-6zbMath0427.93011OpenAlexW2063532086MaRDI QIDQ3864359

Michel Fliess

Publication date: 1980

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0273-0979-1980-14760-6

zbMATH Keywords

Lie pseudogroupstransitive Lie algebras

Mathematics Subject Classification ID

Nonlinear systems in control theory (93C10) Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65) Realizations from input-output data (93B15) Lie groups (22E99) Lie algebras and Lie superalgebras (17B99)

Related Items (14)

Some remarks on estimation algebras ⋮ Geometric control theory ⋮ Geometrical and topological methods in optimal control theory ⋮ Realizations of nonlinear analytic input-output maps ⋮ Unnamed Item ⋮ Fliess series, a generalization of the Ree's theorem, and an algebraic approach to a homogeneous approximation problem ⋮ Transformations of descriptions of nonlinear systems ⋮ Realization theory for linear and bilinear switched systems: A formal power series approach ⋮ Free algebras and noncommutative power series in the analysis of nonlinear control systems: an application to approximation problems ⋮ Realisation locale des systèmes non linéaires, algèbres de Lie filtrees transitives et séries generatrices non commutatives ⋮ A seperation property of realizable Volterra kernels ⋮ Representations of control systems in the Fliess algebra and in the algebra of nonlinear power moments. ⋮ Implementation of the algorithm for constructing homogeneous approximations of nonlinear control systems ⋮ Differential-geometric and group-theoretical methods in optimal control theory

Cites Work

• Unnamed Item
• Matrices de Hankel
• Correspondance entre algèbres de Lie abstraites et pseudo-groupes de Lie transitifs
• A generalization of the closed subgroup theorem to quotients of arbitrary manifolds
• The infinite groups of Lie and Cartan. I: The transitive groups
• Existence and Uniqueness of Realizations of Nonlinear Systems
• Fonctionnelles causales non linéaires et indéterminées non commutatives
• Existence and uniqueness of minimal realizations of nonlinear systems
• Nonlinear controllability and observability
• An algebraic model of transitive differential geometry

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