Realisation locale des systèmes non linéaires, algèbres de Lie filtrees transitives et séries generatrices non commutatives
From MaRDI portal
Publication:1050935
DOI10.1007/BF02095991zbMath0513.93014OpenAlexW2320306398MaRDI QIDQ1050935
Publication date: 1983
Published in: Inventiones Mathematicae (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/143002
Controllability (93B05) Valuations, completions, formal power series and related constructions (associative rings and algebras) (16W60) Nonlinear systems in control theory (93C10) Minimal systems representations (93B20) Observability (93B07) Algebraic methods (93B25) Infinite-dimensional Lie (super)algebras (17B65) Realizations from input-output data (93B15)
Related Items
Nonlinear system immersion, observers and finite-dimensional filters ⋮ Vers une notion de dérivation fonctionnelle causale. (Towards a notion of causal functional derivatives) ⋮ Generating series for networks of Chen-Fliess series ⋮ Décompositions en cascades des systèmes automatiques et feuilletages invariants ⋮ Geometric control theory ⋮ Geometrical and topological methods in optimal control theory ⋮ Observability of smooth control systems ⋮ Discrete-time approximations of Fliess operators ⋮ Formal power series, operator calculus, and duality on Lie algebras ⋮ On a conjecture by Pierre Cartier about a group of associators ⋮ Elimination, fundamental principle and duality for analytic linear systems of partial differential-difference equations with constant coefficients ⋮ The formal Laplace--Borel transform of Fliess operators and the composition product ⋮ SISO Output Affine Feedback Transformation Group and Its Faà di Bruno Hopf Algebra ⋮ On expansions for nonlinear systems error estimates and convergence issues ⋮ Continuity of formal power series products in nonlinear control theory ⋮ Realizations of nonlinear analytic input-output maps ⋮ Nonlinear system identification for multivariable control via discrete-time Chen-Fliess series ⋮ Mathematical Renormalization in Quantum Electrodynamics via Noncommutative Generating Series ⋮ On the optimal continuous decentralized control of non-linear dynamical multivariable systems about the origin ⋮ Left inversion of analytic nonlinear SISO systems via formal power series methods ⋮ Faà di Bruno Hopf algebra of the output feedback group for multivariable Fliess operators ⋮ Non-causal Fliess operators and their shuffle algebra ⋮ Generalized input-output equations and nonlinear realizability ⋮ A unified approach to generating series for mixed cascades of analytic nonlinear input–output systems ⋮ An algebraic approach to hybrid systems ⋮ Independence of Hyperlogarithms over Function Fields via Algebraic Combinatorics ⋮ A Faà di Bruno Hopf algebra for a group of fliess operators with applications to feedback ⋮ Bilinear system interconnections and generating series of weighted Petri nets ⋮ Quadratic control systems ⋮ A geometric approach to feedback stabilization of nonlinear systems with drift ⋮ Hankel singular value functions from Schmidt pairs for nonlinear input-output systems ⋮ A combinatorial Hopf algebra for nonlinear output feedback control systems ⋮ Functional series expansions for continuous-time switched systems ⋮ Computation, on Macsyma, of the minimal differential representation of noncommutative polynomials ⋮ Summations of polylogarithms via Evaluation transform. ⋮ Entropy of generating series for nonlinear input-output systems and their interconnections ⋮ Cascade decomposition of nonlinear systems, foliations and ideals of transitive Lie algebras ⋮ Representations of control systems in the Fliess algebra and in the algebra of nonlinear power moments. ⋮ Macsyma computation of local minimal realization of dynamical systems of which generating power series are finite ⋮ Elimination in control theory ⋮ Fliess operators on \(L_{p}\) spaces: convergence and continuity ⋮ On the support of graph Lie algebras ⋮ On Fliess operators driven by L 2-Itô processes
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Polynomial response maps
- Series formelles et algèbres syntactiques
- Matrices de Hankel
- Correspondance entre algèbres de Lie abstraites et pseudo-groupes de Lie transitifs
- Minimal realizations and canonical forms for bilinear systems
- A generalization of the closed subgroup theorem to quotients of arbitrary manifolds
- The infinite groups of Lie and Cartan. I: The transitive groups
- Prolongements d'homomorphismes d'algèbres de Lie filtrees transitives
- Deformation of transitive Lie algebras
- Linear differential systems with singularities and an application to transitive Lie algebras
- A Finiteness Criterion for Nonlinear Input–Output Differential Systems
- Lie Brackets and Local Controllability: A Sufficient Condition for Scalar-Input Systems
- Realizations of nonlinear systems and abstract transitive Lie algebras
- Existence and Uniqueness of Realizations of Nonlinear Systems
- Fonctionnelles causales non linéaires et indéterminées non commutatives
- Dynamical Realizations of Finite Volterra Series
- Existence and uniqueness of minimal realizations of nonlinear systems
- Iterated path integrals
- Nonlinear controllability and observability
- Uniqueness of weakly minimal analytic realizations
- Mathematical Description of Linear Dynamical Systems
- An algebraic model of transitive differential geometry
- Controllability of nonlinear systems
