Invariants for feedback equivalence and Cauchy characteristic multifoliations of nonlinear control systems
type: Item
instance of: scholarly article
title: Invariants for feedback equivalence and Cauchy characteristic multifoliations of nonlinear control systems
zbMATH Open document ID: 0646.93030
DOI: 10.1007/BF00047284
author: Robert Hermann
published in: Acta Applicandae Mathematicae
publication date: 1988-01-01T00:00:00Z
review text: The author develops in an abstract and formal way a theoretical framework for feedback equivalence of general nonlinear control systems \[ (1)\quad \dot x=f(x,u). \] In particular, the global aspects of equivalence are focused, and the role of Cauchy characteristics is emphasized. Let W be the submodule of vector fields associated with (1). The Cauchy characteristic system is defined by \[ (2)\quad C(W)=\{v\in W: [v,W]\subset W\}. \] Introducing the derived system W \(1=W+[W,W]\), allows us to iterate (2). Thus, a nested sequence of Cauchy characteristic systems is obtained. In this way, the author identifies geometric and numerical invariants under global feedback equivalence. The cases of affine and linear systems are considered. Finally, necessary conditions for global linearization under feedback are presented.
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 58A30
Mathematics Subject Classification ID: 93C15
Mathematics Subject Classification ID: 93B27
Mathematics Subject Classification ID: 57R30
Mathematics Subject Classification ID: 37C80
zbMATH DE Number: 4055476
zbMATH Keywords: feedback equivalence
zbMATH Keywords: nonlinear control systems
zbMATH Keywords: Cauchy characteristics
zbMATH Keywords: geometric and numerical invariants
zbMATH Keywords: global linearization
reviewed by: Andrea Bacciotti
MaRDI profile type: Publication
cites work: Some comments on global linearization of nonlinear systems
cites work: Global state and feedback equivalence of nonlinear systems
cites work: Global $(f,g)$-Invariance of Nonlinear Systems
cites work: Q5597890
cites work: Über Systeme von linearen partiellen Differentialgleichungen erster Ordnung
cites work: Invariants of Pfaffian Systems
cites work: Structures feuilletées et cohomologie à valeur dans un faisceau de groupoïdes
cites work: E. Cartan's geometrie theory of partial differential equations
cites work: Some differential geometric aspects of the Lagrange variational problem
cites work: The theory of equivalence of Pfaffian systems and input systems under feedback
cites work: The geometric theory of deformation and linearization of Pfaffian systems and its applications to system theory and mathematical physics. I
cites work: The Formal Linearization of a Semisimple Lie Algebra of Vector Fields about a Singular Point
cites work: Q4054852
cites work: Q3727807
cites work: Q5531621
cites work: Differential geometry and the calculus of variations
cites work: Formal linearization of vector fields and related cohomology. I, II
cites work: Q4772438
cites work: Nonlinear controllability and observability
cites work: Q3728749
cites work: Q3332867
cites work: Nonlinear control systems: An introduction
cites work: Q3951974
cites work: Q3731454
cites work: On the Equivalence of Control Systems and the Linearization of Nonlinear Systems
cites work: Q5658761
cites work: Q4743396
cites work: Control design for multivariable non-linear time-varying systems
cites work: Q5337746
cites work: On the linear equivalents of nonlinear systems
Recommended article: Q3197704
Recommended article: Q3832393
Recommended article: On feedback invariants for linear dynamical systems
Recommended article: On controlled invariance for fully nonlinear systems
Recommended article: Invariance control for a class of cascade nonlinear systems
Recommended article: On feedback equivalence of nonlinear systems
Recommended article: Controlled and Conditioned Invariance for Polynomial and Rational Feedback Systems
Recommended article: Equi-invariability, bounded invariance complexity and L-stability for control systems
Recommended article: Feedback equivalence for a class of nonlinear singularly perturbed systems
Recommended article: Controllability, robustness and invariance of invertible systems with nonlinear dynamics
description: scientific article; zbMATH DE number 4055476