Local controllability of control systems with feedback
type: Item
instance of: scholarly article
title: Local controllability of control systems with feedback
zbMATH Open document ID: 0633.93013
DOI: 10.1007/BF00940008
published in: Journal of Optimization Theory and Applications
publication date: 1989-01-01T00:00:00Z
review text: We prove sufficient conditions for the instantaneous local controllability of nonlinear (nonsmooth) control systems with feedback. We introduce for that purpose the high-order variation of the reachable map, which is related strongly to its shape. It is a direction in which the reachable map evolves. The cone of variations is convex. This allows one to prove the following theorem: if there exist variations \(v_ 1\),..., \(v_ p\) such that \(\theta\) \(\in int co\{v_ 1,...,v_ p\}\), then the system is small-time locally controllable at the point of equilibrium. We provide a short proof of the main result due to \textit{H. Sussmann} [see, e.g., SIAM J. Control Optimization 16, 790-802 (1978; Zbl 0391.93004)] and extend it to differential inclusions.
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 49J52
Mathematics Subject Classification ID: 93C15
Mathematics Subject Classification ID: 93B03
Mathematics Subject Classification ID: 26E25
zbMATH DE Number: 4031491
zbMATH Keywords: differential inclusions
zbMATH Keywords: small-time local controllability
zbMATH Keywords: control systems with feedback
zbMATH Keywords: differential calculus of set-valued maps
zbMATH Keywords: reachable sets
zbMATH Keywords: nonlinear (nonsmooth) control systems
zbMATH Keywords: reachable map
author: Hélène Frankowska
MaRDI profile type: Publication
cites work: An open mapping principle for set-valued maps
cites work: Control systems which generate decomposable Lie algebras
cites work: Local Controllability and Bilinearization
cites work: Classical Solutions of Differential Equations with Multi-Valued Right-Hand Side
cites work: Optimization and nonsmooth analysis
cites work: Q3324260
cites work: Nonlinear Controllability via Lie Theory
cites work: Contrôlabilité des Systèmes non Linéaires
cites work: System Theory on Group Manifolds and Coset Spaces
cites work: Nonlinear controllability and observability
cites work: A Sufficient Condition for Local Controllability
cites work: Lie Brackets and Local Controllability: A Sufficient Condition for Scalar-Input Systems
cites work: Q3337276
cites work: Controllability of nonlinear systems
cites work: A General Theorem on Local Controllability
cites work: Q3782303
cites work: The Maximum Principle for an Optimal Solution to a Differential Inclusion with End Points Constraints
cites work: Local Controllability and Infinitesimal Generators of Semigroups of Set-Valued Maps
description: scientific article; zbMATH DE number 4031491