$n$ -Dimensional controllability with $(n-1)$ controls

Author

Hunt, Louis R.

Author_Institution

Texas Technical University, Lubbock, TX, USA

Volume

Issue

fYear

1982

fDate

2/1/1982 12:00:00 AM

Firstpage

113

Lastpage

117

Abstract

Let $M$ be a connected real-analytic $n$ -dimensional manifold, $f, g_{1}, ... ,g_{n-1}$ be complete real-analytic vector fields on $M$ which are linearly independent at some point of $M$ , and $u_{1}, ... , u_{n-1}$ be real-valued controls. Consider the controllability of the system $\\dot{x}(t)=f(x(t)) + \\sum \\min{i=1}\\max {n-1} u_{i}(t)g_{i}(x(t)), x(0)=x_{0} in M$ . Necessary and sufficient conditions are given so that this system is controllable on any simply connected domain $D$ contained in $M$ on which $g_{1},... ,g_{n-1}$ are linearly independent. These conditions depend on the computation of Lie brackets at those points where $f, g_{1}, ... ,g_{n-1}$ are linearly dependent.

Keywords

Controllability, nonlinear systems; Algebra; Control systems; Controllability; Integral equations; Kalman filters; Mathematics; Modules (abstract algebra); Sufficient conditions;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.1982.1102876

Filename

1102876

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=837972

-Dimensional controllability with controls

Hunt, Louis R.

jour

$n$ -Dimensional controllability with $(n-1)$ controls