## Abstract

We present an introduction to the qualitative theory of nonlinear control systems, with the main emphasis on controllability properties of such systems. We introduce the differential geometric language of vector fields, Lie bracket, distributions, foliations etc. One of the basic tools is the orbit theorem of Stefan and Sussmann. We analyse the basic controllability problems and give criteria for complete controllability, accessibility and related properties, using certain Lie algebras of ve fields defined by the system. A problem of path approximation is considered as an application of the developed theory. We illustrate our considerations with examples of simple systems or systems appearing in applications. The notes start from an elementary level and are self-contained. (author)

## Citation Formats

Jakubczyk, B.
Introduction to geometric nonlinear control; Controllability and lie bracket.
IAEA: N. p.,
2002.
Web.

Jakubczyk, B.
Introduction to geometric nonlinear control; Controllability and lie bracket.
IAEA.

Jakubczyk, B.
2002.
"Introduction to geometric nonlinear control; Controllability and lie bracket."
IAEA.

@misc{etde_20901513,

title = {Introduction to geometric nonlinear control; Controllability and lie bracket}

author = {Jakubczyk, B}

abstractNote = {We present an introduction to the qualitative theory of nonlinear control systems, with the main emphasis on controllability properties of such systems. We introduce the differential geometric language of vector fields, Lie bracket, distributions, foliations etc. One of the basic tools is the orbit theorem of Stefan and Sussmann. We analyse the basic controllability problems and give criteria for complete controllability, accessibility and related properties, using certain Lie algebras of ve fields defined by the system. A problem of path approximation is considered as an application of the developed theory. We illustrate our considerations with examples of simple systems or systems appearing in applications. The notes start from an elementary level and are self-contained. (author)}

place = {IAEA}

year = {2002}

month = {Jul}

}

title = {Introduction to geometric nonlinear control; Controllability and lie bracket}

author = {Jakubczyk, B}

abstractNote = {We present an introduction to the qualitative theory of nonlinear control systems, with the main emphasis on controllability properties of such systems. We introduce the differential geometric language of vector fields, Lie bracket, distributions, foliations etc. One of the basic tools is the orbit theorem of Stefan and Sussmann. We analyse the basic controllability problems and give criteria for complete controllability, accessibility and related properties, using certain Lie algebras of ve fields defined by the system. A problem of path approximation is considered as an application of the developed theory. We illustrate our considerations with examples of simple systems or systems appearing in applications. The notes start from an elementary level and are self-contained. (author)}

place = {IAEA}

year = {2002}

month = {Jul}

}