This textbook on the differential geometric approach to nonlinear
control grew out of a set of lecture notes, which were prepared for a
course on nonlinear system theory, given by us for the first time during
the fall semester of 1988 . The audience consisted mostly of graduate
students, taking part in the Dutch national Graduate Program on Systems
and Control . The aim of this course is to give a general introduction
to modern nonlinear control theory (with an emphasis on the differential
geometric approach), as well as to provide students specializing in
nonlinear control theory with a firm starting point for doing research
in this area . One of our primary objectives was to give a
self-contained treatment of all the topics to be included. Since the
literature on nonlinear geometric control theory is rapidly expanding
this forced us to limit ourselves in the choice of topics . The task of
selecting topics was further aggravated by the continual shift in
emphasis in the nonlinear control literature over the last years .
Therefore, we decided to concentrate on some rather solid and clear-cut
achievements of modern nonlinear control, which can be expected to be of
remaining interest in the near future. Needless to say, there is also a
personal bias in the topics we have finally selected.
