The early days of geometric nonlinear control

Around 1970 the study of nonlinear control systems took a sharp turn. In part, this was driven by the hope for a more inclusive theory which would be applicable to various newly emerging aerospace problems lying outside the scope of linear theory, and also by the gradual realization that tools from differential geometry, and Lie theory in particular, could be seen as providing a remarkably nice fit with what seemed to be needed for the wholesale extension of linear control theory into a nonlinear setting. This paper discusses an initial phase of the development of geometric nonlinear control, including material on the broader context from which it emerged. We limit our account to developments occurring up to the early 1980s, not because the field stopped developing at that point but rather to limit the scope of the project to something manageable. Even so, because of the volume and diversity of the literature we have had to be selective, even within the given time frame.