There are many texts on linear control theory, and a number of introductions to nonlinear
control theory and in particular its differential geometric formulation, which is important for …

With this paper we recall some of the formal framework developed in classical analytical
mechanics with emphasis on constrained systems. It can be used in describing …

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 …

Nonholonomic systems are control systems which depend linearly on the control. Their
underlying geometry is the sub-Riemannian geometry, which plays for these systems the …

Mathematical control theory has evolved from the study of practical problems in engineering
and sciences to the elaboration of deep, important concepts in mathematics and applied …

This paper gives a general formulation of the theory of nonholonomic control systems on a
Riemannian manifold modeled by second-order differential equations and using the unique …

We present a dictionary between gauge theory and control theory. This is useful for
problems involving the control of the orientations of deformable bodies (robots, gymnasts) by …

Beginning around 1963 with the paper of Hermann [1] there began to be developed a theory
of controllability that included nonlinear effects in a mathematically natural way. By the early …

Various versions of the notes have been used for the course “Geometric Control Theory”
given at the Royal Institute of Technology (KTH), and its predecessor “Advanced Systems …

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 …