This essay highlights the contributions of geometric control theory to the calculus of
variations. The Maximum Principle is recognized as a covariant necessary condition of …

This paper is devoted to a detailed analysis of the geodesic problem on matrix Lie groups,
with left invariant metric, by examining representations of embeddings of geodesic flows in …

We consider n-dimensional extensions of some classical problems on curves which satisfy
certain curvature constraints. The problems of elastica, Delaunay, and Dubins are treated …

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 …

Optimal control has strongly influenced geometry since the early days of both subjects. In
particular, it played a crucial role in the birth of differential geometry in the nineteenth century …

Necessary conditions for existence of normal extremals in optimal control of systems subject
to nonholonomic constraints are derived as solutions of a constrained second order …

This paper studies the optimal motion control of mechanical systems through a discrete
geometric approach. At the core of our formulation is a discrete Lagrange-d'Alembert …

This paper shows how left and right actions of Lie groups on a manifold may be used to
complement one another in a variational reformulation of optimal control problems …

This book is divided into two parts. The first addresses the simpler variational problems in
parametric and nonparametric form. The second covers extensions to optimal control theory …

In this paper, we study a discrete variational optimal control problem for a rigid body. The
cost to be minimized is the external torque applied to move the rigid body from an initial …