The aim of this paper is to present a short historical/scientific review on nonholonomic
mechanics, with special emphasis on the latest developments. Indeed, the use of differential …

Since the second half of the 20th century, Pontryagin's Maximum Principle has been widely
discussed and used as a method to solve optimal control problems in medicine, robotics …

This paper extends the Gotay-Nester and the Dirac theories of constrained systems in order
to deal with Dirac dynamical systems in the integrable case. Integrable Dirac dynamical …

In this paper, a numerical method for solving the constrained optimal control of time-varying
singular systems with quadratic performance index is presented. Presented method is based …

The work done by Isaac Newton more than three hundred years ago, continues being a path
to increase our knowledge of Nature. To better understand all the ideas behind it, one of the …

A geometric setup for constrained variational calculus is presented. The analysis deals with
the study of the extremals of an action functional defined on piecewise differentiable curves …

We geometrically describe optimal control problems in terms of Morse families in the
Hamiltonian framework. These geometric structures allow us to recover the classical first …

Abstract Pontryagin's Maximum Principle is an outstanding result for solving optimal control
problems by means of optimizing a specific function on some particular variables, the so …

Candidates to be solutions to optimal control problems, called extremals, are found using
Pontryagin's Maximum Principle [9]. This Principle gives necessary conditions for optimality …

For the last forty years, differential geometry has provided a means of understanding optimal
control theory. Usually the best strategy to solve a difficult problem is to transform it into a …