In this paper we present a definition of" configuration controllability" for mechanical systems
whose Lagrangian is kinetic energy with respect to a Riemannian metric minus potential …

A geometric approach to time-dependent optimal control problems is proposed. This
formulation is based on the Skinner and Rusk formalism for Lagrangian and Hamiltonian …

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 …

Variational integrators for Euler--Lagrange equations and Hamilton's equations are a class
of structure-preserving numerical methods that respect the conservative properties of such …

Contact Hamiltonian systems are a generalization of the Hamiltonian systems of classical
mechanics. The action is added as an extra variable in phase space, and symplectic …

Adjoint systems are widely used to inform control, optimization, and design in systems
described by ordinary differential equations or differential-algebraic equations. In this paper …

This paper analyzes the optimal control problem of cubic polynomials on compact Lie
groups from a Hamiltonian point of view and its symmetries. The dynamics of the problem is …

Using recent characterisations of topologies of spaces of vector fields for general regularity
classes—eg, Lipschitz, finitely differentiable, smooth, and real analytic—characterisations …

We present a KAM theorem for presymplectic dynamical systems. The theorem has a “a
posteriori” format. We show that given a Diophantine frequency ω and a family of …

This paper addresses the problem of feedback invariance in geometric control theory by
overviewing a framework that is inherently feedback-invariant. Crucial to the coherence of …