Narrow Results

In this paper we study the tracking control of Lagrangian systems subject to frictionless unilateral constraints. The stability analysis incorporates the hybrid and nonsmooth dynamical feature of the overall system. The difference between tracking control for unconstrained systems and unilaterally constrained ones, is explained in terms of closed-loop desired trajectories and control signals. This work provides details on the conditions of existence of controllers which guarantee stability. It is shown that the design of a suitable transition phase desired trajectory, is a crucial step. Some simulation results provide information on the robustness aspects. Finally the extension towards the case of multiple impacts, is considered.

We study mechanical systems that can be recast into the form of a system of genuine Euler–Lagrange equations. The equations of motions of such systems are initially equivalent to the system of Lagrange equations of some Lagrangian $L$, including a covariant force field. We find necessary and sufficient conditions for the existence of a differentiable function $\mathrm{\Phi }:ℝ\to ℝ$ such that the initial system is equivalent to the system of Euler–Lagrange equations of the deformed Lagrangian $\mathrm{\Phi }(L)$.

This work applies the contact formalism of classical mechanics and classical field theory, introduced by Herglotz and later developed in the context of contact geometry, to describe electromagnetic systems with dissipation. In particular, we study an electron in a non-perfect conductor and a variation of the cyclotron radiation. In order to apply the contact formalism to a system governed by the Lorentz force, it is necessary to generalize the classical electromagnetic gauge and add a new term in the Lagrangian. We also apply the k-contact theory for classical fields to model the behavior of electromagnetic fields themselves under external damping. In particular, we show how the theory describes the evolution of electromagnetic fields in media under some circumstances. The corresponding Poynting theorem is derived. We discuss its applicability to the Lorentz dipole model and to a highly resistive dielectric.

We study the Aubry set which appears in Mather theory of convex Hamiltonian systems from the point of view of symplectic geometry.

We present a design methodology for a robust Luenberger-type state observer for nDOF-Lagrangian systems. The observer maintains its characteristic of exponential convergence to the steady-state in spite of the presence of bounded parameter variations and bounded external disturbances. The observer incorporates a discontinuous term in the feedback signal, so the stability proof is based on analysis tools for variable structure systems. The design methodology is experimentally illustrated.