This letter deals with interconnection and damping assignment for discrete-time port-Hamiltonian systems. Based on a novel state representation, suitably shaped to address energy-based control design, the nonlinear controller is characterized solution explicitly computed in linear case. The design worked out exact sampled-data model of mechanical system confirms effectiveness controller.

The Hénon–Heiles Hamiltonian was introduced in 1964 [M. Hénon, C. Heiles, Astron. J. 69 (1964) 73] as a mathematical model to describe the chaotic motion of stars in a galaxy. By canonically transforming the classical Hamiltonian to a Birkhoff– Gustavson normal form, Delos and Swimm obtained a discrete quantum mechanical energy spectrum. The aim of the present work is to first quantize the clas...

In this paper we discuss energy conservation issues related to the numerical solution of the semilinear wave equation. As is well known, this problem can be cast as a Hamiltonian system that may be autonomous or not, depending on the prescribed boundary conditions. We relate the conservation properties of the original problem to those of its semi-discrete version obtained by the method of lines...

We consider the simplest nontrivial supersymmetric quantum mechanical system involving higher derivatives. We unravel the existence of additional bosonic and fermionic integrals of motion forming a nontrivial algebra. This allows one to obtain the exact solution both in the classical and quantum cases. The supercharges Q, Q̄ are not anymore Hermitially conjugate to each other, which allows for t...

An argument is presented to explain the fact that the same mean-field results apply to several spin glass models, such as the 'random-energy' model and the large-p Potts glass model. The dilute simplest spin glass model is solved, yielding the same mean-field results. The argument is based on the fact that the symmetry of the discrete-spin system can be determined by the discrete-spin type or b...

In this paper, we construct a highly simplified mathematical model for studying the problem of conjugate heat transfer in gas turbine blades and their cooling ducts. Our simple focuses on relevant coupling structures aims to reduce unrelated complexity as much possible. Then, apply port-Hamiltonian formalism its subsystems investigate interconnections. Finally, spatial discretization system pro...

In the present tutorial we address a problem with a long history, which remains of great interest to date due to its many important applications: It concerns the existence and stability of periodic and quasiperiodic orbits in N degree of freedom Hamiltonian systems and their connection with discrete symmetries. Of primary importance in our study is what we call nonlinear normal modes (NNMs), i....

In this paper we discuss a weak version of KAM theory for symplectic maps which arise from the discretization of the minimal action principle. These maps have certain invariant sets, the Mather sets, which are the generalization of KAM tori in the non-differentiable case. These sets support invariant measures, the Mather measures, which are action minimizing measures. We generalize viscosity so...

Continuous relaxations play an important role in discrete optimization, but have not seen much use in approximate probabilistic inference. Here we show that a general form of the Gaussian Integral Trick makes it possible to transform a wide class of discrete variable undirected models into fully continuous systems. The continuous representation allows the use of gradient-based Hamiltonian Monte...