Closed Curves on Convex Hypersurfaces and Periods of Nonlinear Oscillations.
Comparative vibration analysis of a parametrically nonlinear excited oscillator using HPM and numerical method.
Composite control of the -link chained mechanical systems
In this paper, a new control concept for a class of underactuated mechanical system is introduced. Namely, the class of -link chains, composed of rigid links, non actuated at the pivot point is considered. Underactuated mechanical systems are those having less actuators than degrees of freedom and thereby requiring more sophisticated nonlinear control methods. This class of systems includes among others frequently used for the modeling of walking planar structures. This paper presents the stabilization...
Connecting fast-slow systems and Conley index theory via transversality.
Coupled string-beam equations as a model of suspension bridges
We consider nonlinearly coupled string-beam equations modelling time-periodic oscillations in suspension bridges. We prove the existence of a unique solution under suitable assumptions on certain parameters of the bridge.
Decentralized control and synchronization of time-varying complex dynamical network
A new class of controlled time-varying complex dynamical networks with similarity is investigated and a decentralized holographic-structure controller is designed to stabilize the network asymptotically at its equilibrium states. The control design is based on the similarity assumption for isolated node dynamics and the topological structure of the overall network. Network synchronization problems, both locally and globally, are considered on the ground of decentralized control approach. Each sub-controller...
Determination of coupled sway, roll, and yaw motions of a floating body in regular waves.
Determining the domain of attraction of hybrid non–linear systems using maximal Lyapunov functions
In this article a method is presented to find systematically the domain of attraction (DOA) of hybrid non-linear systems. It has already been shown that there exists a sequence of special kind of Lyapunov functions in a rational functional form approximating a maximal Lyapunov function that can be used to find an estimation for the DOA. Based on this idea, an improved method has been developed and implemented in a Mathematica-package to find such Lyapunov functions for a class of hybrid (piecewise...
Deterministické fyzikální soustavy s chaotickým chováním
Discrete breathers in anharmonic models with acoustic phonons
Discrete time markovian agents interacting through a potential
A discrete time stochastic model for a multiagent system given in terms of a large collection of interacting Markov chains is studied. The evolution of the interacting particles is described through a time inhomogeneous transition probability kernel that depends on the ‘gradient’ of the potential field. The particles, in turn, dynamically modify the potential field through their cumulative input. Interacting Markov processes of the above form have been suggested as models for active biological transport...
Drive network to a desired orbit by pinning control
The primary objective of the present paper is to develop an approach for analyzing pinning synchronization stability in a complex delayed dynamical network with directed coupling. Some simple yet generic criteria for pinning such coupled network are derived analytically. Compared with some existing works, the primary contribution is that the synchronization manifold could be chosen as a weighted average of all the nodes states in the network for the sake of practical control tactics, which displays...
Dynamical interaction of an elastic system and a vibro-impact absorber.
Dynamical systems and the homology norm of a 3-manifold II.
Dynamiques recuites de type Feynman-Kac : résultats précis et conjectures
Soit U une fonction définie sur un ensemble fini E muni d'un noyau markovien irréductible M. L'objectif du papier est de comparer théoriquement deux procédures stochastiques de minimisation globale de U : le recuit simulé et un algorithme génétique. Pour ceci on se placera dans la situation idéalisée d'une infinité de particules disponibles et nous ferons une hypothèse commode d'existence de suffisamment de symétries du cadre (E,M,U). On verra notamment que contrairement au recuit simulé, toute...
Energy dissipation and hysteresis cycles in pre-sliding transients of kinetic friction
The problem of transient hysteresis cycles induced by the pre-sliding kinetic friction is relevant for analyzing the system dynamics, e.g., of micro- and nano-positioning instruments and devices and their controlled operation. The associated energy dissipation and consequent convergence of the state trajectories occur due to the structural hysteresis damping of contact surface asperities during reversals, and it is neither exponential (i.e., viscous type) nor finite-time (i.e., Coulomb type). In...
Escape time from potential wells of strongly nonlinear oscillators with slowly varying parameters.
Estabilidad orbital de satélites estacionarios.
For a satellite about an oblate planet in rotation about its axis of greatest inertia, conditions are given under which there may appear, in a frame fixed in the planet, two positions of equilibria with characteristic exponents that are purely imaginary. In which case, after appropriate normalization by Lie transformation executed mechanically through a symbolic algebraic processor, the theorem of Arnold about non definite quadratic forms is applied. It is concluded that the equilibria are stable...
Feedback stabilization of a boundary layer equation
We are interested in the feedback stabilization of a fluid flow over a flat plate, around a stationary solution, in the presence of perturbations. More precisely, we want to stabilize the laminar-to-turbulent transition location of a fluid flow over a flat plate. For that we study the Algebraic Riccati Equation (A.R.E.) of a control problem in which the state equation is a doubly degenerate linear parabolic equation. Because of the degenerate character of the state equation, the classical existence...
Feedback stabilization of a boundary layer equation
We are interested in the feedback stabilization of a fluid flow over a flat plate, around a stationary solution, in the presence of perturbations. More precisely, we want to stabilize the laminar-to-turbulent transition location of a fluid flow over a flat plate. For that we study the Algebraic Riccati Equation (A.R.E.) of a control problem in which the state equation is a doubly degenerate linear parabolic equation. Because of the degenerate character of the state equation, the classical existence...