This paper is has addressed the Single Flexible Link Robot. The dynamical model is derived using Euler-Lagrange equation and then a proper controller is designed to suppress a  vibration based-on Input-Shaping (IS) method. But, IS control method is an open loop strategy. Due to the weakness of open loop control systems, a closed loop IS control system is proposed. The achieved closed loop c...

We examine various phenomena induced by white Gaussian random perturbations in the response of nonlinear dynamical systems. In the rst part of this work, digital and analog experiments are conducted on a simple single-degree-of-freedom oscillator with piecewise linear restoring force and harmonic forcing. They reveal that small noise perturbations can give rise to large deviations of the respon...

Motivated by questions in biology, we investigate the stability of equilibria of the dynamical system x = P (t)∇f(x) which arise as critical points of f , under the assumption that P (t) is positive semi-definite. It is shown that the condition ∫ ∞ λ1(P (t)) dt = ∞, where λ1(P (t)) is the smallest eigenvalue of P (t), plays a key role in guaranteeing uniform asymptotic stability and in providin...

Semi-active base isolation system has been proposed mainly to mitigate the base drift of isolated structures while in most cases, its application causes the maximum acceleration of superstructure to be increased. In this paper, designing optimal semi-active base isolation system composed of linear base isolation system with low damping and magneto-rheological (MR) damper has been studied for co...

We give an effective sufficient condition for a variational problem with infinite horizon on a Riemannian manifold M to admit a smooth optimal synthesis, i. e. a smooth dynamical system on M whose positive semi-trajectories are solutions to the problem. To realize the synthesis we construct a well-projected to M invariant Lagrange submanifold of the extremals’ flow in the cotangent bundle T ∗M ...

The conformance testing problem for dynamical systems asks, given two dynamical models (e.g., as Simulink diagrams), whether their behaviors are “close” to each other. In the semi-formal approach to conformance testing, the two systems are simulated on a large set of tests, and a metric, defined on pairs of real-valued, real-timed trajectories, is used to determine a lower bound on the distance...

Given an unknown attractor A in a continuous dy-namical system, how we can discover the topology and dynamics of A? As a practical matter, how can we do so from only a nite amount of information? One way of doing so is to produce a semi-conjugacy from A onto a model system M whose topology and dynamics are known. The complexity of M then provides a lower bound for the complexity of A. The Conle...

The notion of entropy was introduced by Clausius in 1850, and some of the main steps towards the consolidation of the concept were taken by Boltzmann and Gibbs. Since then several extensions and reformulations have been developed in various disciplines with motivations and applications in different subjects, such as statistical mechanics, information theory, and dynamical systems. Fujii and Kam...

We consider dynamical systems that are equivariant under a noncompact Lie group of symmetries and the drift of relative equilibria in such systems In particular we investigate how the drift for a parametrized family of normally hyperbolic relative equilibria can change character at what we call a drift bifurcation To do this we use results of Arnold to analyze parametrized families of elements ...