Distributions of particles being transported through a nonlinear Hamiltonian system are studied. Using normal form techniques, a procedure to obtain invariant functions of moments of the distribution is given. These functions are invariant for the given Hamiltonian system and are called dynamic moment invariants. These techniques are used to obtain dynamic moment invariants for the nonlinear pe...

In this paper, dynamic structure neural network controller based on feedback linearization is proposed. The proposed method can adapt the neural network structure dynamically while it can guarantee the stability and tracking precision of system. The dynamic structure wavelet network controller is introduced in the system simulation and the performance of the controller on a system with nonlinea...

Dynamic Ratcheting (DR) is a nonlinear dynamic phenomenon occurring in hysteretic damping systems. It means the structural plastic deformation increases asymmetrically in successive cycles under an earthquake excitation. Although it is generally recognized that DR is closely related to the frequency contents of an earthquake excitation applied to thestructure, no targeted analysis has bee...

A neural network based approach is presented for controlling two distinct types of nonlinear systems. The first corresponds to nonlinear systems with parametric uncertainties where the parameters occur nonlinearly. The second corresponds to systems for which stabilizing control structures cannot be determined. The proposed neural controllers are shown to result in closed-loop system stability u...

The method of structural identification nonlinear dynamic systems is offered in the conditions of uncertainty. The method of construction the set containing the data about a nonlinear part of system is developed. The concept of identifiability system for a solution of a problem structural identification is introduced. The special class of structures S for a solution of problem identification is...

There is a basic assumption in using state feedback control, i.e., we assume that all the state variables are available for direct measurements. However, in many situations the complete state is not available; so it is necessary to obtain an estimate of the current state of the given system from measurements of its output. For this purpose, Luenberger (1964, 1966) showed how to construct an obs...

One approach for representing uncertainty is the use of fuzzy sets or fuzzy numbers. A new approach is described for the solution of nonlinear dynamic systems with parameters and/or initial states that are uncertain and represented by fuzzy sets or fuzzy numbers. Unlike current methods, which address this problem through the use of sampling techniques and do not account rigorously for the effec...

Accurate estimation of state variables and model parameters is essential for efficient process operation. The Bayesian formulation of the estimation problem suggests a general solution for nonlinear systems. However, a practically feasible implementation of the solution has not been available until recently. Most existing methods have had to rely on simplifying assumptions to obtain an approxim...