Nonlinear Dynamic System Identification in the Spectral Domain Using Particle-Bernstein Polynomials

Nonlinear System Identification Using Particle Filters

Particle filters are computational methods opening up for systematic inference in nonlinear/non-Gaussian state space models. The particle filters constitute the most popular sequential Monte Carlo (SMC) methods. This is a relatively recent development and the aim here is to provide a brief exposition of these SMC methods and how they are key enabling algorithms in solving nonlinear system ident...

Nonlinear system identification using clustering algorithm and particle swarm optimization

The identification of nonlinear systems operating in a stochastic environment is an important problem in various discipline science and engineering. Fuzzy modeling and especially the T-S fuzzy model draw the attention of several researchers in recent decades this is due to their potential to approximate highly nonlinear behavior. An algorithm allowing the identification of the premise and conse...

Numerical Solutions of the Nonlinear Fractional-Order Brusselator System by Bernstein Polynomials

In this paper we propose the Bernstein polynomials to achieve the numerical solutions of nonlinear fractional-order chaotic system known by fractional-order Brusselator system. We use operational matrices of fractional integration and multiplication of Bernstein polynomials, which turns the nonlinear fractional-order Brusselator system to a system of algebraic equations. Two illustrative exampl...

Identification of Shapes Using A Nonlinear Dynamic System

Unimodal density estimation using Bernstein polynomials

The estimation of probability density functions is one of the fundamental aspects of any statistical inference. Many data analyses are based on an assumed family of parametric models, which are known to be unimodal (e.g., exponential family, etc.). Often a histogram suggests the unimodality of the underlying density function. Parametric assumptions, however, may not be adequate for many inferen...