An On-Line Tracker for a Stochastic Chaotic System Using Observer/Kalman Filter Identification Combined with Digital Redesign Method

Abstract

This is the first paper to present such a digital redesign method for the (conventional) OKID system and apply this novel technique for nonlinear system identification. First, the Observer/Kalman filter Identification (OKID) method is used to obtain the lower-order state-space model for a stochastic chaos system. Then, a digital redesign approach with the high-gain property is applied to improve and replace the observer identified by OKID. Therefore, the proposed OKID combined with an observer-based digital redesign novel tracker not only suppresses the uncertainties and the nonlinear perturbations, but also improves more accurate observation parameters of OKID for complex Multi-Input Multi-Output systems. In this research, Chen's stochastic chaotic system is used as an illustrative example to demonstrate the effectiveness and excellence of the proposed methodology.

Parameters Identification of Nonlinear Lorenz Chaotic System and its Application to High Precision Model Reference Synchronization

“…Based on the measurable input and output info, the OKID identifies the discrete-time linear system for describing the input-output relation and the corresponding observer/steadystate Kalman filter gain at the same time. The OKID has been realized in several engineering practices, such as [29], [30], and [31]. However, the performance was not investigated for the nonlinear Lorenz chaotic system.…”

A New Chaotic System with Line of Equilibria: Dynamics, Passive Control and Circuit Design

“…Various control methods have been used for controlling chaotic systems such as adaptive control [23], sliding mode control [24], active control [25], passive control [26], Pecora-Carroll control [27], impulsive control [28], fuzzy control [29], optimal control [30], digital redesign control [31] and many others [32][33]. The concept of passivity theory has been found to be a nice tool in in various domains of science and engineering such as robotic [34], signal processing [35], permanent-magnet synchronous motors chaotic system [36], hopfield neural network [37], nuclear spin generator system [38], synchronization [39], compass-like biped robot [40] and complexity [41].…”