We present an innovative adaptive, model following control scheme and apply it to control a chaotic system with unknown parameters. We illustrate the proposed approach with control of Duffing oscillator problem. The same idea is used to solve three important problems: suppression of chaos, anticontrol of chaos and chaos synchronization. We propose to use ‘approximators’ linearly parameterized b...

Abstract The chaotic system plays an important role in electronic and electrical equipment, computer cryptography, computer communication and so on. In this paper, we established three new six-dimensional complex chaotic systems and one new ten-dimensional complex chaotic system. The regularity to generate high-dimensional chaotic system is also found by overlaying a series of low-dimensional c...

Aiming at the feature extraction of weak periodic signal in early fault of machinery, a novel weak periodic signal detection with Duffing oscillator based on empirical mode decomposition (EMD) was presented. The chaotic character of Duffing oscillator was analyzed, and the Melnikov method of determining chaotic threshold of Duffing oscillators was discussed. The principle of weak signal detecti...

This paper concerns global phase structures of a time-delayed-feedback controlled two-well Duffing system. The remains of a global stretch and fold structure along an unstable manifold, which develops from an unstable fixed point in function space, reveals that the global chaotic dynamics is inherited from the original system by the controlled system. The remains of the original chaotic dynamic...

This paper presents a fuzzy controller to solve a master-slave chaos synchronization problem. At first, the method of traditional sliding mode control is considered, which utilizes the discontinuous sign function to make the system state reaching a sliding surface. Next, fuzzy rules are determined according to the Lyapunov theorem, and the fuzzy controller is designed for chaos synchronization....

Abstract The chaotic system plays an important role in information communication, electrical equipment, computer cryptography and so on. In this paper, four new high-dimensional complex hyperchaotic systems are found. A new overlaying regularity to generate a new high-dimensional complex hyperchaotic system is found by overlaying a series of low-dimensional chaotic system with the Duffing chaot...

Problem of unknown encoded parameter reconstruction is solved by means of procedure of design of adaptive observer for chaotic Duffing system. Unlike known analogues, the problem in question is only solved using measurements of output of chaotic system and in conditions of full parametrical uncertainty. Copyright © 2008 IFAC

this paper introduces a technique for controlling a class of uncertain chaotic systems using an adaptive fuzzy proportional-integrator-derivative (pid) controller with h∞ tracking performance. the purpose of this work is to achieve optimal tracking performance of the controller using backtracking search algorithm (bsa). bsa, which is a novel heuristic algorithm, has an easy structure with singl...

We have studied experimentally a chaotic cryptosystem, which is based on the inverse system approach. We applied this method to a second order nonlinear circuit (master circuit), which is described by a Duffing equation. We present the implementation of the slave circuit with the inverse system approach and we demonstrate the decryption when the information signal has several forms (sinusoidal ...