A General Approach in the Design of Active Controllers for Nonlinear Systems Exhibiting Chaos

Abstract

A general framework for local control of nonlinearity in nonautonomous systems using feedback strategies is considered in this work. In particular, it is shown that a system exhibiting chaos can be driven to a desired periodic motion by designing a combination of feedforward controller and a time-varying controller. The design of the time-varying controller is achieved through an application of Lyapunov–Floquet transformation which guarantees the local stability of the desired periodic orbit. If it is desired that the chaotic motion be driven to a fixed point, then the time-varying controller can be replaced by a constant gain controller which can be designed using classical techniques, viz. pole placement, etc. A sinusoidally driven Duffing's oscillator and the well-known Rossler system are chosen as illustrative examples to demonstrate the application.

An optimal linear control design for nonlinear systems

“…If the function ) ( t x is a solution of equation (13) These are exactly the same desired trajectory and parameters as reported by Sinha et al (2000). For these parameters, the system (14) without control possesses a chaotic attractor, shown in Fig.…”

Projeto de Controle de Caos Aplicado a uma Estrutura com Comportamento Caótico

“…Naárea de controle de caos vários métodos para se realizar o controle foram propostos [2, 4,5] com o objetivo de se eliminar o comportamento caótico tornando o sistema com um movimento periódico, ou alterando-se o movimento para um ponto ou trajetória desejada. Dentre as estratégias de controle com realimentação a mais popularé o método OGY [4].…”

Control of New 3D Chaotic System

“…Therefore, various controllers have been proposed to achieve the stabilization of chaotic systems [3][4][5][6][7][8][9]. In [10], the output regulation problem for the Sprott-G chaotic system (1994) has been studied in detail.…”