Journal ArticleDOI
A general approach in the design of active controllers for nonlinear systems exhibiting chaos
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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.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.read more
Citations
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Journal ArticleDOI
On control and synchronization in chaotic and hyperchaotic systems via linear feedback control
TL;DR: In this article, a linear feedback control for nonlinear systems has been formulated under an optimal control theory viewpoint, where the stability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function which can clearly be seen as the solution of the Hamilton-Jacobi-Bellman equation.
Journal ArticleDOI
Adaptive control of discrete-time chaotic systems: a fuzzy control approach
Gang Feng,Guanrong Chen +1 more
TL;DR: Using the T–S model of discrete-time chaotic systems, an adaptive control algorithm is developed based on some conventional adaptive control techniques and is shown to be globally stable, and its robustness is discussed.
Journal ArticleDOI
On an optimal control design for Rössler system
TL;DR: In this article, an optimal control strategy that directs the chaotic motion of the Rossler system to any desired fixed point is proposed, and the chaos control problem is then formulated as an infinite horizon optimal control nonlinear problem that was reduced to a solution of the associated Hamilton-Jacobi-Bellman equation.
Journal ArticleDOI
The dynamic behavior of a parametrically excited time-periodic MEMS taking into account parametric errors
Nelson José Peruzzi,Fábio Roberto Chavarette,José Manoel Balthazar,Angelo Marcelo Tusset,Amanda Liz Pacifico Manfrim Perticarrari,Reyolando M. L. R. F. Brasil +5 more
TL;DR: In this paper, the mathematical model of an electroni cationic micro-electromechanical system (MEMS) is presented and the model is extended to the case of a single electron.
Journal ArticleDOI
A reducing of a chaotic movement to a periodic orbit, of a micro-electro-mechanical system, by using an optimal linear control design
TL;DR: In this article, the authors analyzed the non-linear dynamics of a particular micro-electro-mechanical system and used a technique of the optimal linear control for reducing the irregular (chaotic) oscillatory movement of the nonlinear systems to a periodic orbit.
References
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Journal ArticleDOI
Continuous control of chaos by self-controlling feedback
TL;DR: In this paper, the stabilization of unstable periodic orbits of a chaotic system is achieved either by combined feedback with the use of a specially designed external oscillator, or by delayed self-controlling feedback without using of any external force.
Journal ArticleDOI
On feedback control of chaotic continuous-time systems
Guanrong Chen,X. Dong +1 more
TL;DR: In this article, the authors extended the ideas and techniques developed previously by the present authors for controlling discrete-time chaotic dynamic systems using traditional feedback control strategies to continuous time chaotic systems and provided a rigorous mathematical theory and some computer simulations to support and visualize such controllability of the chaotic Duffing equation.
Journal ArticleDOI
From Chaos to Order - Perspectives and Methodologies in Controlling Chaotic Nonlinear Dynamical Systems
Guanrong Chen,Xiaoning Dong +1 more
TL;DR: An overview of the different interpretations and approaches in the investigation of controlling chaos for various nonlinear dynamical systems and its potential applications in nonlinear systems science and engineering is offered.
Journal ArticleDOI
Control of a chaotic system
Thomas L. Vincent,Jianzu Yu +1 more
TL;DR: In this paper, two different controllers are designed for the Lorenz system subject to a control input, one based on linear methods and another based on a nonlinear analysis, and the objective of the controller is to drive the system to one of the unstable equilibrium points associated with uncontrolled chaotic motion.
Journal ArticleDOI
An open-plus-closed-loop (OPCL) control of complex dynamic systems
E. Atlee Jackson,Ioan Grosu +1 more
TL;DR: In this paper, a new method of contmlfing arbitrary nonlinear dynamic systems, dx/dt = F(x, t) (x C N'), is presented.
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