1 Simplification of a Control Methodology for a Class of Uncertain Chaotic Systems (original) (raw)
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Simplified robust adaptive control of a class of time-varying chaotic systems
COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 2008
Purpose-To develop a simplified robust control scheme for a class of nonlinear time-varying uncertain chaotic systems. Design/methodology/approach-By means of input-to-state stability theory, a new robust adaptive control scheme is designed, which is simpler than the one proposed by Li et al. and applicable to a larger class of nonlinear systems. Only one parameter is adjusted in the controller and the scheme assures that all the signals remain bounded. The behavior of the proposed control scheme is also analyzed through simulations on the Rössler system. Findings-By adjusting only one parameter in the controller and imposing only one mild assumption on the time-varying parameters, the proposed control algorithm assures that all the signal remain bounded and that the state of the original system will follow a desired trajectory defined either by the trajectory and its first time derivative, or given by a reference model. Research limitations/implications-The results are limited to a particular class of nonlinear systems where the dimension of the input vector is equal to the order of the system (dimension of the state vector). Practical implications-The main advantage of the proposed method is that the modification introduced leads to a substantially simpler adaptive robust controller whose practical implementation will be easier. Originality/value-The contribution of the proposed method is in the simplification of the control algorithm applied to a class of nonlinear time-varying uncertain chaotic systems. This will be useful for control engineers to control complex industrial plants.
Considering the effect of random perturbations on the chaotic system, a new adaptive tracking control is presented for a large class of uncertain chaotic systems using the invariance principle of differential equations, where the bound of random perturbations is not necessarily known in advance and it is estimated through an adaptive control process. It is theoretically proved that this approach can make the perturbed chaotic system track any desired reference signal; in addition, we can see that this method can apply to almost all uncertain chaotic systems and it is simpler and easier to implement in practical application. In the end, we take the perturbed Lorenz system as an example to illustrate that the proposed scheme is effective. r
OBSERVER-BASED ADAPTIVE FEEDBACK CONTROLLER OF A CLASS OF CHAOTIC SYSTEMS
International Journal of Bifurcation and Chaos, 2006
In this paper, an observer-based adaptive feedback controller is developed for a class of chaotic systems. This controller does not need the availability of state variables. It can be used for tracking a smooth orbit that can be a limit cycle or a chaotic orbit of another system. This adaptive feedback controller is constructed with the aid of its H ∞ control technique to achieve the H ∞ tracking performance. Based on Lyapunov stability theorem, the proposed adaptive feedback control system can guarantee the stability of whole closed-loop system and obtain good tracking performance as well. To demonstrate the efficiency of the proposed scheme, two wellknown chaotic systems, namely Chua's circuit and Lur'e system are considered as illustrative examples.
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This paper presents a control strategy, which is based on sliding mode control, adaptive control, and fuzzy logic system for controlling the chaotic dynamics. We consider this control paradigm in chaotic systems where the equations of motion are not known. The proposed control strategy is robust against the external noise disturbance and system parameter variations and can be used to convert the chaotic orbits not only to the desired periodic ones but also to any desired chaotic motions. Simulation results of controlling some typical higher order chaotic systems demonstrate the effectiveness of the proposed control method.
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This paper investigates the problem of chaos control and synchronization for new chaotic dynamical system and proposes a simple adaptive feedback control method for chaos control and synchronization under a reasonable assumption. In comparison with previous methods, the present control technique is simple both in the form of the controller and its application. Based on Lyapunov's stability theory, adaptive control law is derived such that the trajectory of the new system with unknown parameters is globally stabilized to the origin. In addition, an adaptive control approach is proposed to make the states of two identical systems with unknown parameters asymptotically synchronized. Numerical simulations are shown to verify the analytical results.
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Controlling chaos is stabilizing one of the unstable periodic orbits either to its equilibrium point or to a stable periodic orbit by means of an appropriate continuous signal injected to the system. On the other hand, chaos synchronization refers to a procedure where two chaotic oscillators (either identical or nonidentical) adjust a given property of their motion to a common behavior. This research paper concerns itself with the Adaptive control and synchronization of a new chaotic system with unknown parameters. Based on the Lyapunov direct method (LDM), the Adaptive control techniques (ACTs) are designed in such a way that the trajectory of the new chaotic system is globally stabilized to one of its equilibrium points of the uncontrolled system. Moreover, the Adaptive control law is also applied to achieve the synchronization state of two identical systems and two different chaotic systems with fully unknown parameters. The parameters identification, chaos control and synchronization of the chaotic system have been carried out simultaneously by the Adaptive controller. All simulation results are carried out to corroborate the effectiveness and the robustness of the proposed methodology and possible feasibility for synchronizing two chaotic systems by using Mathematica 9.
Adaptive Control of Accumulative Error for Nonlinear Chaotic Systems
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We present an adaptive control scheme of accumulative error to stabilize the unstable fixed point for chaotic systems which only satisfies local Lipschitz condition, and discuss how the convergence factor affects the convergence and the characteristics of the final control strength. We define a minimal local Lipschitz coefficient, which can enlarge the condition of chaos control. Compared with other adaptive methods, this control scheme is simple and easy to implement by integral circuits in practice. It is also robust against the effect of noise. These are illustrated with numerical examples.
An adaptive feedback control of linearizable chaotic systems
Chaos, Solitons & Fractals, 2003
This paper proposes an adaptive feedback controller for a class of chaotic systems. This controller can be used for tracking a smooth orbit that can be a limit cycle or a chaotic orbit of another system. Based on Lyapunov approach, the adaptation law is determined to tune the controller gain vector in order to track a predetermined linearizing feedback control. To demonstrate the efficiency of the proposed scheme, two well-known chaotic systems namely ChuaÕs circuit and a LurÕe-like system are considered as illustrative examples. (M. Feki). 0960-0779/03/$ -see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 0 -0 7 7 9 ( 0 2 ) 0 0 2 0 3 -5 Chaos, Solitons and Fractals 15 (2003) 883-890 www.elsevier.com/locate/chaos