A robust controller for chaotic systems under external excitation

Tsai, Hsun-Heng; Fuh, Chyun-Chau; Chang, Chiang-Nan

doi:10.1016/s0960-0779(01)00213-2

Cited by 48 publications

(21 citation statements)

References 20 publications

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“…There are several approaches to chaos targeting which exist, the most prominent being OGY (Romeiras et al, 1992). OGY functions by offering time dependent perturbations in the from of feedback to a system parameter, which in turn maintains the system at a fixed operating point (Tsai et al, 2002). A further method of chaos control has been shown in (Pyragas, 1992) where unstable orbits were stabilised via the use of delay feedback perturbations.…”

Section: Traditional Controller Designmentioning

confidence: 99%

The artificial epigenetic network

Turner

Lones

Fuente

et al. 2013

2013 IEEE International Conference on Evolvable Systems (ICES)

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The term epigenetics refers to typically heritable biological mechanisms which facilitate stable yet reversible modifications of gene expression or phenotype state, without alteration of the underlying genetic code. More specifically, epigenetic mechanisms allow organisms to control which genes are active at a given time. In eukaryotes, epigenetic mechanisms have essential roles in gene regulation, cellular differentiation and genetic packaging. These epigenetic mechanisms give rise to functionality which DNA alone is generally incapable of providing.This thesis takes inspiration from the fields of genetics and epigenetics, and builds a computational model which captures the beneficial properties of epigenetics in silico. This computational model is referred to as the artificial epigenetic network. The artificial epigenetic network can dynamically control which genes within the network are active at a given time, allowing certain groups of genes to become specialised towards specific aspects of a task.Hence, the artificial epigenetic network can contain many different regulatory circuits, each with specific properties. This gives the networks the ability to more readily express a wider range of dynamical behaviours, which were found to produce a number computational benefits. The artificial epigenetic network is applied to a diverse range of control tasks, each with varying dynamics, to ascertain how the functionality of the artificial epigenetic structures effects the functionality of the network. An emergent property is that the epigenetic structures can partition the network into functional units corresponding to the logical decomposition of the tasks, and control these units with a switch like behaviour. This provides an interface, where a user can gain control over the complex dynamics of the target domain via the activation or deactivation of these switches.3

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Section: Traditional Controller Designmentioning

confidence: 99%

The artificial epigenetic network

Turner

Lones

Fuente

et al. 2013

2013 IEEE International Conference on Evolvable Systems (ICES)

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“…In the past few decades, various approaches for tracking control have been presented, such as fuzzy control approach [1] , composite tracking control approach [2] , adaptive control approach [3] , sliding mode control approach [4] , etc. Because sliding mode control has attractive features such as fast response, good transient response and insensitivity to variations in system parameters and external disturbances [5−11] , it is a substantial method for the tracking control design of nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

“…In [20,21] This paper applies global sliding mode control to study the tracking control problem for a class of differential inclusion systems. The main contributions of this paper lie in the following aspects: 1) the system model is a generalized model of those considered in [4,8,9]; 2) an extensive reaching law is proposed to design a sliding mode controller to make the error system asymptotically stable.…”

Section: Introductionmentioning

confidence: 99%

Tracking Control of a Class of Differential Inclusion Systems via Sliding Mode Technique

Liu

Song

2014

Int. J. Autom. Comput.

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Abstract:The tracking problem for a class of differential inclusion systems is investigated. Using global sliding mode control approach, a tracking control is proposed such that the output of a differential inclusion system tracks the desired trajectory asymptotically. An extensive reaching law is proposed to achieve the chattering reduction. Finally, an example is given to illustrate the validity of the proposed design.

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“…In 1992 another approach, based on delayed feedback control, was presented for stabilizing unstable periodic orbits of continuous time chaotic systems, called Pyragas method [4]. In recent years, many nonlinear techniques for chaos control were used, such as feedback linearization [5][6][7], sliding mode control [8][9][10], Lyapunov based control [11][12][13] and fuzzy system based control [14][15][16]. In all of the mentioned methods the chaotic system has a deterministic differential equation; there is no random parameter or random excitation on the system governing equation.…”

Section: Introductionmentioning

confidence: 99%

“…The sliding mode control with some modification is used for controlling stochastic chaos toward desired unstable periodic orbits of the deterministic chaotic system. It must be noted that the conventional techniques of chaos control which are based on the sliding mode method [8][9][10]30,31] are commonly used only for deterministic systems. It is shown that the convergence of the stochastic states to the desired periodic orbit can not be completely achieved but tracking error variance will converge to an arbitrarily small bound around zero by applying the proposed sliding mode control.…”

Section: Introductionmentioning

confidence: 99%

Control of stochastic chaos using sliding mode method

Salarieh

Alasty

2009

Journal of Computational and Applied Mathematics

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a b s t r a c tStabilizing unstable periodic orbits of a deterministic chaotic system which is perturbed by a stochastic process is studied in this paper. The stochastic chaos is modeled by exciting a deterministic chaotic system with a white noise obtained from derivative of a Wiener process which eventually generates an Ito differential equation. It is also assumed that the chaotic system being studied has some model uncertainties which are not random. The sliding mode controller with some modifications is used for stochastic chaos suppression. It is shown that the system states converge to the desired orbit in such a way that the error covariance converges to an arbitrarily small bound around zero. As some case studies, the stabilization of 1-cycle and 2-cycle orbits of chaotic Duffing and Φ 6 Van der Pol systems is investigated by applying the proposed method to their corresponding stochastically perturbed systems. Simulation results show the effectiveness of the method and the accuracy of the statements proved in the paper.

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A robust controller for chaotic systems under external excitation

Cited by 48 publications

References 20 publications

The artificial epigenetic network

The artificial epigenetic network

Tracking Control of a Class of Differential Inclusion Systems via Sliding Mode Technique

Control of stochastic chaos using sliding mode method

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