Controlling chaos and deterministic directed transport in inertia ratchets using backstepping control

Vincent, U. E.; Njah, A. N.; Laoye, J. A.

doi:10.1016/j.physd.2007.04.003

Cited by 57 publications

(32 citation statements)

References 43 publications

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“…(17) and slave system (18) asymptotically synchronize, then the systems (19) and (20) which were derived from the change of space also asymptotically synchronize, such that…”

Section: Model Descriptionmentioning

confidence: 99%

“…MPS means that the master and slave systems could be synchronized up to a constant scaling matrix. Recently, various control methods which include adaptive control [17,18] and active control [7,19,20] have been introduced. Most of the works done on MPS of chaotic systems have used active control method since it is easy to design a control input and to deal with equations including scaling functions.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive Control for Modified Projective Synchronization-Based Approach for Estimating All Parameters of a Class of Uncertain Systems: Case of Modified Colpitts Oscillators

Kammogne

Fotsin

2014

Journal of Chaos

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A method of estimation of all parameters of a class of nonlinear uncertain dynamical systems is considered, based on the modified projective synchronization (MPS). The case of modified Colpitts oscillators is investigated. Through a suitable transformation of the dynamical system, sufficient conditions for achieving synchronization are derived based on Lyapunov stability theory. Global stability and asymptotic robust synchronization of the considered system are investigated. The proposed approach offers a systematic design procedure for robust adaptive synchronization of a large class of chaotic systems. The combined effect of both an additive white Gaussian noise (AWGN) and an artificial perturbation is numerically investigated. Results of numerical simulations confirm the effectiveness of the proposed control strategy.

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“…(17) and slave system (18) asymptotically synchronize, then the systems (19) and (20) which were derived from the change of space also asymptotically synchronize, such that…”

Section: Model Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Adaptive Control for Modified Projective Synchronization-Based Approach for Estimating All Parameters of a Class of Uncertain Systems: Case of Modified Colpitts Oscillators

Kammogne

Fotsin

2014

Journal of Chaos

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“…There are many methods available for controlling a chaotic system such as active control [90][91][92], adaptive control [93][94][95][96][97][98][99][100][101], sliding mode control [102,103], backstepping control [104][105][106], etc.…”

Section: Introductionmentioning

confidence: 99%

A Novel 3-D Circulant Highly Chaotic System with Labyrinth Chaos

Vaidyanathan

2016

Advances in Chaos Theory and Intelligent Control

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In this work, we describe a novel 3-D circulant highly chaotic system with labyrinth chaos. The novel chaotic system is a nine-term polynomial system with six sinusoidal nonlinearities. The phase portraits of the novel circulant chaotic system are illustrated and the dynamic properties of the novel circulant chaotic system are discussed. The novel circulant chaotic system has infinitely many equilibrium points and it exhibits labyrinth chaos. We show that all the equilibrium points of the novel circulant chaotic system are saddle-foci and hence they are unstable. The Lyapunov exponents of the novel circulant chaotic system are obtained as L 1 = 10.3755, L 2 = 0 and L 3 = −10.4113. Thus, the Maximal Lyapunov Exponent (MLE) of the novel chaotic system is obtained as L 1 = 10.3755, which is a large value. This shows that the novel 3-D circulant chaotic system is highly chaotic. Also, the Kaplan-Yorke dimension of the novel circulant highly chaotic system is obtained as D K Y = 2.9966. Since the Kaplan-Yorke dimension of the the novel circulant chaotic system has a large value and close to three, the novel circulant chaotic system with labyrinth chaos exhibits highly complex behaviour. Since the sum of the Lyapunov exponents is negative, the novel chaotic system is dissipative. Next, we derive new results for the global chaos control of the novel circulant highly chaotic system with unknown parameters using adaptive control method. We also derive new results for the global chaos synchronization of the identical novel circulant highly chaotic systems with unknown parameters using adaptive control method. The main control results are established using Lyapunov stability theory. MATLAB simulations are depicted to illustrate the phase portraits of the novel circulant highly chaotic system and also the adaptive control results derived in this work.

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“…Since Ott, Grebogi, and Yorke (OGY) [1] first proposed chaos control in 1990, chaos control has been applied in many areas, such as information science, medicine, biology, and engineering. In recent years, many successful methods have been reported [2][3], such as small perturbations control [4], feedback control [5,6], impulsive control [7,8], the back-stepping method [9,10], adaptive control [11][12][13][14][15][16][17][18], neural networks control [19], fuzzy control [20], sliding mode control [21][22][23], and disturbance-observer-based control [24].…”

Section: Introductionmentioning

confidence: 99%

The Dynamic Feedback Matrix Control for Multidimensional Chaotic Systems

Zhang¹,

Liu²

2013

Asian Journal of Control

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Multidimensional chaotic systems are difficult to control because of their nonlinearity and coupling relationship among state variables. We present the error feedback matrix for nonlinear systems, which contains coupling information of state variables and updates online according to the gradient descent method. The error feedback matrix is similar to the state feedback matrix for linear systems, however, the former is time-varying and converges to a constant matrix. Using the coupling relationship, we give a simple controller only by a few elements of the matrix and present whole matrix control and partial matrix control. Finally, we apply these schemes to a three-dimensional Henon system and make mathematical analysis and simulation experiments, which verify the effectiveness of the proposed controllers. in Wiley Online Library 297-303 820 Fig. 2. The Henon system is driven to (0.8861, 0.8861, 0.8861), starting from (1,0,−1) with η = 0.2. Here, red lines denote xk(1) and uk(1), green lines denote xk(2) and uk (2), and blue lines denote xk(3) and uk(3). This notation remains consistent in the following.

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Controlling chaos and deterministic directed transport in inertia ratchets using backstepping control

Cited by 57 publications

References 43 publications

Adaptive Control for Modified Projective Synchronization-Based Approach for Estimating All Parameters of a Class of Uncertain Systems: Case of Modified Colpitts Oscillators

Adaptive Control for Modified Projective Synchronization-Based Approach for Estimating All Parameters of a Class of Uncertain Systems: Case of Modified Colpitts Oscillators

A Novel 3-D Circulant Highly Chaotic System with Labyrinth Chaos

The Dynamic Feedback Matrix Control for Multidimensional Chaotic Systems

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