Robust adaptive tracking control for a class of uncertain chaotic systems

Zhi, Li; Chen, Guanrong; Song-jiao, Shi; Han, Chongzhao

doi:10.1016/s0375-9601(03)00115-4

Cited by 55 publications

(45 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…So far, many chaos controllers have been developed through adding an extra input uðtÞ in each subsystem of (1), that is, _ xðtÞ ¼ A i xðtÞ þ uðtÞ [6,[14][15][16][17]. Recently, a new T-S model with impulse effects has been proposed for chaos control, where each impulse is viewed as a controller to be designed [10,11].…”

Section: Preliminariesmentioning

confidence: 99%

“…Due to recent advances made in the applications of chaos to chemical reactions, power converters, biological systems, information processing, secure communications, etc., controlling complex chaotic dynamics for engineering applications has newly emerged as an attractive field accompanied by rapid development in its theories and methodologies [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. For example, linear state feedback [2] and Lyapunov-type methods [3] have been used for linear and nonlinear control-design purposes, respectively.…”

Section: Introductionmentioning

confidence: 99%

“…There are several attempts in the literature to study their effects. For instance, in [13], an input-output control scheme was used for chaos suppression in a class of uncertain chaotic systems, while in [14], an adaptive controller was designed based on Lyapunov stability theory for a class of chaotic systems with time-varying, unknown and bounded parameters, which led to the global asymptotic tracking of the desired bounded trajectories. Furthermore, in [15,16], a static output feedback approach was used to stabilize T-S fuzzy systems with time-varying norm bounded uncertainties, while in [17], an input-output approach based on data obtained from the underlying dynamical system was developed for modeling the adaptive control of an unknown chaotic system.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Unified impulsive fuzzy-model-based controllers for chaotic systems with parameter uncertainties via LMI

Zhang

Khadra

Yang

et al. 2010

Communications in Nonlinear Science and Numerical Simulation

View full text Add to dashboard Cite

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Unified impulsive fuzzy-model-based controllers for chaotic systems with parameter uncertainties via LMI

Zhang

Khadra

Yang

et al. 2010

Communications in Nonlinear Science and Numerical Simulation

View full text Add to dashboard Cite

“…Also, the aforementioned methods cannot handle time-varying parameters, which may exist in a chaotic system. Recently, new methods based on adaptive robust control strategy have been introduced in efforts to control chaotic and nonlinear systems with time-varying uncertainties [26][27][28]. However, these methods are designed based on the vector control input signal.…”

Section: Introductionmentioning

confidence: 99%

Robust synchronization of Rossler systems with mismatched time-varying parameters

Arefi

Jahed‐Motlagh

2011

Nonlinear Dyn

View full text Add to dashboard Cite

This paper presents robust synchronization algorithms for the Rossler systems in the presence of unknown time-varying parameters. First, an adaptive synchronization algorithm based on the Lyapunov theory is introduced for identical Rossler systems with mismatched uncertainties. This method does not require a priori information regarding the bound of uncertainties. In addition, this technique is such that the states of the synchronization error system are uniformly ultimately bounded. Since in practice the parameters of the drive and response systems are not necessarily the same, two synchronization approaches are used for the drive and response systems with different parameters. In the first approach, a simple controller is designed for the nominal error system, as if there is no uncertainty in the system. The stability analysis is then investigated as the uncertainties are reintroduced, and it is shown that the size of the uncertainties directly affects the synchronization performance. To deal with this problem, an H ∞ controller is designed in which the effects of unknown bounded uncertainties can be attenuated at an appropriate level. It is shown that, using these two approaches, the Rossler systems M.M. Arefi · M.R. Jahed-Motlagh ( ) can be synchronized effectively and the synchronization error is uniformly ultimately bounded. Numerical simulations confirm the effectiveness of the proposed methods.

show abstract

“…The chaos represents an interesting topic because irregular oscillations can be undesirable in some physical systems. Control and synchronization schemes for different chaotic systems have been explored by various researchers since long [1][2][3][4][5][6][7][8]. These systems find applications in spread spectrum waveforms, secure communication, cryptography and they are utilized as chaotic sources in transmitter-receiver schemes [9][10][11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Observer-based synchronization scheme for a class of chaotic systems using contraction theory

Sharma

Kar

2010

Nonlinear Dyn

View full text Add to dashboard Cite

In this paper, an adaptive synchronization scheme is proposed for a class of nonlinear systems. The design utilizes an adaptive observer, which is quite useful in establishing a transmitter-receiver kind of synchronization scheme. The proposed approach is based on contraction theory and provides a very simple way of establishing exponential convergence of observer states to actual system states. The class of systems addressed here has uncertain parameters, associated with the part of system dynamics that is a function of measurable output only. The explicit conditions for the stability of the observer are derived in terms of gain selection of the observer. Initially, the case without uncertainty is considered and then the results are extended to the case with uncertainty in parameters of the system. An application of the proposed approach is presented to synchronize the family of N chaotic systems which are coupled through the output variable only. The numerical results are presented for designing an adaptive observer for the chaotic Chua system to verify the efficacy of the proposed approach. Explicit bounds on observer gains are derived by exploiting the properties of the chaotic attractor exhibited by Chua's system. Convergence of uncertain parameters is also analyzed for this case and numerical simulations depict the convergence of parameter estimates to their true value.

show abstract

Robust adaptive tracking control for a class of uncertain chaotic systems

Cited by 55 publications

References 10 publications

Unified impulsive fuzzy-model-based controllers for chaotic systems with parameter uncertainties via LMI

Unified impulsive fuzzy-model-based controllers for chaotic systems with parameter uncertainties via LMI

Robust synchronization of Rossler systems with mismatched time-varying parameters

Observer-based synchronization scheme for a class of chaotic systems using contraction theory

Contact Info

Product

Resources

About