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Adaptive finite-time synchronization of cross-strict feedback hyperchaotic systems with parameter uncertainties

Hai-Yan Li, Yun-An Hu, Rui-Qi Wang (2013)


This paper is concerned with the finite-time synchronization problem for a class of cross-strict feedback underactuated hyperchaotic systems. Using finite-time control and backstepping control approaches, a new robust adaptive synchronization scheme is proposed to make the synchronization errors of the systems with parameter uncertainties zero in a finite time. Appropriate adaptive laws are derived to deal with the unknown parameters of the systems. The proposed method can be applied to a variety...

Chaotic behavior and modified function projective synchronization of a simple system with one stable equilibrium

Zhouchao Wei, Zhen Wang (2013)


By introducing a feedback control to a proposed Sprott E system, an extremely complex chaotic attractor with only one stable equilibrium is derived. The system evolves into periodic and chaotic behaviors by detailed numerical as well as theoretical analysis. Analysis results show that chaos also can be generated via a period-doubling bifurcation when the system has one and only one stable equilibrium. Based on Lyapunov stability theory, the adaptive control law and the parameter update law are derived...

Degenerate Hopf bifurcations and the formation mechanism of chaos in the Qi 3-D four-wing chaotic system

Hongtao Liang, Yanxia Tang, Li Li, Zhouchao Wei, Zhen Wang (2013)


In order to further understand a complex 3-D dynamical system proposed by Qi et al, showing four-wing chaotic attractors with very complicated topological structures over a large range of parameters, we study degenerate Hopf bifurcations in the system. It exhibits the result of a period-doubling cascade to chaos from a Hopf bifurcation point. The theoretical analysis and simulations demonstrate the rich dynamics of the system.

Dynamics analysis and robust modified function projective synchronization of Sprott E system with quadratic perturbation

Zhen Wang, Wei Sun, Zhouchao Wei, Xiaojian Xi (2014)


Hopf bifurcation, dynamics at infinity and robust modified function projective synchronization (RMFPS) problem for Sprott E system with quadratic perturbation were studied in this paper. By using the method of projection for center manifold computation, the subcritical and the supercritical Hopf bifurcation were analyzed and obtained. Then, in accordance with the Poincare compactification of polynomial vector field in R 3 , the dynamical behaviors at infinity were described completely. Moreover, a...

Finite-time synchronization of chaotic systems with noise perturbation

Jie Wu, Zhi-cai Ma, Yong-zheng Sun, Feng Liu (2015)


In this paper, we investigate the finite-time stochastic synchronization problem of two chaotic systems with noise perturbation. We propose new adaptive controllers, with which we can synchronize two chaotic systems in finite time. Sufficient conditions for the finite-time stochastic synchronization are derived based on the finite-time stability theory of stochastic differential equations. Finally, some numerical examples are examined to demonstrate the effectiveness and feasibility of the theoretical...

Generalized synchronization and control for incommensurate fractional unified chaotic system and applications in secure communication

Hongtao Liang, Zhen Wang, Zongmin Yue, Ronghui Lu (2012)


A fractional differential controller for incommensurate fractional unified chaotic system is described and proved by using the Gershgorin circle theorem in this paper. Also, based on the idea of a nonlinear observer, a new method for generalized synchronization (GS) of this system is proposed. Furthermore, the GS technique is applied in secure communication (SC), and a chaotic masking system is designed. Finally, the proposed fractional differential controller, GS and chaotic masking scheme are...

Hamilton-Jacobi-Bellman equations for the optimal control of a state equation with memory

Guillaume Carlier, Rabah Tahraoui (2010)

ESAIM: Control, Optimisation and Calculus of Variations

This article is devoted to the optimal control of state equations with memory of the form: x ˙ ( t ) = F ( x ( t ) , u ( t ) , 0 + A ( s ) x ( t - s ) d s ) , t > 0 , with initial conditions x ( 0 ) = x , x ( - s ) = z ( s ) , s > 0 . Denoting by y x , z , u the solution of the previous Cauchy problem and: v ( x , z ) : = inf u V { 0 + e - λ s L ( y x , z , u ( s ) , u ( s ) ) d s } where V is a class of admissible controls, we prove that v is the only viscosity solution of an Hamilton-Jacobi-Bellman equation of the form: λ v ( x , z ) + H ( x , z , x v ( x , z ) ) + D z v ( x , z ) , z ˙ = 0 in the sense of the theory of viscosity solutions in infinite-dimensions of Crandall and Lions.

Optimal, adaptive and single state feedback control for a 3D chaotic system with golden proportion equilibria

Hassan Saberi Nik, Ping He, Sayyed Taha Talebian (2014)


In this paper, the problems on purposefully controlling chaos for a three-dimensional quadratic continuous autonomous chaotic system, namely the chaotic Pehlivan-Uyaroglu system are investigated. The chaotic system, has three equilibrium points and more interestingly the equilibrium points have golden proportion values, which can generate single folded attractor. We developed an optimal control design, in order to stabilize the unstable equilibrium points of this system. Furthermore, we propose...

Periodic parametric perturbation control for a 3D autonomous chaotic system and its dynamics at infinity

Zhen Wang, Wei Sun, Zhouchao Wei, Shanwen Zhang (2017)


Periodic parametric perturbation control and dynamics at infinity for a 3D autonomous quadratic chaotic system are studied in this paper. Using the Melnikov's method, the existence of homoclinic orbits, oscillating periodic orbits and rotating periodic orbits are discussed after transferring the 3D autonomous chaotic system to a slowly varying oscillator. Moreover, the parameter bifurcation conditions of these orbits are obtained. In order to study the global structure, the dynamics at infinity...

Robust control of chaos in modified FitzHugh-Nagumo neuron model under external electrical stimulation based on internal model principle

Yuan Jiang, Jiyang Dai (2011)


This paper treats the question of robust control of chaos in modified FitzHugh-Nagumo neuron model under external electrical stimulation based on internal model principle. We first present the solution of the global robust output regulation problem for output feedback system with nonlinear exosystem. Then we show that the robust control problem for the modified FitzHugh-Nagumo neuron model can be formulated as the global robust output regulation problem and the solvability conditions for the output...

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