This paper investigates the adaptive chaos control and synchronization of the Shaw chaotic system (Shaw, 1981) with unknown parameters. First, we design adaptive control laws to stabilize the Shaw chaotic system with unknown parameters to its unstable equilibrium at the origin based on the adaptive control theory and Lyapunov stability theory. Next, we derive adaptive control laws to achieve gl...

Considering the effects of external perturbations on the state vector and the output of the original system, this paper proposes a new adaptive integral observer method to deal with chaos synchronization between the drive and response systems with unknown parameters. The analysis and proof are given by means of the Lyapunov stability theorem and Barbalat lemma. This approach has fewer constrain...

Chaotic synchronization is the key technology of secure communication. In this paper, an impulsive control method for chaotic synchronization of two coupled Lorenz chaotic system was proposed. The global asymptotic synchronization of two Lorenz systems was realized by using the linear error feedback of the state variables of the drive system and the response system as impulsive control signal. ...

A hybrid projective synchronization scheme for two identical fractional-order chaotic systems is proposed in this paper. Based on the stability theory of fractional-order systems, a controller for the synchronization of two identical fractional-order chaotic systems is designed. This synchronization scheme needs not to absorb all the nonlinear terms of response system. Hybrid projective synchro...

An adaptive control scheme is developed to study the generalized adaptive chaos synchronization with uncertain chaotic parameters behavior between two identical chaotic dynamic systems. This generalized adaptive chaos synchronization controller is designed based on Lyapunov stability theory and an analytic expression of the adaptive controller with its update laws of uncertain chaotic parameter...

Advanced large-wing-span aircraft result in more structural flexibility and the potential for instability or poor handling qualities. These shortcomings call stability augmentation systems that entail active control. Consequently, in-flight estimation of wing shape is beneficial control very flexible aircraft. This paper proposes a new methodology estimating states based on extended Kalman filt...

Zero-lag synchronization (ZLS) between chaotic units, which do not have self-feedback or a relay unit connecting them, is experimentally demonstrated for two mutually coupled chaotic semiconductor lasers. The mechanism is based on two mutual coupling delay times with certain allowed integer ratios, whereas for a single mutual delay time ZLS cannot be achieved. This mechanism is also found numer...

It is a long-standing debate among ecologists whether chaotic dynamics are likely to occur in food web systems. Simple mathematical models predict frequent chaotic dynamics for food webs of relatively low complexity suggesting that the long-term dynamics of natural populations could be essentially unpredictable. This result is at odds with observations from the field where chaos appears to be r...

A new strategy of control is formulated for chaos synchronization of non-identical chaotic systems with different orders using the Borne and Gentina practical criterion associated with the Benrejeb canonical arrow form matrix, to drift the stability property of dynamic complex systems. The designed controller ensures that the state variables of controlled chaotic slave systems globally synchron...

This work presents an observer-based adaptive control approach for time-delay chaotic systems with uncertainty. The chaotic system is initially expressed with the Takagi-Sugeno (T-S) fuzzy model. The design of the adaptive fuzzy observer is introduced based on the assumptions of chaotic system properties. Next, the design principle is applied to stabilization and tracking problems. Based on Lya...