Control and synchronization of the generalized Lorenz system with mismatched uncertainties using backstepping technique and time‐delay estimation

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Generalized Synchronization with Uncertain Parameters of Nonlinear Dynamic System via Adaptive Control

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 parameters is shown. The generalized adaptive synchronization with uncertain parameters between two identical new Lorenz-Stenflo systems is taken as three examples to show the effectiveness of the proposed method. The numerical simulations are shown to verify the results

Adaptive Projective Lag Synchronization of T and Lu Chaotic Systems

In this paper, the synchronization problem of T chaotic system and Lu chaotic system is studied. The parameter of the drive T chaotic system is considered unknown. An adaptive projective lag control method and also parameter estimation law are designed to achieve chaos synchronization problem between two chaotic systems. Then Lyapunov stability theorem is utilized to prove the validity of the proposed control method. After that, some numerical simulations are performed to assess the performance of the proposed method. The results show high accuracy of the proposed method in control and synchronization of chaotic systems

Comparing performance on chaos control via adaptive output-feedback

"Performance of four controllers is experimentally compared and evaluated in context of chaos suppression. Four output-feedback controllers are used in experi- ments for comparison. First three schemes utilize an adaptive observer to estimate the states and parameter required for feeding back and with different techniques, which are: (i) feedback linearization, (ii) backstepping, and (iii) sliding mode. The fourth scheme is a (low-parameterized) robust adaptive feedback. A simple class of dynamical systems that exhibit chaotic behavior, called P-class, is considered as benchmark due to involves distinct chaotic systems. The need of comparison is motivated to ask: What is the suitable adaptive scheme to suppress chaos in an specific implementation? Results show a trend on different applications, are illustrated experimentally by means circuits, and are discussed in terms of control effort. This comparative study is important to select a feedback scheme in specific implementations; for example, synchronization of complex networks.

Synchronization and Anti-Synchronization of Two Identical Hyperchaotic Systems Based on Active Backstepping Design

This paper presents an active backstepping design method for synchronization and anti-synchronization of two identical hyperchaotic Chen systems. The proposed control method, combining backstepping design and active control approach, extends the application of backstepping technique in chaos control. Based on this method, different combinations of controllers can be designed to meet the needs of different applications. Numerical simulations are shown to verify the results

Multi-switching combination synchronization of chaotic systems

A novel synchronization scheme is proposed for a class of chaotic systems, extending the concept of multi-switching synchronization to combination synchronization such that the state variables of two or more driving systems synchronize with different state variables of the response system, simultaneously. The new scheme, multi-switching combination synchronization (MSCS), represents a significant extension of earlier multi-switching schemes in which two chaotic systems, in a driver-response configuration, are multi-switched to synchronize up to a scaling factor. In MSCS, the chaotic driving systems multi-switch a response chaotic system in combination synchronization. For certain choices of the scaling factors, MSCS reduces to multi-switching synchronization, implying that the latter is a special case of MSCS. A theoretical approach to control design, based on backstepping, is presented and validated using numerical simulations