In this paper, an observability approach to the synchronization of chaotic and hyperchaotic systems is presented. The proposed method allows the reconstruction of a chaotic attractor from a scalar observable and its derivatives. The method is based on the concept of algebraic observability; hence, it is directly applicable to all chaotic algebraic systems. Moreover, it is shown that a sliding differentiator, derived by a second-order suboptimal control algorithm, can be used to reconstruct the time derivatives of the observable. This makes it possible to estimate the system state, i.e., chaos synchronization, in a finite time.
An algebraic observability approach to chaos synchronisation by sliding differentiators
CANNAS, BARBARA;USAI, ELIO
2002-01-01
Abstract
In this paper, an observability approach to the synchronization of chaotic and hyperchaotic systems is presented. The proposed method allows the reconstruction of a chaotic attractor from a scalar observable and its derivatives. The method is based on the concept of algebraic observability; hence, it is directly applicable to all chaotic algebraic systems. Moreover, it is shown that a sliding differentiator, derived by a second-order suboptimal control algorithm, can be used to reconstruct the time derivatives of the observable. This makes it possible to estimate the system state, i.e., chaos synchronization, in a finite time.
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