Abstract
In this chapter, we deal with the synchronization and parameter estimations of an uncertain Rikitake system. The strategy consists in proposing a slave system that has to follow asymptotically the unknown Rikitake system, referred to as the master system. The gains of the slave system are adjusted continually according to a convenient adaptation control law until the measurable output errors converge to zero. The convergence analysis is carried out using Barbalat’s lemma.
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Notes
- 1.
Here we denote the vector states related to the master and slave systems by w 1 and w 2 , respectively. That is, \(w_{i}^{T} = (x_{i},y_{i},z_{i})\) ; for i ={ 1, 2}.
- 2.
Barbalat’s lemma states that if the differential function f(t) has a finite limit as t → ∞, and if df ∕dt is uniformly continuous, then df ∕dt → 0 as t → ∞. A consequence of this lemma is that if f ∈ L 2 and df ∕dt is bounded, then f → 0 as t → ∞.
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Martínez-Guerra, R., Pérez-Pinacho, C.A., Gómez-Cortés, G.C. (2015). Synchronization of an Uncertain Rikitake System with Parametric Estimation. In: Synchronization of Integral and Fractional Order Chaotic Systems. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-15284-4_5
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DOI: https://doi.org/10.1007/978-3-319-15284-4_5
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