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Robust Synchronization of Chaotic Systems via Feedback pp 51–97Cite as

Robust Synchronization of Chaotic Systems: A Proportional Integral Approach

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Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 378))

Abstract

In previous chapter the chaos suppression was discussed. However, there is one more interesting problem in chaos control: the synchronization. Synchronize means to share the same time and signifies that two or more events occurs at same time. In nonlinear science diverse synchronization phenomena have been found in chaotic systems. Thus, such a problem results in very interesting dynamical phenomena and has technological applications, as in communication [1], and scientific impact as, for example, in animal gait [2],[3] or cells of human organs [4]. A continuation path for synchronization is in spatially extended systems [5] where synchronization phenomena are already being studied. Other interesting issues on synchronization is, on the one hand, the cost of synchronizing chaotic systems [6]; that is, to measure the energy required to achieve chaotic synchronization. Here, the control theory can be exploited to include cost function at design of synchronization command by computing optimal, sub-optimal and/or robust controllers [7]. On the other, the geometrical properties of synchronization are also a raising theme [8], [9]. Here, geometrical control theory can be used to compute the invariant manifolds [10]. This Chapter is related to the robust synchronization, and is centred on the robust analysis and some interpretations about robustness in synchronization. To this end we exploit the simpler controller in Chapter 2: the Proportional-Integral feedback and some approaches.

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Authors
  1. Ricardo Femat
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  2. Gualberto Solis-Perales
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Femat, R., Solis-Perales, G. (2008). Robust Synchronization of Chaotic Systems: A Proportional Integral Approach. In: Robust Synchronization of Chaotic Systems via Feedback. Lecture Notes in Control and Information Sciences, vol 378. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69307-9_3

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  • DOI: https://doi.org/10.1007/978-3-540-69307-9_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69306-2

  • Online ISBN: 978-3-540-69307-9

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