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Synchronization of fractional-order chaotic system via adaptive PID controller. (English) Zbl 1206.93059
Baleanu, Dumitru (ed.) et al., New trends in nanotechnology and fractional calculus applications. Selected papers based on the presentations at the workshop new trends in science and technology (NTST 08), and the workshop fractional differentiation and its applications (FDA 09), Ankara, Türkei, November 2008. Dordrecht: Springer (ISBN 978-90-481-3292-8/hbk; 978-90-481-3293-5/ebook). 445-452 (2010).
Chaos in hard spring ${\varphi }^{6}$-van der Pol oscillator, and its modelling and control with Fractional-Order Calculus (FOC) are studied in this research. An adaptive PID controller with fractional order adaptation mechanism is proposed to synchronize fractional-order chaotic system. PID coefficients are updated using the gradient method when a proper sliding surface is chosen. Fractional-order ${\varphi }^{6}$-van der Pol oscillator is used as case study to verify the proposed method.
##### MSC:
 93C40 Adaptive control systems 93B51 Design techniques in systems theory 34K37 Functional-differential equations with fractional derivatives 70Q05 Control of mechanical systems (general mechanics)