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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. For the entire collection see [Zbl 1196.65021].

93C40Adaptive control systems
93B51Design techniques in systems theory
34K37Functional-differential equations with fractional derivatives
70Q05Control of mechanical systems (general mechanics)
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