Modeling and identification of systems with fractional order integral an differential

A universal model of fractional-order differential equation is proposed. It is derived in form hyper neuron, based on a representation of the solution of the equation by finite increments and a modified form of the Riemann-Liouville. Implemented method for identifying parameters of objects by fractional differential equations is described on the base hyper neuron and modified genetic algorithms. Accuracy of calculations is incased due to excluding of circular references and dynamic correction of the fractional integration error. This allows to use hyper neuron as inlined model of such objects in the digital control systems and in conjunction with genetic algorithm it is used for the identification of their parameters with high accuracy. 

Full text (pdf)

[1] Rutkowska D., Pilinski М., Rutkowski L. Sieci neuronowe, algorytmy genetyczne i systemy rozmyte, (1999), Naukowe PWN, Warszawa, pp. 452 (In Polish).

[2] Busher V. V. The model of system with fractional integral and fractional differential in SIMULINK, (2011), Elektromekhanichni i enerhozberihayuchi systemy Publ., Kremenchuk, Vol. 4/2011, pp.138–142 (In Russian). http://archive.mdct.ru/portal/natural/Ees/2011_4/140.pdf

[3] Busher V. V. Evolution algorithms as method of identification of climate control system objects described by fractional equations, (2010), Electrotechnic and computing systems, Technica Publ., Kyev No02(78), pp.68–72 (In Russian). archive.nbuv.gov.ua/portal/natural/emeo/2011_78/068-072.pdf

[4] Busher V. V. Identification of the elements of climate systems of differential equations of fractional order, (2010), Elektromashynobud. ta elektroobladn., Technica Publ., Kyev, Vol. 75, pp.68–70 (In Russian). archive.nbuv.gov.ua/portal/ natural/emeo/2010_75/068-070.pdf

[5] Uchaikin V. V. Fractional differential model of dynamic memory, (2001), Matematyka y mekhanyka Publ., pp.14 (In Russian).

[6] Uchaikin V. V. Anomalous Diffusion and Fractional Stable Distributions ,(2003), Journal of Experimental and Theoretical Physics Publ., No. 4, pр.810-825 (In English).

[7] Hyl'mutdynov A., Ushakov P., Hyl'metdynov M. Fractional operators: synthesis and implementation criteria, (2008), Nelyneynuy myr Publ., No. 8, pр.452-463 (In Russian).

[8] Busher, V. V. Martynyuk V. V., Naydenko E. V. Energy indicators and parameters ultracapacitors in dynamic modes, (2012), Vymiryuval'na ta obchyslyuval'na tekhnika v tekhnolohichnykh protsesakh Publ., Khmel'nyts'kyy, . No. 1, pр.44-50 (In Russian). archive.nbuv.gov.ua/portal/Natural/Vtot/2012_1/31bus.pdf

[9] Busher V. V. Synthesis of process control systems with integrated fractional-differentiating properties, (2012), Vostochno–Evropeiskii Zhurnal Peredovykh Tekhnologii. Energosberegayushchie Tekhnologii i Oborudovanie Publ., Kharkov, Ukraine, Vol.4/3 (58), pp. 32–37 (In Russian). archive.nbuv.gov.ua/portal/natural/Vejpt/ 2012_4_3/...4.../32_37.pdf