Open AccessNumerical simulation of the fractional-order control system
Author(s) -
Xing Cai,
F. Liu
Publication year - 2007
Publication title -
journal of applied mathematics and computing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.45
H-Index - 36
eISSN - 1865-2085
pISSN - 1598-5865
DOI - 10.1007/bf02831971
Subject(s) - mathematics , theory of computation , uniqueness , convergence (economics) , stability (learning theory) , fractional calculus , numerical analysis , numerical stability , ordinary differential equation , term (time) , order (exchange) , dynamical system (definition) , dynamical systems theory , differential equation , mathematical analysis , computer science , algorithm , physics , finance , quantum mechanics , machine learning , economics , economic growth
Multi-term fractional differential equations have been used to simulate fractional-order control system. It has been demonstrated the necessity of the such controllers for the more efficient control of fractionalorder dynamical system. In this paper, the multi-term fractional ordinary differential equations are transferred into equivalent a system of equations. The existence and uniqueness of the new system are proved. A fractional order difference approximation is constructed by a decoupled technique and fractional-order numerical techniques. The consistence, convergence and stability of the numerical approximation are proved. Finally, some numerical results are presented to demonstrate that the numerical approximation is a computationally efficient method. The new method can be applied to solve the fractional-order control system
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