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Numerical simulation of the fractional-order control system. (English) Zbl 1130.93029

Summary: Multi-term fractional differential equations have been used to simulate fractional-order control system. It has been demonstrated the necessity of such controllers for the more efficient control of fractional-order dynamical system. In this paper, the multi-term fractional ordinary differential equations are transferred into an equivalent 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.

MSC:

93C10 Nonlinear systems in control theory
34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)
34K26 Singular perturbations of functional-differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
28A33 Spaces of measures, convergence of measures
93C15 Control/observation systems governed by ordinary differential equations
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