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Research Papers: Control

Finite-Time Controllability of Fractional-Order Systems

[+] Author and Article Information
Jay L. Adams

Department of Electrical and Computer Engineering, The University of Akron, Akron, OH 44325-3904jla36@uakron.edu

Tom T. Hartley

Department of Electrical and Computer Engineering, The University of Akron, Akron, OH 44325-3904thartley@uakron.edu

J. Comput. Nonlinear Dynam 3(2), 021402 (Jan 28, 2008) (5 pages) doi:10.1115/1.2833919 History: Received June 07, 2007; Revised November 30, 2007; Published January 28, 2008

In this paper, the conditions that lead to a system output remaining at zero with zero input are considered. It is shown that the initialization of fractional-order integrators plays a key role in determining whether the integrator output will remain at a zero with zero input. Three examples are given that demonstrate the importance of initialization for integrators of order less than unity, inclusive. Two examples give a concrete illustration of the role that initialization plays in keeping the output of a fractional-order integrator at zero once it has been driven to zero. The implications of these results are considered, with special consideration given to the formulation of the fractional-order optimal control problem.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 4

Control signal and response of semi-integrator system

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Figure 1

Response for various values of a with u(t)=−12

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Figure 2

Response for various values of a with u(t)=−12

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Figure 3

Semi-integrator response for u(t)=−1 for t∊[0,π4)

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