期刊
COMPUTERS & MATHEMATICS WITH APPLICATIONS
卷 59, 期 5, 页码 1644-1655出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2009.08.006
关键词
Optimal control; Time-optimal control; Fractional calculus; Fractional order optimal control; Fractional dynamic systems; RIOTS_95 Optimal Control Toolbox
In this article, we discuss fractional order optimal control problems (FOCPs) and their solutions by means of rational approximation. The methodology developed here allows us to solve a very large class of FOCPs (linear/nonlinear, time-invariant/time-variant, SISO/MIMO, state/input constrained, free terminal conditions etc.) by converting them into a general, rational form of optimal control problem (OCP). The fractional differentiation operator used in the FOCP is approximated using Oustaloup's approximation into a state-space realization form. The original problem is then reformulated to fit the definition used in general-purpose optimal control problem (OCP) solvers such as RIOTS_95, a solver created as a Matlab toolbox. Illustrative examples from the literature are reproduced to demonstrate the effectiveness of the proposed methodology and a free final time OCP is also solved. (C) 2009 Elsevier Ltd. All rights reserved.
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