An approximate method for numerically solving fractional order optimal control problems of general form

被引：160

作者：

Tricaud, Christophe ^{[1
]}

Chen, YangQuan ^{[1
]}

机构：

[1] Utah State Univ, Dept Elect & Comp Engn, Ctr Self Organizing & Intelligent Syst, Logan, UT 84322 USA

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2010年 / 59卷 / 05期

关键词：

Optimal control; Time-optimal control; Fractional calculus; Fractional order optimal control; Fractional dynamic systems; RIOTS_95 Optimal Control Toolbox; FORMULATION; SCHEME;

D O I：

10.1016/j.camwa.2009.08.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：1644 / 1655

页数：12

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