An approximate method for numerically solving fractional order optimal control problems of general form
An approximate method for numerically solving fractional order optimal control problems of general form
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DOI：
10.1016/j.camwa.2009.08.006
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发表时间：
2010-03-01
影响因子：
2.9
通讯作者：
Chen, YangQuan
中科院分区：
文献类型：
--
作者：
Tricaud, Christophe;Chen, YangQuan
本文讨论分数阶最优控制问题及其有理逼近解法。这里开发的方法使我们能够解决一个非常大的类FOCP（线性/非线性，时不变/时变，SISO/MIMO，状态/输入约束，自由终端条件等）。通过将它们转化为最优控制问题（OCP）的一般合理形式。分数阶微分算子中使用的FOCP近似使用Oustaloup的状态空间实现形式。然后重新制定原始问题，以适应通用最优控制问题（OCP）求解器（如RIOTS_95，作为Matlab工具箱创建的求解器）中使用的定义。从文献中的说明性的例子被复制，以证明所提出的方法的有效性和自由的最后时间OCP也解决了。(C)2009爱思唯尔有限公司保留所有权利。
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.