一种求解最优控制问题的变时间节点控制向量参数化方法

doi:10.11949/j.issn.0438-1157.20141128

化工学报 ›› 2015, Vol. 66 ›› Issue (2): 640-646.DOI: 10.11949/j.issn.0438-1157.20141128

一种求解最优控制问题的变时间节点控制向量参数化方法

李国栋, 刘兴高

浙江大学控制系, 工业控制技术国家重点实验室, 浙江杭州 310027

收稿日期:2014-07-28 修回日期:2014-11-13 出版日期:2015-02-05 发布日期:2015-02-05
通讯作者: 刘兴高
基金资助:
国家自然科学基金项目(U1162130)。

A variable time nodes control vector parameterization approach for solving optimal control problems

LI Guodong, LIU Xinggao

State Key Laboratory of Industry Control Technology, Department of Control, Zhejiang University, Hangzhou 310027, Zhejiang, China

Received:2014-07-28 Revised:2014-11-13 Online:2015-02-05 Published:2015-02-05
Supported by:
supported by the National Natural Science Foundation of China (U1162130).

摘要/Abstract

摘要：

控制向量参数化方法是求解最优控制问题的一种常用数值方法。它通过离散化控制时域,将控制向量近似地表示成一组参数化的函数。离散化后的时间网格通常是固定的,其划分会影响到最优控制问题数值求解的精度和效率。为了同时优化控制参数和时间网格节点,提出了一种时间节点可变的控制向量参数化方法。推导出了最优控制性能指标对时间参数的导数与对时间分段长度导数之间的关系,得到了性能指标的梯度表达式。用两个经典最优控制实例对所提出的方法进行了测试,结果表明所提出方法能够更好地逼近最优控制轨迹。

关键词: 过程控制, 控制向量参数化, 变时间节点, 优化, 算法

Abstract:

Control vector parameterization (CVP) is a frequently used numerical method for solving optimal control problems, where the control vector is approximated by a group of parametric functions through time discretization. Usually, the discretized time grid is fixed, and its partition will affect accuracy and performance of the numerical solution of optimal control problem. To optimize both the control parameters and the time grid nodes, a CVP method with variable time nodes was proposed. Based on the derived relationship between the gradients of time nodes and the ones of interval lengths, the gradient equations for parameters were presented. The proposed method was demonstrated to have better approximation ability for the optimal control trajectories on two classic optimal control problems.

Key words: process control, control vector parameterization, variable time nodes, optimization, algorithm

中图分类号:

TQ021.8

李国栋, 刘兴高. 一种求解最优控制问题的变时间节点控制向量参数化方法[J]. 化工学报, 2015, 66(2): 640-646.

LI Guodong, LIU Xinggao. A variable time nodes control vector parameterization approach for solving optimal control problems[J]. CIESC Journal, 2015, 66(2): 640-646.

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一种求解最优控制问题的变时间节点控制向量参数化方法

A variable time nodes control vector parameterization approach for solving optimal control problems

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