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

LI Guodong; LIU Xinggao

doi:10.11949/j.issn.0438-1157.20141128

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

更新时间：2025-12-10

- A variable time nodes control vector parameterization approach for solving optimal control problems
- CIESC Journal Issue 2, Pages: 640-646(2015)
- 作者机构：
  
  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
- 作者简介：
- 基金信息：
- DOI：10.11949/j.issn.0438-1157.20141128
  CLC： Q021.8
- Online First：05 February 2015，
  
  Published：05 February 2015
- 稿件说明：
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LI Guodong, LIU Xinggao. A variable time nodes control vector parameterization approach for solving optimal control problems[J]. CIESC Journal, 2015, (2): 640-646.
DOI：

LI Guodong, LIU Xinggao. A variable time nodes control vector parameterization approach for solving optimal control problems[J]. CIESC Journal, 2015, (2): 640-646. DOI： 10.11949/j.issn.0438-1157.20141128.

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。

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.

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