| 摘要: |
| 传统的均匀参数化方法在求解固定终端时刻最优控制问题时,不能精确地逼近最优控制轨迹。针对这一问题,提出一种非均匀控制向量参数化的数值解法。首先将控制时域离散化为不同长度的时间段,各时间段长度作为新的优化参数;然后引入时间尺度因子,将非均匀参数化的最优控制问题转化为标准化时域上的均匀参数化问题;最后建立目标和约束函数的Hamilton函数,通过求解伴随方程计算梯度,采用序列二次规划方法获得数值解。针对两个经典的化工过程最优控制问题进行仿真研究,仿真结果验证了所提出算法的有效性。 |
| 关键词: 最优控制 化工过程 非均匀控制向量参数化 序列二次规划(SQP) 固定终端时刻 |
| DOI：10.3969/j.issn.1673-5005.2011.05.034 |
| 分类号::TP 273 |
| 文献标识码:A |
| 基金项目:国家自然科学基金项目(60974039);国家科技重大专项课题(2008ZX05011) |
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| A non uniform control vector parameterization approach for optimal control problems |
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LEI Yang, LI Shu rong, ZHANG Qiang, ZHANG Xiao dong
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(College of Information and Control Engineering in China University of Petroleum, Qingdao 266555, China)
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| Abstract: |
| The traditional uniform control vector parameterization method can not obtain accurate optimal control policy when solving optimal control problems with fixed final time. For this reason, a non uniform control vector parameterization approach was proposed. Firstly, the given time interval was divided into several time stages of varying lengths which were defined as new optimization parameters. Secondly, the original optimal control problem was transformed into a uniform parameterization problem by introducing a time scaling factor. Finally, the adjoint equations were solved to obtain the gradients by constructing the Hamilton functions of objective and constraint functions. The numerical solution was obtained by sequential quadratic programming method. Simulation results on two optimal control problems of chemical process show the effectiveness of the proposed method. |
| Key words: optimal control chemical process non uniform control vector parameterization sequential quadratic programming (SQP) fixed final time |
