| 基于非均匀参数化的自由终端时间最优控制问题求解 |
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| 引用本文： | 雷阳,李树荣,张强,张晓东.基于非均匀参数化的自由终端时间最优控制问题求解[J].系统科学与数学,2012,32(3):277-287. |
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| 作者姓名： | 雷阳 李树荣 张强 张晓东 |
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| 作者单位： | 中国石油大学(华东)自动化系,青岛,266580 |
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| 基金项目： | 国家自然科学基金，国家科技重大专项，中央高校基本科研业务费专项资金，山东省自然科学基金(ZR2011FM002)资助课题 |
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| 摘 要： | 针对自由终端时间最优控制问题,提出了一种基于非均匀控制向量参数化的数值解法.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控制变量.通过引入标准化的时间变量,原问题转化为均匀参数化的固定终端时间最优控制问题.建立目标和约束函数的Hamilton函数,通过求解伴随方程获得目标和约束函数的梯度,采用序列二次规划(SQP)获得数值解.针对两个经典的化工过程自由终端时间最优控制问题进行仿真研究,验证了所提出算法的可行性和有效性.
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| 关 键 词： | 自由终端时间 最优控制 非均匀参数化 SQP 化工过程 |
FREE FINAL TIME OPTIMAL CONTROL BASED ON NON-UNIFORM CONTROL VECTOR PARAMETERIZATION |
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| LEI Yang
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LI Shurong
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ZHANG Qiang
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ZHANG Xiaodong.FREE FINAL TIME OPTIMAL CONTROL BASED ON NON-UNIFORM CONTROL VECTOR PARAMETERIZATION[J].Journal of Systems Science and Mathematical Sciences,2012,32(3):277-287. |
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| Authors: | LEI Yang LI Shurong ZHANG Qiang ZHANG Xiaodong |
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| Institution: | (Department of Automation,China University of Petroleum(East China),Qingdao 266580) |
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| Abstract: | A non-uniform control vector parameterization based numerical approach is proposed for free final time optimal control problems.The given time interval is divided into several time stages of varying lengths which are defined as new control variables.By introducing a normalized time variable,the original problem is transformed into a fixed final time optimal control problem which is solved by using uniform control vector parameterization.By constructing the Hamilton functions of objective and constraint functions,the adjoint equations are solved to obtain the gradients.The numerical solution is obtained by sequential quadratic programming(SQP) method.Simulation study on two optimal control problems of chemical process shows the feasibility and effectiveness of the proposed method. |
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| Keywords: | Free final time optimal control non-uniform control vector parameterization SQP chemical process |
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