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基于非均匀参数化的自由终端时间最优控制问题求解 被引量：2

FREE FINAL TIME OPTIMAL CONTROL BASED ON NON-UNIFORM CONTROL VECTOR PARAMETERIZATION
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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. 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.
作者 雷阳 李树荣 张强 张晓东
机构地区 中国石油大学(华东)自动化系
出处 《系统科学与数学》 CSCD 北大核心 2012年第3期277-287,共11页 Journal of Systems Science and Mathematical Sciences
基金 国家自然科学基金(60974039) 国家科技重大专项(2011ZX05011) 中央高校基本科研业务费专项资金(27R1105018A) 山东省自然科学基金(ZR2011FM002)资助课题
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 non-uniform control vector parameterization SQP chemical process
分类号 O232 [理学—运筹学与控制论]
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参考文献16

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同被引文献19

  • 1张兵,杜文莉,颜学峰,钱锋.时间最短控制问题求解的分级优化策略[J].华东理工大学学报（自然科学版）,2007,33(1):100-103. 被引量：2
  • 2Xiang X L, Jiang Y. Optimal controls of systems governed by a class of integro-diferential equa- tions. Journal of Guizhou University (Natural Sciences), 2003, 20(4): 335-342.
  • 3Wu C Z, Teo K L, Zhao Y, Yan W Y. An optimal control problem involving impulsive integrod- ifferential systems. Optimization Methods and Software, 2007, 22(3): 531-549.
  • 4Kaya C Y, Noakes J L. Computational method for time-optimal switching control. Journal of Optimization Theory and Applications, 2003, 117(1): 69-92.
  • 5Lee Y C E, Fung E H K, Lee H W J. Control parametrization enhancing technique and simulation on the design of a flexible rotating beam. Journal of Optimization Theory and Applications, 2008, 136: 247-259.
  • 6Teo K L, Goh C J, Wong K H. A Unified Computational Approach to Optimal Control Problems. New York: Longman, 1991.
  • 7Teo K L, Goh C J. A computational method for a class of optimal relaxed control problems. Journal of Optimization Theory and Applications, 1989, 60(1): 117-132.
  • 8Teo K L, Jennings L S. OptimM control with a cost on changing control. Journal of Optimization Theory and Applications, 1991, 68(2): 335-356.
  • 9Mehne H H, Borzabadi A H. A numerical method for solving optimal control problems using state parametrization. Numer. Algor., 2006, 42: 165-169.
  • 10Wu C Z, Teo K L, Zhao Y, Yah W Y. Solving an identification problem as an impulsive optimal parameter selection problem. Computers and Mathematics with Applications, 2005, 50: 217-229.

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系统科学与数学
2012年 第3期

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