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浙江大学学报(工学版)
J4  2010, Vol. 44 Issue (7): 1247-1250    DOI: 10.3785/j.issn.1008-973X.2010.07.002
自动化技术     
约束优先边值固定最优控制嵌套优化方法
刘兴高, 陈珑
浙江大学 工业控制技术国家重点实验室,浙江 杭州 310027
Nested constraintpreferred optimization method for fixed boundary optimal control problem
LIU Xing-gao, CHEN Long
State Key Laboratory of Industry Control Technology, Zhejiang University, Hangzhou 310027, China
 全文: PDF 
摘要：

针对边值固定的最优控制问题,提出一种约束优先嵌套优化方法,将边值固定问题转化为嵌套的2个边值无约束最优控制问题.将两点步长梯度法实行内层优化求解满足边值约束的可行控制策略,与无记忆拟牛顿法实行外层优化求解最优目标函数相结合,避免了罚函数法的不足,提高了优化算法收敛的稳定性和高效性.同时引入一种特殊的控制变量转换方法,通过中间变量和函数转换消除控制边界约束.经典实例的研究结果表明,该算法在收敛性能和求解效率方面具有显著的优越性.
关键词： 最优控制;  边值固定;  约束优先算法;  两点步长梯度法;  无记忆拟牛顿法    
Abstract:

A nested constraintpreferred optimization algorithm was proposed in order to reduce the fixed boundary optimal control problem to bilevel free boundary optimization problem. A twopoint step size gradient method was employed to solve the boundary constraint of the inner problem for feasible control policy, and was combined with the memoryless quasiNewton method which applied to the outer problem in order to achieve the optimal objective value. Then the shortcoming of penalty function method was overcomed, and the convergence stability and efficiency of the algorithm were improved. Furthermore, a special scheme was introduced to eliminate the boundary constraint of control variable by using the temporal variable and the function transformation. Several classical cases showed the prominent advantage of the algorithm on the convergence performance and the solving efficiency.
Key words:  optimal control    fixed boundary    constraint-preferred approach    two-point step size gradient method    memoryless quasiNewton method
出版日期: 2010-07-22
:  TP 273.1  
基金资助:

国家自然科学基金资助项目(50876093);浙江省科技厅国际合作项目（2009C34008）；国家“863”高技术研究发展计划资助项目（2006AA05Z226）.
作者简介: 刘兴高（1968—）,男,湖北荆州人,教授,博导,从事复杂系统建模、优化与控制的研究.E-mail:lxg@zjuem.zju.edu.cn
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引用本文:

刘兴高, 陈珑. 约束优先边值固定最优控制嵌套优化方法[J]. J4, 2010, 44(7): 1247-1250.

LIU Xin-Gao, CHEN Long. Nested constraintpreferred optimization method for fixed boundary optimal control problem. J4, 2010, 44(7): 1247-1250.

链接本文:

http://www.zjujournals.com/xueshu/eng/CN/10.3785/j.issn.1008-973X.2010.07.002    或    http://www.zjujournals.com/xueshu/eng/CN/Y2010/V44/I7/1247

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