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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
    
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
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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.

Published: 01 July 2010
CLC:  TP 273.1  
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Cite this article:

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

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


约束优先边值固定最优控制嵌套优化方法

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.

［1］ BIEGLER L T. An overview of simultaneous strategies for dynamic optimization ［J］. Chemical Engineering and Processing, 2007,46(11): 10431053.

［2］ 林可鸿,贺益君,陈德钊.混合优化人工免疫网络用于过程动态优化［J］.浙江大学学报：工学版,2008,42(12): 21812186.

LIN Kehong, HE Yijun, CHEN Dezhao. Hybrid optimal artificial immune network and it’s application to dynamic process optimization ［J］. Journal of Zhejiang University: Engineering Science, 2008, 42(12): 21812186.

［3］ 陈珑,刘兴高.改进正交配置算法及其在化工过程动态优化问题中的应用［J］.仪器仪表学报,2009,S30(6): 389394.

CHEN Long, LIU Xinggao. Improved orthogonal collocation method and its application to dynamic optimization problems of chemical process ［J］. Chinese Journal of Scientific Instrument, 2009,S30(6): 389394.

［4］ ZAVALA V M, BLEGLER L T. The advancedstep NMPC controller: optimality, stability and robustness ［J］. Automatica, 2009, 45(1): 8693.

［5］ 陶卉. 工业过程动态优化研究［D］.杭州: 浙江大学, 2006.

TAO Hui. Research on dynamic optimization of industrial process ［D］. Hangzhou: Zhejiang University, 2006.

［6］ DADEBO S A, MCAULEY K B. Dynamic optimization of constrained chemical engineering problems using dynamic programming ［J］. Computers and Chemical Engineering, 1995, 19(5): 513525.

［7］ BARZILAI J, BORWEIN J M. Twopoint step size gradient methods ［J］. IMA Journal of Numerical Analysis, 1988, 8(1): 141148.

［8］ 戴彧红,袁亚湘.非线性共轭梯度法［M］.上海：上海科学技术出版社,2000: 7149.

［9］ 张兵,陈德钊.化工动态优化方法的研究与应用［D］.浙江：浙江大学,杭州: 浙江大学,2004.

ZHANG bing, CHEN Dezhao. Solutions study for chemical dynamic optimization and their application ［D］. Hangzhou: Zhejiang University, 2004.

［10］ GOH C J, TEO L K. Control parameterization: a unified approach to optimal control problems with general constraints ［J］. Automatica, 1988, 24(1): 318.

［11］ LUUS R. Optimal control by dynamic programming using accessible grid points and region reduction ［J］. Hungarian Journal of Industrial Chemistry, 1989, 17(4): 523543.

［12］ RAJESH J, GUPTA K, KUSUMAKAR H S, et al. Dynamic optimization of chemical processes using ant colony framework［J］. Computers and Chemistry, 2001, 25(6): 583595.
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