处理动态优化问题中控制变量路径约束的方法

胡云卿; 刘兴高

doi:10.3724/SP.J.1004.2013.00440

处理动态优化问题中控制变量路径约束的方法

doi: 10.3724/SP.J.1004.2013.00440 cstr: 32138.14.SP.J.1004.2013.00440

1.
浙江大学工业控制技术国家重点实验室杭州 310027

详细信息

通讯作者:
刘兴高

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出版历程
- 收稿日期: 2011-05-06
- 修回日期: 2012-10-31
- 刊出日期: 2013-04-20

Methods to Deal with Control Variable Path Constraints in Dynamic Optimization Problems

1.
State Key Laboratory of Industry Control Technology, Zhejiang University, Hangzhou 310027

摘要

摘要: 目前国际上对动态优化问题中的状态变量路径约束已有一些研究,但专门处理控制变量路径约束的方法却鲜见报道. 本文首先介绍两种分别基于三角函数变换、约束算子截断来处理控制变量路径约束的方法,然后提出一种基于光滑化的二次罚函数方法. 光滑化罚函数方法不仅能够处理控制变量路径约束,而且还能同时处理关于状态变量的路径约束. 最后使用目前流行的控制变量参数化 (Control variable parameterization, CVP)策略对最终获得的、不再含控制变量路径约束的动态优化问题求解. 实例测试一展现了三种方法各自的特点;实例测试二表明了光滑罚函数方法的有效性和优越性.
- 动态优化 /
- 路径约束 /
- 控制变量 /
- 控制变量参数化
Abstract: Many researchers have reported their methods to handle the state variable path constraints in dynamic optimization problems. However, very few of them mentioned the techniques to deal with the control variable path constraints. This paper firstly introduces two ways to eliminate the control variable path constraints, then presents a smoothed quadratic penalty function method which can optimize the dynamic problems with control and state variable path constraints at the same time. The final transformed problem is solved by control variable parameterization (CVP) strategy in the study. Test on Case 1 demonstrates the characteristics of the three techniques; test on Case 2 indicates the effectiveness and the superiority of the proposed smoothed penalty function method.
- Dynamic optimization /
- path constraint /
- control variable /
- control variable parameterization (CVP)

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[1]

Biegler L T, Grossmann I E. Retrospective on optimization. Computers and Chemical Engineering, 2004, 28(8): 1169-1192[2] Asgari S A, Pishvaie M R. Dynamic optimization in chemical processes using region reduction strategy and control vector parameterization with an ant colony optimization algorithm. Chemical Engineering and Technology, 2008, 31(4): 507-512[3] Balku S, Yuceer M, Berber R. Control vector parameterization approach in optimization of alternating aerobic-anoxic systems. Optimal Control Applications and Methods, 2009, 30(6): 573-584[4] Gugat M, Herty M. The smoothed-penalty algorithm for state constrained optimal control problems for partial differential equations. Optimization Methods and Software, 2010, 25(4): 573-599[5] Vega M P, Mancini M C, Calcada L A. Multi-objective dynamic optimization of fixed bed dryers: simulation and experiments. In: Proceedigns of the 19th European Symposium on Computer Aided Process Engineering. Amsterdam: Elsevier Science, 2009. 147-152[6] Hirmajer T, Balsa-Canto E, Banga J R. DOTcvpSB, a software toolbox for dynamic optimization in systems biology. Bmc Bioinformatics, 2009, 10[7] Fikar M, Kovacs Z, Czermak P. Dynamic optimization of batch diafiltration processes. Journal of Membrane Science, 2010, 355(1-2): 168-174[8] Ni B C, Sourkounis C. Stochastic dynamic optimization for wind energy converters. International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 2011, 30(1): 265-279[9] Biegler L T. Large-scale nonlinear programming: an integrating framework for enterprise-wide dynamic optimization. In: Proceedings of the 17th European Symposium on Computer Aided Process Engineering. Amsterdam: Elsevier Science, 2007. 575-582[10] Bloss K F, Biegler L T, Schiesser W E. Dynamic process optimization through adjoint formulations and constraint aggregation. Industrial and Engineering Chemistry Research, 1999, 38(2): 421-432[11] Bell M L, Sargent R W H. Optimal control of inequality constrained DAE systems. Computers and Chemical Engineering, 2000, 24(11): 2385-2404[12] Luus R. Handling inequality constraints in optimal control by problem reformulation. Industrial and Engineering Chemistry Research, 2009, 48(21): 9622-9630[13] Pantelides C C. The mathematical modelling of transient system using differential-algebraic equations. Computers and Chemical Engineering, 1988, 12[14] Zhang Bing, Chen De-Zhao, Wu Xiao-Hua. Graded optimization strategy and its application to chemical dynamic optimization with fixed boundary. Journal of Chemical Industry and engineering Society of China, 2005, 56(7): 1276-1280 (张兵, 陈德钊, 吴晓华. 分级优化用于边值固定的化工动态优化问题. 化工学报, 2005, 56(7): 1276-1280)[15] Fiacco A V, McCormick G P. Nonlinear Programming: Sequential Unconstrained Minimization Techniques. Philadelphia: SIAM, 1990[16] Chen X, Nashed Z, Qi L. Smoothing methods and semismooth methods for nondifferentiable operator equations. SIAM Journal on Numerical Analysis, 2001, 38(4): 1200-1216[17] Vassiliadis V S. Computational Solution of Dynamic Optimization Problems with General Differential-algebraic Constraints [Ph.D. dissertation], University of London, UK, 1993

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