一种高效的快速近似控制向量参数化方法

李国栋; 胡云卿; 刘兴高

doi:10.16383/j.aas.2015.c140031

一种高效的快速近似控制向量参数化方法

doi: 10.16383/j.aas.2015.c140031

1.
浙江大学工业控制技术国家重点实验室杭州 310027;
2.
南车株洲电力机车研究所有限公司株州 412001

基金项目:

国家高技术研究发展计划(863计划)(2006AA05Z226);国家自然科学基金(U1162130);浙江省杰出青年科学基金项目(R4100133)资助

详细信息

作者简介:
李国栋浙江大学控制科学与工程系博士研究生.主要研究方向为过程最优控制.E-mail:liguodong_008@163.com

通讯作者:
刘兴高浙江大学控制科学与工程系教授.主要研究方向为工业过程建模、优化与控制.本文通信作者. E-mail:liuxg@iipc.zju.edu.cn

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出版历程
- 收稿日期: 2014-01-14
- 修回日期: 2014-05-28
- 刊出日期: 2015-01-20

An Efficient Fast Approximate Control Vector Parameterization Method

1.
State Key Laboratory of Industry Control Technology, Zhejiang University, Hangzhou 310027;
2.
CSR Zhuzhou Institute Co. Ltd., Zhuzhou 412001

Funds:

Supported by National High Technology Research and Development Program of China (863 Program) (2006AA05Z226), National Natural Science Foundation of China (U1162130), and Outstanding Youth Science Foundation of Zhejiang Province (R4 100133)

摘要

摘要: 控制向量参数化(Control vector parameterization, CVP) 方法是目前求解流程工业中最优操作问题的主流数值方法,然而,该方法的主要缺点之一是计算效率较低,这是因为在求解生成的非线性规划(Nonlinear programming, NLP) 问题时,需要随着控制参数的调整,反复不断地求解相关的微分方程组,这也是CVP 方法中最耗时的部分.为了提高CVP 方法的计算效率,本文提出一种新颖的快速近似方法,能够有效减少微分方程组、函数值以及梯度的计算量.最后,两个经典的最优控制问题上的测试结果及与国外成熟的最优控制软件的比较研究表明:本文提出的快速近似CVP 方法在精度和效率上兼有良好的表现.
- 流程工业 /
- 最优控制 /
- 控制向量参数化 /
- 计算效率 /
- 快速近似
Abstract: The control vector parameterization (CVP) method is currently popular for solving optimal control problems in process industries. However, one of its main disadvantages is the low computational efficiency, because the relevant differential equations in solving the generated nonlinear programming (NLP) problem should be calculated repeatedly with the adjustment of control, which is the most time-consuming part of the CVP method. A new fast approximate approach with less computational expenses on differential equations, function values and gradients is therefore proposed to improve the computational efficiency of the CVP method in this paper. The proposed approach is demonstrated to have marked advantages in terms of accuracy and efficiency, in contrast to mature optimal control softwares, on two classic optimal control problems.
- Process industry /
- optimal control /
- control vector parameterization (CVP) /
- computational efficiency /
- fast approximate

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参考文献(25)

[1]	Grossmann I E, Biegler L T. Future perspective on optimization. Computers and Chemical Engineering, 2004, 28(8): 1193-1218
[2]	Kirk D E. Optimal Control Theory: An Introduction. New York: Dover Publications, 2004.
[3]	Peng Hai-Jun, Gao Qiang, Wu Zhi-Gang, Zhong Wan-Xie. A mixed variable variational method for optimal control problems with applications in aerospace control. Acta Automatica Sinica, 2011, 37(10): 1248-1255(彭海军, 高强, 吴志刚, 钟万勰. 求解最优控制问题的混合变量变分方法及其航天控制应用. 自动化学报, 2011, 37(10): 1248-1255)
[4]	Hu Yun-Qing, Liu Xing-Gao, Xue An-Ke. A penalty method for solving inequality path constrained optimal control problems. Acta Automatica Sinica, 2013, 39(12): 1996-2001(胡云卿, 刘兴高, 薛安克. 带不等式路径约束最优控制问题的惩罚函数法. 自动化学报, 2013, 39(12): 1996-2001)
[5]	Sun Yong, Zhang Mao-Rui, Liang Xiao-Ling. Improved Gauss pseudospectral method for solving nonlinear optimal control problem with complex constraints. Acta Automatica Sinica, 2013, 39(5): 672-678(孙勇, 张卯瑞, 梁晓玲. 求解含复杂约束非线性最优控制问题的改进Gauss伪谱法. 自动化学报, 2013, 39(5): 672-678)
[6]	Houska B, Ferreau H J, Diehl M. ACADO toolkit —— an open-source framework for automatic control and dynamic optimization. Optimal Control Applications and Methods, 2011, 32(3): 298-312
[7]	Hirmajer T, Balsa-Canto E, Banga J. Dotcvp: Dynamic Optimization Toolbox with Control Vector Parameterization Approach for Handling Continuous and Mixed-integer Dynamic Optimization Problems. Technical Report, Instituto de Investigaciones Marinas, 2008.
[8]	Binder T, Cruse A, Cruz Villar C A, Marquardt W. Dynamic optimization using a wavelet based adaptive control vector parameterization strategy. Computers and Chemical Engineering, 2000, 24(2-7): 1201-1207
[9]	Srinivasan B, Palanki S, Bonvin D. Dynamic optimization of batch processes: I. Characterization of the nominal solution. Computers and Chemical Engineering, 2003, 27(1): 1-26
[10]	Szymkat M, Korytowski A. Method of monotone structural evolution for control and state constrained optimal control problems. In: Proceedings of the 2003 European Control Conference (ECC). Cambridge: University of Cambridge, 2003.
[11]	Schlegel M, Stockmann K, Binder T, Marquardt W. Dynamic optimization using adaptive control vector parameterization. Computers and Chemical Engineering, 2005, 29(8): 1731-1751
[12]	Loxton R C, Teo K L, Rehbock V. Optimal control problems with multiple characteristic time points in the objective and constraints. Automatica, 2008, 44(11): 2923-2929
[13]	Loxton R C, Teo K L, Rehbock V, Yiu K F C. Optimal control problems with a continuous inequality constraint on the state and the control. Automatica, 2009, 45(10): 2250-2257
[14]	Hu Yun-Qing, Liu Xing-Gao. Methods to deal with control variable path constraints in dynamic optimization problems. Acta Automatica Sinica, 2013, 39(4): 440-449
[15]	Assassa F, Marquardt W. Dynamic optimization using adaptive direct multiple shooting. Computers and Chemical Engineering, 2014, 60: 242-259
[16]	Teo K L, Jennings L S, Lee H W J, Rehbock V. The control parameterization enhancing transform for constrained optimal control problems. The Journal of the Australian Mathematical Society, Series B: Applied Mathematics. 1999, 40(3): 314-335
[17]	Vassiliadis V S. Computational Solution of Dynamic Optimization Problems with General Differential-algebraic Constraints [Ph.D. dissertation], Imperial College London (University of London), UK, 1993.
[18]	Vassiliadis V S, Canto E B, Banga J R. Second-order sensitivities of general dynamic systems with application to optimal control problems. Chemical Engineering Science, 1999, 54(17): 3851-3860
[19]	Canto E B, Banga J R, Alonso A A, Vassiliadis V S. Restricted second order information for the solution of optimal control problems using control vector parameterization. Journal of Process Control, 2002, 12(2): 243-255
[20]	Banga J R, Balsa-Canto E, Moles C G, Alonso A A. Dynamic optimization of bioprocesses: efficient and robust numerical strategies. Journal of Biotechnology, 2005, 117(4): 407-419
[21]	Sager S. Numerical Methods for Mixed-Integer Optimal Control Problems. Tönning, Lübeck, Marburg: Der Andere Verlag, 2005.
[22]	Betts J T. Practical Methods for Optimal Control and Estimation Using Nonlinear Programming (2nd Edition). Philadelphia, PA: SIAM, 2010.
[23]	Teo K L, Goh C J, Wong K H. A Unified Computational Approach to Optimal Control Problems. Essex: Longman Scientific and Technical, 1991.
[24]	Loxton R C, Lin Q, Rehbock V, Teo K L. Control parameterization for optimal control problems with continuous inequality constraints: new convergence results. Numerical Algebra, Control, and Optimization, 2012, 2(3): 571-599
[25]	Biegler L T. Nonlinear Programming: Concepts, Algorithms, and Applications to Chemical Processes. New York: Society for Industrial and Applied, 2010.