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## 留言板

 引用本文: 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.
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. doi: 10.3724/SP.J.1004.2013.01996
 Citation: 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.

## A Penalty Method for Solving Inequality Path Constrained Optimal Control Problems

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 (R4100133)

• 摘要: 控制变量参数化（Control variable 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，但如果问题中包含路径约束，特别是不等式路径约束时，CVP方法则需要考虑专门的处理手段.为了克服该缺点，本文提出一种基于L1精确惩罚函数的方法，能够有效处理关于控制变量、状态变量、甚至控制变量/状态变量复杂耦合形式下的不等式路径约束.此外，为了能使用基于梯度的成熟优化算法，本文还引进了最新出现的光滑化技巧对非光滑的惩罚项进行磨光.最终得到了能高效处理不等式路径约束的改进型CVP架构，并给出相应数值算法.经典的带不等式路径约束最优控制问题上的测试结果及与国外文献报道的比较研究表明：本文所提出的改进型CVP 架构及相应算法在精度和效率上兼有良好表现.
•  [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 Your: Dover Publications, 2004. 464 [3] Bell M L, Sargent R W H. Optimal control of inequality constrained DAE systems. Computers and Chemical Engineering, 2000, 24(11): 2385-2404 [4] 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 [5] Feehery W F. Dynamic Optimization with Path Constraints[Ph.D. dissertation], MIT, Cambridge, MA, 1998 [6] Luus R. Handling inequality constraints in optimal control by problem reformulation. Industrial and Engineering Chemistry Research, 2009, 48(21): 9622-9630 [7] Chen T W C, Vassiliadis V S. Inequality path constraints in optimal control: a finite iteration ε-convergent scheme based on pointwise discretization. Journal of Process Control, 2005, 15(3): 353-362 [8] Biegler L T. Nonlinear Programming: Concepts, Algorithms, and Applications to Chemical Processes. Philadelphia: Society for Industrial and Applied Mathematics, 2010. 415 [9] Bryson A E, Ho Y C. Applied Optimal Control: Optimization, Estimation, and Control. Florence: Taylor and Francis, 1975. 496 [10] Fiacco A V, McCormick G P. Nonlinear Programming: Sequential Unconstrained Minimization Techniques. Philadelphia: Society for Industrial Mathematics, 1990. 437 [11] Bai Fu-Sheng. Exact Penalty Methods in Nonlinear Programming[Ph.D. dissertation], Shanghai University, China, 2004 (白富生. 非线性规划中的精确罚函数[博士学位论文], 上海大学, 中国, 2004) [12] Vassiliadis V S. Computational Solution of Dynamic Optimization Problems with General Differential-Algebraic Constraints[Ph.D. dissertation], University of London, London, 1993 [13] Jacobson D H, Lele M M. A transformation technique for optimal control problems with a state variable inequality constraint. IEEE Transactions on Automatic Control, 1969, 14(5): 457-464 [14] Gritsis D M. The Dynamic Simulation and Optimal Control of Systems Described by Index two Differential-Algebraic Equations[Ph.D. dissertation], University of London, London, 1990

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##### 出版历程
• 收稿日期:  2012-05-15
• 修回日期:  2012-08-14
• 刊出日期:  2013-12-20

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