An Improved Control Vector Iteration Approach for Nonlinear Dynamic Optimization. II. Problems with Path Constraints

doi:10.1016/S1004-9541(14)60001-X

Chin.J.Chem.Eng. ›› 2014, Vol. 22 ›› Issue (2): 141-145.DOI: 10.1016/S1004-9541(14)60001-X

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An Improved Control Vector Iteration Approach for Nonlinear Dynamic Optimization. II. Problems with Path Constraints

HU Yunqing¹, LIU Xinggao¹, XUE Anke²

1 State Key Laboratory of Industry Control Technology, Zhejiang University, Hangzhou 310027, China;
2 Institute of Information and Control, Hangzhou Dianzi University, Hangzhou 310018, China

Received:2012-08-04 Revised:2012-10-08 Online:2014-01-28 Published:2014-02-05
Contact: LIU Xinggao
Supported by:
Supported by the National Natural Science Foundation of China (U1162130), the National High Technology Research and Development Program of China (2006AA05Z226), and Outstanding Youth Science Foundation of Zhejiang Province (R4100133).

An Improved Control Vector Iteration Approach for Nonlinear Dynamic Optimization. II. Problems with Path Constraints

胡云卿¹, 刘兴高¹, 薛安克²

1 State Key Laboratory of Industry Control Technology, Zhejiang University, Hangzhou 310027, China;
2 Institute of Information and Control, Hangzhou Dianzi University, Hangzhou 310018, China

通讯作者: LIU Xinggao
基金资助:
Supported by the National Natural Science Foundation of China (U1162130), the National High Technology Research and Development Program of China (2006AA05Z226), and Outstanding Youth Science Foundation of Zhejiang Province (R4100133).

Abstract

Abstract: This paper considers dealing with path constraints in the framework of the improved control vector iteration (CVI) approach. Two available ways for enforcing equality path constraints are presented, which can be directly incorporated into the improved CVI approach. Inequality path constraints are much more difficult to deal with, even for small scale problems, because the time intervals where the inequality path constraints are active are unknown in advance. To overcome the challenge, the l₁ penalty function and a novel smoothing technique are introduced, leading to a new effective approach. Moreover, on the basis of the relevant theorems, a numerical algorithm is proposed for nonlinear dynamic optimization problems with inequality path constraints. Results obtained from the classic batch reactor operation problem are in agreement with the literature reports, and the computational efficiency is also high.

Key words: nonlinear dynamic optimization, control vector iteration, path constraint, penalty function method

摘要： This paper considers dealing with path constraints in the framework of the improved control vector iteration (CVI) approach. Two available ways for enforcing equality path constraints are presented, which can be directly incorporated into the improved CVI approach. Inequality path constraints are much more difficult to deal with, even for small scale problems, because the time intervals where the inequality path constraints are active are unknown in advance. To overcome the challenge, the l₁ penalty function and a novel smoothing technique are introduced, leading to a new effective approach. Moreover, on the basis of the relevant theorems, a numerical algorithm is proposed for nonlinear dynamic optimization problems with inequality path constraints. Results obtained from the classic batch reactor operation problem are in agreement with the literature reports, and the computational efficiency is also high.

关键词: nonlinear dynamic optimization, control vector iteration, path constraint, penalty function method

HU Yunqing, LIU Xinggao, XUE Anke. An Improved Control Vector Iteration Approach for Nonlinear Dynamic Optimization. II. Problems with Path Constraints[J]. Chin.J.Chem.Eng., 2014, 22(2): 141-145.

胡云卿, 刘兴高, 薛安克. An Improved Control Vector Iteration Approach for Nonlinear Dynamic Optimization. II. Problems with Path Constraints[J]. Chinese Journal of Chemical Engineering, 2014, 22(2): 141-145.

References

1 Biegler, L.T., Nonlinear Programming: Concepts, Algorithms, and Applications to Chemical Processes, SIAM, Philadelphia (2010).

2 Woranee, P., Paisan, K., Amornchal, A., "Batch-to-batch optimization of batch crystallization processes", Chin. J. Chem. Eng., 16 (1), 26-29 (2008).

3 Hu, Y.Q., Liu, X.G., Xue, A.K., "An improved control vector iteration approach for nonlinear dynamic optimization. I. problems without path constraints", Chin. J. Chem. Eng., 20 (6), 1053-1058 (2012).

4 Jacobson, D.H., Lele, M.M., "A transformation technique for optimal control problems with a state variable inequality constraint", IEEE Trans. Auto. Control, 14 (5), 457-464 (1969).

5 Vassiliadis, V.S., "Computational solution of dynamic optimization problems with general differential-algebraic constraints", Ph.D. Thesis, University of London, London, UK (1993).

6 Feehery, W.F., "Dynamic optimization with path constraints", Ph.D. Thesis, MIT, Boston, USA (1998).

7 Bloss, K.F., Biegler, L.T., Schiesser, W.E., "Dynamic process optimization through adjoint formulations and constraint aggregation", Ind. Eng. Chem. Res., 38 (2), 421-432 (1999).

8 Bell, M.L., Sargent, R.W.H., "Optimal control of inequality con-strained DAE systems", Comput. Chem. Eng., 24 (11), 2385-2404 (2000).

9 Chen, T.W.C., Vassiliadis, V.S., "Inequality path constraints in optimal control: a finite iteration ε-convergent scheme based on pointwise discretization", J. Process. Contr., 15 (3), 353-362 (2005).

10 Luus, R., "Handling inequality constraints in optimal control by problem reformulation", Ind. Eng. Chem. Res., 48 (21), 9622-9630 (2009).

11 Meng, Z., Dang, C., Jiang, M., Shen, R., "A smoothing objective penalty function algorithm for inequality constrained optimization problems", Numer. Func. Anal. Opt., 32 (7), 806-820 (2011).

12 Hindmarsh, A.C., Brown, P.N., Grant, K.E., Lee, S.L., Serban, R., Shumaker, D.E., Woodward, C.S., "SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers", ACM Trans. Math. Software, 31 (3), 363-396 (2005).

13 Bryson, A.E., Ho, Y.C., Applied Optimal Control: Optimization, Estimation, and Control, Taylor & Francis, New York (1975).

14 Han, S.P., Mangasarian, O.L., "Exact penalty functions in nonlinear programming", Math. Program., 17 (1), 251-269 (1979).

An Improved Control Vector Iteration Approach for Nonlinear Dynamic Optimization. II. Problems with Path Constraints

An Improved Control Vector Iteration Approach for Nonlinear Dynamic Optimization. II. Problems with Path Constraints

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