An Improved Control Vector Iteration Approach for Nonlinear Dynamic Optimization (Ⅰ) Problems Without Path Constraints*

Chinese Journal of Chemical Engineering ›› 2012, Vol. 20 ›› Issue (6): 1053-1058.

An Improved Control Vector Iteration Approach for Nonlinear Dynamic Optimization (Ⅰ) Problems Without 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

收稿日期:2012-04-12 修回日期:2012-07-21 出版日期:2012-12-28 发布日期:2012-12-28
通讯作者: LIU Xinggao,E-mail:liuxg@iipc.zju.edu.cn
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);the Outstanding Youth Science Foundation;Zhejiang Province (R4100133)

An Improved Control Vector Iteration Approach for Nonlinear Dynamic Optimization (Ⅰ) Problems Without 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:2012-04-12 Revised:2012-07-21 Online:2012-12-28 Published:2012-12-28
Supported by:
Supported by the National Natural Science Foundation of China (U1162130);the National High Technology Research and Development Program of China (2006AA05Z226);the Outstanding Youth Science Foundation;Zhejiang Province (R4100133)

摘要/Abstract

摘要： This study proposes an efficient indirect approach for general nonlinear dynamic optimization problems without path constraints.The approach incorporates the virtues both from indirect and direct methods: it solves the optimality conditions like the traditional indirect methods do,but uses a discretization technique inspired from direct methods.Compared with other indirect approaches,the proposed approach has two main advantages: (1) the discretized optimization problem only employs unconstrained nonlinear programming (NLP) algorithms such as BFGS (Broyden-Fletcher-Goldfarb-Shanno),rather than constrained NLP algorithms,therefore the computational efficiency is increased; (2) the relationship between the number of the discretized time intervals and the integration error of the four-step Adams predictor-corrector algorithm is established,thus the minimal number of time intervals that under desired integration tolerance can be estimated.The classic batch reactor problem is tested and compared in detail with literature reports,and the results reveal the effectiveness of the proposed approach.Dealing with path constraints requires extra techniques,and will be studied in the second paper.

关键词: nonlinear dynamic optimization, control vector iteration, discretization

Abstract: This study proposes an efficient indirect approach for general nonlinear dynamic optimization problems without path constraints.The approach incorporates the virtues both from indirect and direct methods: it solves the optimality conditions like the traditional indirect methods do,but uses a discretization technique inspired from direct methods.Compared with other indirect approaches,the proposed approach has two main advantages: (1) the discretized optimization problem only employs unconstrained nonlinear programming (NLP) algorithms such as BFGS (Broyden-Fletcher-Goldfarb-Shanno),rather than constrained NLP algorithms,therefore the computational efficiency is increased; (2) the relationship between the number of the discretized time intervals and the integration error of the four-step Adams predictor-corrector algorithm is established,thus the minimal number of time intervals that under desired integration tolerance can be estimated.The classic batch reactor problem is tested and compared in detail with literature reports,and the results reveal the effectiveness of the proposed approach.Dealing with path constraints requires extra techniques,and will be studied in the second paper.

Key words: nonlinear dynamic optimization, control vector iteration, discretization

胡云卿, 刘兴高, 薛安克. An Improved Control Vector Iteration Approach for Nonlinear Dynamic Optimization (Ⅰ) Problems Without Path Constraints^*[J]. Chinese Journal of Chemical Engineering, 2012, 20(6): 1053-1058.

HU Yunqing, LIU Xinggao, XUE Anke. An Improved Control Vector Iteration Approach for Nonlinear Dynamic Optimization (Ⅰ) Problems Without Path Constraints^*[J]. Chin.J.Chem.Eng., 2012, 20(6): 1053-1058.

参考文献

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An Improved Control Vector Iteration Approach for Nonlinear Dynamic Optimization (Ⅰ) Problems Without Path Constraints^*

An Improved Control Vector Iteration Approach for Nonlinear Dynamic Optimization (Ⅰ) Problems Without Path Constraints^*

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