A novel analytical second‐order sensitivity calculation approach using the finite element method for chemical engineering problems. (4th November 2019) - Lv, Lu; Xiao, Long; Ma, Weihua; Wang, Wenhai; Qi, Zhenqiang; Zhang, Zeyin; Ye, Song; Liu, Ping; Xu, Guoqiang; Zheng, Zongzhun; Wang, Sen; Liu, Xinggao
Abstract: This paper presents an effective orthogonal collocation approach to approximate dynamic optimization problems into nonlinear programming problems, where the resulting problems can then be usually solved by first‐order sensitivity based algorithms. However, the results obtained fail to satisfy the timeliness and accuracy requirements of some dynamic optimization problems. A novel collocation approach with second‐order sensitivity information is therefore first proposed to improve the efficiency of the method. The resulting nonlinear programming problem is obtained through the orthogonal collocation on finite element combined with a single shooting approach. Three benchmark optimal control problems are considered to demonstrate the performance of the presented approach. Comparisons among the proposed approach, the BFGS method, and other literature solutions are also carried out in detail. Numerical results validate the effectiveness of the proposed method and the time saving benefit.