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《Journal of the Chemical Industry and Engineering Society of China》 2010-02
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Global versus local orthogonal collocation in simultaneous approach

CHEN Yang,SHAO Zhijiang,QIAN Jixin,WANG Kexin (State Key Laboratory of Industrial Control Technology,Institute of Industrial Process Control, Zhejiang University,Hangzhou 310027,Zhejiang,China)  
Most of the dynamic optimal control problems in chemical engineering can be written in the form of differential algebraic equations(DAEs).Simultaneous approach is an important method for solving these problems.The discretization strategies often used in this approach are local methods,for instance, orthogonal collocation on finite elements(OCFE),which has many advantages.Pseudo-spectral(PS),as a global method,has its own unique properties.It may offer a rapid convergence rate for the approximation of analytic functions and has high precision and low computational effort with a simple structure.As the representations of local method and global method respectively,OCFE and PS were compared.The collocation points and their different distributions were presented,and the degree of freedom(DOF) of non-linear programming(NLP) after discretization was discussed,as well as the criteria were offered to ensure the DOF of the NLPs.At last,a continuous case and a discontinuous case were studied,and it was concluded that if the problem was smooth enough then the convergence of PS was better than that of OCFE.
【Fund】: 国家重点基础研究发展计划项目(2009CB320603)~~
【CateGory Index】: TQ021.8
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