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A simultaneous approach for singular optimal control based on partial moving grid
Author(s) -
Chen Weifeng,
Ren Yinyin,
Zhang Guijun,
Biegler Lorenz T.
Publication year - 2019
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.16584
Subject(s) - mathematical optimization , grid , optimal control , convergence (economics) , computer science , heuristic , process (computing) , mathematics , geometry , economics , economic growth , operating system
Singular optimal control plays an important role in process engineering, including optimal operation of batch and semi‐batch reactions. However, for many practical applications, accurate solution of singular optimal control profiles is still an open issue. In particular, numerical optimization must deal with an ill‐conditioned problem that often leads to very slow convergence or failure. Starting from the nested approach in our previous work in 2016, this study develops a more efficient strategy for singular control through a heuristic approach for the outer problem. The approach includes three stages. Starting from a coarse distribution of finite elements, sufficiently many finite elements are inserted where control profiles are steep and fixed gridpoints are inserted on the basis of error estimation of state profiles. Then, moving gridpoints are inserted where the modified switching function is violated. Initial junctions are obtained by moving the latest inserted gridpoints. Moreover, further mesh refinements are considered based on switching point detection and a moving grid point update strategy, until modified switching conditions are satisfied over the whole‐time span. A key feature of this approach is that only a subset of finite elements needs to move during optimization. Complexity of the optimization formulation is considerably decreased compared to our previous work. This approach is demonstrated on eight classical singular control problems with known solutions, as well as six complex singular control problems drawn from the chemical engineering literature.

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