2009
DOI: 10.1021/ie801806t
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Handling Inequality Constraints in Optimal Control by Problem Reformulation

Abstract: Establishment of optimal control for systems, where constraints involve both control and state, is very difficult. In some problems the difficulty is reduced significantly by transforming the optimal control problem. For illustration, the optimal control of a nonisothermal fed-batch reactor with heat removal constraint is considered. Although there are only two control variables, the feed rate and the temperature, the heat removal rate constraint makes the optimal control problem very difficult. To parametrize… Show more

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Cited by 7 publications
(3 citation statements)
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“…In many instances, strict satisfaction of the constraints over a time interval may be necessary for safety reasons or to avoid production of off-specification products. Although iterative dynamic programming (IDP) is not supported by rigorous mathematical analysis in the same way as some of the other dynamic optimization algorithms, , it has been found to be a reliable method for cross-checking the results obtained by other methods and for establishing the global optimum for many problems. According to Biegler and Grossmann, the IDP algorithm does not work well for dynamic optimization problems that include constraints on the state variables. Bounds on state variables are handled in IDP by adding a penalty term to the objective function to penalize the constraint violation.…”
Section: Introductionmentioning
confidence: 99%
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“…In many instances, strict satisfaction of the constraints over a time interval may be necessary for safety reasons or to avoid production of off-specification products. Although iterative dynamic programming (IDP) is not supported by rigorous mathematical analysis in the same way as some of the other dynamic optimization algorithms, , it has been found to be a reliable method for cross-checking the results obtained by other methods and for establishing the global optimum for many problems. According to Biegler and Grossmann, the IDP algorithm does not work well for dynamic optimization problems that include constraints on the state variables. Bounds on state variables are handled in IDP by adding a penalty term to the objective function to penalize the constraint violation.…”
Section: Introductionmentioning
confidence: 99%
“…By using a large number of time stages to allow for accurate switching and a sufficiently high value of the penalty function factor, the state constraint could be satisfied throughout the time period. A more recent paper by Luus 10 on constraint reformulation uses the same approach. However, a large number of time stages results in increased computational time, and using higher value of the penalty function factor to drive the state constraint violation to zero results in a conservative solution to the problem.…”
Section: Introductionmentioning
confidence: 99%
“…For instance, Dynamic Programming (DP) was developed based on Hamilton-Jacobi-Bellman formulation that transformed the original problem into a system of partial differential equations (Bellman, 1957), which was extended to include path constraints on state and control variables (Luus, 1990). Several works have further dedicated to the application of DP to batch and semi-batch reactor optimization since then (Rosen & Luus, 1992, Luus, 1994, Bojkov & Luus, 1996, Guntern et al, 1998, Luus & Okongwu, 1999, Luus, 2006, 2009. Alternative solution methods were proposed.…”
Section: Optimization-based Approachesmentioning
confidence: 99%