Approximate dynamic programming based optimal control applied to an integrated plant with a reactor and a distillation column with recycle
An approximate dynamic programming (ADP) method has shown good performance in solving optimal control problems in many small-scale process control applications. The offline computational procedure of ADP constructs an approximation of the optimal "cost-to-go" function, which parameterizes...
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| Veröffentlicht in: | AIChE journal Jg. 55; H. 4; S. 919 - 930 |
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01.04.2009
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| Abstract | An approximate dynamic programming (ADP) method has shown good performance in solving optimal control problems in many small-scale process control applications. The offline computational procedure of ADP constructs an approximation of the optimal "cost-to-go" function, which parameterizes the optimal control policy with respect to the state variable. With the approximate "cost-to-go" function computed, a multistage optimization problem that needs to be solved online at every sample time can be reduced to a single-stage optimization, thereby significantly lessening the real-time computational load. Moreover, stochastic uncertainties can be addressed relatively easily within this framework. Nonetheless, the existing ADP method requires excessive offline computation when applied to a high-dimensional system. A case study of a reactor and a distillation column with recycle was used to illustrate this issue. Then, several ways were proposed to reduce the computational load so that the ADP method can be applied to high-dimensional integrated plants. The results showed that the approach is much more superior to NMPC in both deterministic and stochastic cases. © 2009 American Institute of Chemical Engineers AIChE J, 2009 |
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| AbstractList | An approximate dynamic programming (ADP) method has shown good performance in solving optimal control problems in many small-scale process control applications. The offline computational procedure of ADP constructs an approximation of the optimal cost-to-go function, which parameterizes the optimal control policy with respect to the state variable. With the approximate "cost-to- go" function computed, a multistage optimization problem that needs to be solved online at every sample time can be reduced to a single-stage optimization, thereby significantly lessening the real-time computational load. Moreover, stochastic uncertainties can be addressed relatively easily within this framework. Nonetheless, the existing ADP method requires excessive offline computation when applied to a high-dimensional system. A case study of a reactor and a distillation column with recycle was used to illustrate this issue. Then, several ways were proposed to reduce the computational load so that the ADP method can be applied to high-dimensional integrated plants. The results showed that the approach is much more superior to NMPC in both deterministic and stochastic cases. [PUBLICATION ABSTRACT] An approximate dynamic programming (ADP) method has shown good performance in solving optimal control problems in many small-scale process control applications. The offline computational procedure of ADP constructs an approximation of the optimal "cost-to-go" function, which parameterizes the optimal control policy with respect to the state variable. With the approximate "cost-to-go" function computed, a multistage optimization problem that needs to be solved online at every sample time can be reduced to a single-stage optimization, thereby significantly lessening the real-time computational load. Moreover, stochastic uncertainties can be addressed relatively easily within this framework. Nonetheless, the existing ADP method requires excessive offline computation when applied to a high-dimensional system. A case study of a reactor and a distillation column with recycle was used to illustrate this issue. Then, several ways were proposed to reduce the computational load so that the ADP method can be applied to high-dimensional integrated plants. The results showed that the approach is much more superior to NMPC in both deterministic and stochastic cases. © 2009 American Institute of Chemical Engineers AIChE J, 2009 An approximate dynamic programming (ADP) method has shown good performance in solving optimal control problems in many small-scale process control applications. The offline computational procedure of ADP constructs an approximation of the optimal cost-to-go function, which parameterizes the optimal control policy with respect to the state variable. With the approximate cost-to-go function computed, a multistage optimization problem that needs to be solved online at every sample time can be reduced to a single-stage optimization, thereby significantly lessening the real-time computational load. Moreover, stochastic uncertainties can be addressed relatively easily within this framework. Nonetheless, the existing ADP method requires excessive offline computation when applied to a high-dimensional system. A case study of a reactor and a distillation column with recycle was used to illustrate this issue. Then, several ways were proposed to reduce the computational load so that the ADP method can be applied to high-dimensional integrated plants. The results showed that the approach is much more superior to NMPC in both deterministic and stochastic cases. |
| Author | Tosukhowong, Thidarat Lee, Jay H. |
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| Cites_doi | 10.1016/S0098-1354(02)00120-5 10.1016/j.jprocont.2005.04.010 10.1002/rnc.822 10.1137/0905052 10.1109/9780470544785 10.1016/S0959-1524(01)00014-2 |
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| Keywords | Uncertainty approximate dynamic programming Approximation Process control dynamic optimization Real time Modeling Real time system Optimization State variable integrated plant Optimal control Non linear model nonlinear optimal control nonlinear model predictive control Dynamic programming Reactor Distillation column Mathematical programming Predictive control |
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| References | Hahn J,Edgar TF. An improved method for nonlinear model reduction using balancing of empirical gramians. Comput Chem Eng. 2002; 26: 1379-1397. Lee JM,Lee JH. Approximate dynamic programming strategies and their applicability for process control: A review and future directions. Int J Control, Automation, and Syst. 2004; 2: 263-278. Bellman RE. Dynamic Programming, New York: Dover Publications, Inc., 2003. Kumar A,Daoutidis P. Nonlinear dynamics and control of process system with recycle. J Process Control. 2002; 12: 475-484. Bertsekas DP,Tsitsiklis J. Neuro-Dynamic Programming. New Hampshire: Athena Scientific; 1996. Lee JM,Kaisare NS,Lee JH. Choice of approximator and design of penalty function for an approximate dynamic programming based control approach. J Process Control. 2006; 16: 135-156. Kaisare NS,Lee JM,Lee JH. Simulation based strategy for nonlinear optimal control: Application to a microbial cell reactor. Int J Robust Nonlinear Control. 2003; 13: 347-363. Wold S,Ruhe A,Wold H,DunnIIIWJ. The colinearity problem in linear regression. The partial least square approach to generalized inverses. SIAM J Sci Comput. 1994; 5: 735-743. Si J,Barto AG,Powell WB,WunschIID. Handbook of Learning and Approximate Dynamic Programming. New Jersey: IEEE Press; 2004. 2003; 13 1996 2002; 26 2005 2004 2003 2004; 2 2001 2006; 16 2002; 12 1994; 5 e_1_2_5_13_2 e_1_2_5_8_2 e_1_2_5_7_2 e_1_2_5_6_2 e_1_2_5_5_2 e_1_2_5_4_2 e_1_2_5_11_2 e_1_2_5_3_2 e_1_2_5_2_2 Lee JM (e_1_2_5_10_2) 2004; 2 Bertsekas DP (e_1_2_5_12_2) 1996 Bellman RE (e_1_2_5_9_2) 2003 |
| References_xml | – reference: Si J,Barto AG,Powell WB,WunschIID. Handbook of Learning and Approximate Dynamic Programming. New Jersey: IEEE Press; 2004. – reference: Kumar A,Daoutidis P. Nonlinear dynamics and control of process system with recycle. J Process Control. 2002; 12: 475-484. – reference: Bellman RE. Dynamic Programming, New York: Dover Publications, Inc., 2003. – reference: Lee JM,Kaisare NS,Lee JH. Choice of approximator and design of penalty function for an approximate dynamic programming based control approach. J Process Control. 2006; 16: 135-156. – reference: Kaisare NS,Lee JM,Lee JH. Simulation based strategy for nonlinear optimal control: Application to a microbial cell reactor. Int J Robust Nonlinear Control. 2003; 13: 347-363. – reference: Hahn J,Edgar TF. An improved method for nonlinear model reduction using balancing of empirical gramians. Comput Chem Eng. 2002; 26: 1379-1397. – reference: Wold S,Ruhe A,Wold H,DunnIIIWJ. The colinearity problem in linear regression. The partial least square approach to generalized inverses. SIAM J Sci Comput. 1994; 5: 735-743. – reference: Lee JM,Lee JH. Approximate dynamic programming strategies and their applicability for process control: A review and future directions. Int J Control, Automation, and Syst. 2004; 2: 263-278. – reference: Bertsekas DP,Tsitsiklis J. Neuro-Dynamic Programming. New Hampshire: Athena Scientific; 1996. – volume: 13 start-page: 347 year: 2003 end-page: 363 article-title: Simulation based strategy for nonlinear optimal control: Application to a microbial cell reactor publication-title: Int J Robust Nonlinear Control – volume: 26 start-page: 1379 year: 2002 end-page: 1397 article-title: An improved method for nonlinear model reduction using balancing of empirical gramians publication-title: Comput Chem Eng – volume: 2 start-page: 263 year: 2004 end-page: 278 article-title: Approximate dynamic programming strategies and their applicability for process control: A review and future directions publication-title: Int J Control, Automation, and Syst – year: 1996 – volume: 5 start-page: 735 year: 1994 end-page: 743 article-title: The colinearity problem in linear regression. The partial least square approach to generalized inverses publication-title: SIAM J Sci Comput – volume: 16 start-page: 135 year: 2006 end-page: 156 article-title: Choice of approximator and design of penalty function for an approximate dynamic programming based control approach publication-title: J Process Control – year: 2005 – volume: 12 start-page: 475 year: 2002 end-page: 484 article-title: Nonlinear dynamics and control of process system with recycle publication-title: J Process Control – year: 2004 – start-page: 30 year: 2001 end-page: 60 – year: 2003 – ident: e_1_2_5_7_2 doi: 10.1016/S0098-1354(02)00120-5 – ident: e_1_2_5_3_2 doi: 10.1016/j.jprocont.2005.04.010 – ident: e_1_2_5_5_2 doi: 10.1002/rnc.822 – ident: e_1_2_5_2_2 – ident: e_1_2_5_6_2 – volume-title: Dynamic Programming year: 2003 ident: e_1_2_5_9_2 – ident: e_1_2_5_13_2 doi: 10.1137/0905052 – volume-title: Neuro‐Dynamic Programming year: 1996 ident: e_1_2_5_12_2 – volume: 2 start-page: 263 year: 2004 ident: e_1_2_5_10_2 article-title: Approximate dynamic programming strategies and their applicability for process control: A review and future directions publication-title: Int J Control, Automation, and Syst – ident: e_1_2_5_11_2 doi: 10.1109/9780470544785 – ident: e_1_2_5_4_2 doi: 10.1016/S0959-1524(01)00014-2 – ident: e_1_2_5_8_2 |
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| SubjectTerms | Applications of mathematics to chemical engineering. Modeling. Simulation. Optimization Applied sciences approximate dynamic programming Chemical engineering Distillation dynamic optimization Dynamic programming Exact sciences and technology integrated plant nonlinear model predictive control nonlinear optimal control Parameter optimization Process control Reactors Stochastic models Uncertainty |
| Title | Approximate dynamic programming based optimal control applied to an integrated plant with a reactor and a distillation column with recycle |
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