Interval enclosures for reachable sets of chemical kinetic flow systems. Part 3: Indirect-bounding method
•We compute the reachable sets for continuous-stirred tank reactors under uncertainty.•The proposed method reduces overestimation using an isomorphic transformation.•The proposed method eliminates the need to know a priori the bounds on the system.•The efficacy of the proposed method is validated on...
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| Published in | Chemical engineering science Vol. 166; pp. 358 - 372 |
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| Format | Journal Article |
| Language | English |
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20.07.2017
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| Abstract | •We compute the reachable sets for continuous-stirred tank reactors under uncertainty.•The proposed method reduces overestimation using an isomorphic transformation.•The proposed method eliminates the need to know a priori the bounds on the system.•The efficacy of the proposed method is validated on different CSTR systems.
In the third paper, in the three-part series, we propose an indirect-bounding approach for constructing rigorous interval enclosures or bounds for the reachable sets of CSTR reaction systems subject to parametric and initial condition uncertainties and flow rate disturbances. Existing comparison-based methods yield conservative enclosures for the reachable sets due to the non-quasi-monotonic and non-cooperative nature of CSTR reaction systems. The proposed indirect-bounding method addresses the overestimation problem by using the isomorphic transformation, developed in Tulsyan and Barton (2017a), to map the system into a transformed state space, where comparison-based methods yield tight bounds. The interval bounds on the original states are then reconstructed using the inverse transformation. This eliminates the need to know a priori an effective enclosure set for the CSTR reaction system, as required by the direct-bounding method in Tulsyan and Barton (2017b). The efficacy of the indirect-bounding method is validated on several example problems. Several comparisons with the direct-bounding method are also presented to demonstrate the improvements achieved with the indirect-bounding method. |
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| AbstractList | •We compute the reachable sets for continuous-stirred tank reactors under uncertainty.•The proposed method reduces overestimation using an isomorphic transformation.•The proposed method eliminates the need to know a priori the bounds on the system.•The efficacy of the proposed method is validated on different CSTR systems.
In the third paper, in the three-part series, we propose an indirect-bounding approach for constructing rigorous interval enclosures or bounds for the reachable sets of CSTR reaction systems subject to parametric and initial condition uncertainties and flow rate disturbances. Existing comparison-based methods yield conservative enclosures for the reachable sets due to the non-quasi-monotonic and non-cooperative nature of CSTR reaction systems. The proposed indirect-bounding method addresses the overestimation problem by using the isomorphic transformation, developed in Tulsyan and Barton (2017a), to map the system into a transformed state space, where comparison-based methods yield tight bounds. The interval bounds on the original states are then reconstructed using the inverse transformation. This eliminates the need to know a priori an effective enclosure set for the CSTR reaction system, as required by the direct-bounding method in Tulsyan and Barton (2017b). The efficacy of the indirect-bounding method is validated on several example problems. Several comparisons with the direct-bounding method are also presented to demonstrate the improvements achieved with the indirect-bounding method. |
| Author | Tulsyan, Aditya Barton, Paul I. |
| Author_xml | – sequence: 1 givenname: Aditya surname: Tulsyan fullname: Tulsyan, Aditya email: tulsyan@mit.edu – sequence: 2 givenname: Paul I. surname: Barton fullname: Barton, Paul I. email: pib@mit.edu |
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| Cites_doi | 10.1002/aic.12125 10.1016/j.ces.2016.12.021 10.1016/j.compchemeng.2009.11.021 10.1016/j.automatica.2004.01.012 10.1007/s00498-015-0153-2 10.1016/j.ces.2017.01.045 10.1063/1.4822377 10.1137/040604388 10.1109/TAC.2005.851439 10.1109/TAC.2009.2028974 10.1016/j.automatica.2012.09.020 |
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| References | Tulsyan, Barton (b0105) 2016 Lygeros (b0060) 2004; 40 Smith (b0100) 2008 Lakshmikantham, Leela (b0055) 1969 Chutinan, Krogh (b0025) 1999 Tulsyan, Barton (b0110) 2016; vol. 49 Chachuat, B., 2010. MC++: A versatile library for McCormick relaxations and Taylor models. Documentation and Source Code available at Althoff, Stursberg, Buss (b0005) 2010; 4 Moore (b0070) 1979 Scott, Barton (b0090) 2013; 49 Cohen, Hindmarsh (b0030) 1996; 10 Tulsyan, Barton (b0120) 2017; 166 Ramdani, Meslem, Candau (b0075) 2009; 54 Kurzhanski (b0045) 2006; vol. 253 Amrhein, Bhatt, Srinivasan, Bonvin (b0010) 2010; 56 Rump (b0080) 1999 Tulsyan, Barton (b0115) 2017; 166 Girard (b0035) 2005 . Singer, Barton (b0095) 2006; 27 Villanueva, Houska, Chachuat (b0125) 2013 Kurzhanski, Varaiya (b0050) 2002; 9 Mitchell, Bayen, Tomlin (b0065) 2005; 50 Aubin, Cellina (b0015) 1984 Scott, Barton (b0085) 2010; 34 Walter (b0130) 1970 Harwood, Barton (b0040) 2016; 28 Smith (10.1016/j.ces.2017.02.047_b0100) 2008 Tulsyan (10.1016/j.ces.2017.02.047_b0115) 2017; 166 Ramdani (10.1016/j.ces.2017.02.047_b0075) 2009; 54 Harwood (10.1016/j.ces.2017.02.047_b0040) 2016; 28 Kurzhanski (10.1016/j.ces.2017.02.047_b0045) 2006; vol. 253 Althoff (10.1016/j.ces.2017.02.047_b0005) 2010; 4 Rump (10.1016/j.ces.2017.02.047_b0080) 1999 Chutinan (10.1016/j.ces.2017.02.047_b0025) 1999 Scott (10.1016/j.ces.2017.02.047_b0085) 2010; 34 Villanueva (10.1016/j.ces.2017.02.047_b0125) 2013 Lygeros (10.1016/j.ces.2017.02.047_b0060) 2004; 40 Singer (10.1016/j.ces.2017.02.047_b0095) 2006; 27 10.1016/j.ces.2017.02.047_b0020 Girard (10.1016/j.ces.2017.02.047_b0035) 2005 Mitchell (10.1016/j.ces.2017.02.047_b0065) 2005; 50 Moore (10.1016/j.ces.2017.02.047_b0070) 1979 Aubin (10.1016/j.ces.2017.02.047_b0015) 1984 Kurzhanski (10.1016/j.ces.2017.02.047_b0050) 2002; 9 Tulsyan (10.1016/j.ces.2017.02.047_b0110) 2016; vol. 49 Tulsyan (10.1016/j.ces.2017.02.047_b0120) 2017; 166 Cohen (10.1016/j.ces.2017.02.047_b0030) 1996; 10 Tulsyan (10.1016/j.ces.2017.02.047_b0105) 2016 Lakshmikantham (10.1016/j.ces.2017.02.047_b0055) 1969 Amrhein (10.1016/j.ces.2017.02.047_b0010) 2010; 56 Walter (10.1016/j.ces.2017.02.047_b0130) 1970 Scott (10.1016/j.ces.2017.02.047_b0090) 2013; 49 |
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| Title | Interval enclosures for reachable sets of chemical kinetic flow systems. Part 3: Indirect-bounding method |
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