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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Bibliographic Details
Published inChemical engineering science Vol. 166; pp. 358 - 372
Main Authors Tulsyan, Aditya, Barton, Paul I.
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 20.07.2017
Subjects
Differential inequalities
Interval arithmetic
Reachable set
Reaction kinetics
Transformation
Transformation
Differential inequalities
Reachable set
Interval arithmetic
Reaction kinetics
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Summary:•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.
ISSN:0009-2509
1873-4405
DOI:10.1016/j.ces.2017.02.047