Interval enclosures for reachable sets of chemical kinetic flow systems. Part 3: Indirect-bounding method

Abstract

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.