Handling Differential Equations with Constraints for Decision Support

Abstract

The behaviour of many systems is naturally modelled by a set of ordinary differential equations (ODEs) which are parametric. Since decisions are often based on relations over these parameters it is important to know them with sufficient precision to make those decisions safe. This is in principle an adequate field to use interval domains for the parameters, and constraint propagation to obtain safe bounds for them. Although complex, the use of interval constraints with ODEs is receiving increasing interest. However, the usual consistency maintenance techniques (box- and local hull-consistency) for interval domains are often insufficient to cope with parametric ODEs. In this paper we propose a stronger consistency requirement, global hull-consistency, and an algorithm to compute it. To speed up this computation we developed an incremental approach to refine as needed the precision of ODEs trajectories. Our methodology is illustrated with an example of decision support in a medical problem (diagnosis of diabetes).