Constraint satisfaction differential problems

Abstract

System dynamics is often modeled by means of parametric differential equations. Despite their expressive power, they are difficult to reason about and make safe decisions, given their non-linearity and the important effects that the uncertainty on data may cause. Either by traditional numerical simulation or relying on constraint based methods, it is difficult to express a number of constraints on the solution functions (for which there are usually no analytical solutions) and these constraints may only be handled passively, with generate and test techniques. In contrast, the framework we propose not only extends the declarativeness of the constraint based approach but also makes an active use of constraints on the solution functions, which makes it particularly suited for a number of decision making problems, such as those arising in the biomedical applications presented in the paper. © Springer-Verlag 2003.