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Constraint Reasoning for Differential Models

Continuous constraint programming is a powerful framework to model and support reasoning for a wide range of decision problems characterized by a set of nonlinear constraints between real valued variables. Uncertainty is represented by intervals of possible values and efficient constraint propagation techniques are used to narrow the bounds of such intervals, eliminating values that assuredly do not satisfy the model constraints. Traditionally the constraint model is specified as a set of nonlinear equations and inequalities which may be inadequate to model dynamical systems. System dynamics is naturally expressed by means of differential equations. This talk will present work done to extend continuous constraint programming for handling differential models. In the extended framework, ordinary differential equations may be included as constraints together with additional information such as initial and boundary conditions or other conditions of interest usually associated with differential problems.