Convex/concave relaxations of parametric ODEs using Taylor models

This paper presents a discretize-then-relax method to construct convex/concave bounds for the solutions of a wide class of parametric nonlinear ODEs. The algorithm builds upon Taylor model methods recently developed for verified solution of parametric ODEs. To enable the propagation of convex/concave state bounds, a new type of Taylor model is introduced, in which convex/concave bounds for the remainder term are computed in addition to the …