Set-valued integration of uncertain dynamic systems with sensitivity analysis capability

This article presents an extension of existing set-valued integrators for nonlinear parametric ODEs to enable sensitivity analysis. The main focus is on continuous-time set-valued integration, and a derivation of auxiliary ODEs describing high-order inclusions of the adjoint trajectories, together with their terminal and transition conditions, is presented based on polynomial model arithmetics. A numerical implementation for the adjoint set-propagation based on SUNDIALS-CVODES is discussed, and this new sensitivity bounding capability is illustrated with two case studies in batch processing and dynamic parameter estimation.