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.

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

Villanueva, Mario E.;
2016-01-01

Abstract

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.
9780444634283
uncertain ODEs, set-valued integration, sensitivity analysis, adjoint system
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11771/21499
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