Sensitivity analysis of uncertain dynamic systems using set-valued integration
File(s)
Published version
Author(s)
Peric, ND
Villanueva, ME
Chachuat, B
Type
Journal Article
Abstract
We present an extension of set-valued integration to enable efficient sensitivity analysis of parameter-dependent ordinary differential equation (ODE) systems, using both the forward and adjoint methods. The focus is on continuous-time set-valued integration, whereby auxiliary ODE systems are derived whose solutions describe high-order inclusions of the parametric trajectories in the form of polynomial models. The forward and adjoint auxiliary ODE systems treat the parameterization error of the original differential variables as a time-varying uncertainty, and propagate the sensitivity bounds forward and backward in time, respectively. This construction enables building on the sensitivity analysis capabilities of state-of-the-art solvers, such as CVODES in the SUNDIALS suite. Several numerical case studies are presented to assess the performance and accuracy of these set-valued sensitivity integrators.
Date Issued
2017-12-19
Date Acceptance
2017-10-16
Citation
SIAM Journal on Scientific Computing, 2017, 39 (6), pp.A3014-A3039
ISSN
1064-8275
Publisher
Society for Industrial and Applied Mathematics
Start Page
A3014
End Page
A3039
Journal / Book Title
SIAM Journal on Scientific Computing
Volume
39
Issue
6
Copyright Statement
c 2017 SIAM. Published by SIAM under the terms of the Creative Commons 4.0 license
License URL
Sponsor
Commission of the European Communities
Engineering & Physical Science Research Council (EPSRC)
Grant Number
PCIG9-GA-2011-293953
EP/K503381/1
Subjects
0102 Applied Mathematics
0103 Numerical And Computational Mathematics
0802 Computation Theory And Mathematics
Numerical & Computational Mathematics
Publication Status
Published