Affine relaxations for the solutions of constrained parametric ordinary differential equations

Affine relaxations for the solutions of constrained parametric ordinary differential equations This work presents a numerical method for evaluating affine relaxations of the solutions of parametric ordinary differential equations. This method is derived from a general theory for the construction of a polyhedral outer approximation of the reachable set (“polyhedral bounds”) of a constrained dynamic system subject to uncertain time‐varying inputs and initial conditions. This theory is an extension of differential inequality‐based comparison theorems. The new affine relaxation method is capable of incorporating information from simultaneously constructed interval bounds as well as other constraints on the states; not only does this improve the quality of the relaxations but it also yields numerical advantages that speed up the computation of the relaxations. Examples demonstrate that tight affine relaxations can be computed efficiently with this method. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Optimal Control Applications and Methods Wiley

Affine relaxations for the solutions of constrained parametric ordinary differential equations

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Publisher
Wiley Subscription Services, Inc., A Wiley Company
Copyright
Copyright © 2018 John Wiley & Sons, Ltd.
ISSN
0143-2087
eISSN
1099-1514
D.O.I.
10.1002/oca.2323
Publisher site
See Article on Publisher Site

Abstract

This work presents a numerical method for evaluating affine relaxations of the solutions of parametric ordinary differential equations. This method is derived from a general theory for the construction of a polyhedral outer approximation of the reachable set (“polyhedral bounds”) of a constrained dynamic system subject to uncertain time‐varying inputs and initial conditions. This theory is an extension of differential inequality‐based comparison theorems. The new affine relaxation method is capable of incorporating information from simultaneously constructed interval bounds as well as other constraints on the states; not only does this improve the quality of the relaxations but it also yields numerical advantages that speed up the computation of the relaxations. Examples demonstrate that tight affine relaxations can be computed efficiently with this method.

Journal

Optimal Control Applications and MethodsWiley

Published: Jan 1, 2018

References

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