Optimality Conditions for Switching Operator Differential Equations

Optimality Conditions for Switching Operator Differential Equations We consider optimal switching of hybrid abstract evolution equations. The framework includes switching semilinear partial differential equations of parabolic or hyperbolic type, discontinuous state resets, switching costs and allows switching of the principle parts of the equations. We present adjoint‐based formulae for the gradient of the cost functional with respect to position and number of switching time points that lead to first order necessary conditions. Moreover, we discuss an alternate‐direction approach for implementing descent methods. As an application we consider optimal open/close‐switching of valves and on/off‐switching control of compressors in a gas network modelled by a graph with simplified euler equations on edges and suitable coupling conditions at nodes. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Proceedings in Applied Mathematics & Mechanics Wiley

Optimality Conditions for Switching Operator Differential Equations

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Publisher
Wiley Subscription Services, Inc., A Wiley Company
Copyright
Copyright © 2017 Wiley Subscription Services
ISSN
1617-7061
eISSN
1617-7061
D.O.I.
10.1002/pamm.201710356
Publisher site
See Article on Publisher Site

Abstract

We consider optimal switching of hybrid abstract evolution equations. The framework includes switching semilinear partial differential equations of parabolic or hyperbolic type, discontinuous state resets, switching costs and allows switching of the principle parts of the equations. We present adjoint‐based formulae for the gradient of the cost functional with respect to position and number of switching time points that lead to first order necessary conditions. Moreover, we discuss an alternate‐direction approach for implementing descent methods. As an application we consider optimal open/close‐switching of valves and on/off‐switching control of compressors in a gas network modelled by a graph with simplified euler equations on edges and suitable coupling conditions at nodes. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Journal

Proceedings in Applied Mathematics & MechanicsWiley

Published: Jan 1, 2017

References

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