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Switching time optimization for a PDE constrained optimal control problem of bang‐bang type
Author(s) -
Vossen Georg
Publication year - 2016
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201610384
Subject(s) - ode , optimal control , type (biology) , mathematical optimization , optimization problem , boundary (topology) , mathematics , boundary value problem , sensitivity (control systems) , control theory (sociology) , computer science , control variable , control (management) , mathematical analysis , engineering , ecology , statistics , electronic engineering , artificial intelligence , biology
We consider a well‐known optimal control problem subject to the heat equation where the control variable appears linearly as a boundary control in a Robin type boundary condition. Here, we describe an alternative numerical method to solve the problem by a switching time optimization approach. The method has so far been successfully applied to ODE problems and offers several advantages according to second order sufficient conditions and sensitivity analysis. We discuss theoretical aspects and present numerical results to illustrate the effectiveness of the method. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)