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Exact penalization of terminal constraints for optimal control problems
Author(s) -
Gugat Martin,
Zuazua Enrique
Publication year - 2016
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2238
Subject(s) - terminal (telecommunication) , constraint (computer aided design) , optimal control , penalty method , partial differential equation , mathematics , norm (philosophy) , mathematical optimization , function (biology) , optimization problem , control theory (sociology) , control (management) , computer science , mathematical analysis , telecommunications , geometry , evolutionary biology , artificial intelligence , political science , law , biology
Summary We study optimal control problems for linear systems with prescribed initial and terminal states. We analyze the exact penalization of the terminal constraints. We show that for systems that are exactly controllable, the norm‐minimal exact control can be computed as the solution of an optimization problem without terminal constraint but with a nonsmooth penalization of the end conditions in the objective function, if the penalty parameter is sufficiently large. We describe the application of the method for hyperbolic and parabolic systems of partial differential equations, considering the wave and heat equations as particular examples. Copyright © 2016 John Wiley & Sons, Ltd.