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Examinations for terminal condition of Lagrange multiplier for heat transfer control problems
Author(s) -
Kurahashi T.,
Kawahara M.
Publication year - 2007
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2107
Subject(s) - lagrange multiplier , constraint algorithm , terminal (telecommunication) , mathematics , multiplier (economics) , control theory (sociology) , optimal control , mathematical optimization , mathematical analysis , control (management) , computer science , macroeconomics , telecommunications , artificial intelligence , economics
This paper presents a method to express the terminal condition of Lagrange multiplier by the solution of the steady adjoint equation. In the control problem based on the adjoint equation method, the terminal condition of Lagrange multiplier has been set zero to satisfy the stationary condition of the extended performance function. Therefore, there is a possibility that the control value near the terminal time cannot be appropriately expressed. To solve this problem, a method to express the terminal condition of Lagrange multiplier by the solution of the steady adjoint equation is proposed and examined. Finally, to confirm the propriety of the proposed method, this method is applied to the sequential control problem, and some remarks are made. Copyright © 2007 John Wiley & Sons, Ltd.