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An optimal control algorithm using the Davidon‐Fletcher‐Powell method with the fibonacci search
Author(s) -
Birta Louis G.,
Trushel Peter J.
Publication year - 1970
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690160310
Subject(s) - minification , mathematics , optimal control , variable (mathematics) , mathematical optimization , fibonacci number , nonlinear system , point (geometry) , class (philosophy) , algorithm , computer science , artificial intelligence , combinatorics , mathematical analysis , physics , geometry , quantum mechanics
A numerical method for solving a class of nonlinear optimal control problems is presented. The approach reformulates the associated two‐point boundary value problem as a multidimensional minimization problem. This problem is, in turn, solved by using the method of Davidon‐Fletcher‐Powell. The one‐dimensional minimization problem implicit in the implementation of the Davidon‐Fletcher‐Powell algorithm is handled with the Fibonacci search technique. Several examples are presented to demonstrate the effectiveness of the method for problems with and without magnitude constraints on the control variable(s).