1. The calculus of variations and functional analysis with optimal control and applications in mechanics, L. P. Lebedev and M. J. Cloud, WorldScientific, Singapore, 2003, xiii+420pp., Price $94.00, ISBN: 981-238-581-9 2. An introduction to modern variational techniques in mechanics and engineering, B. Z. Vujanovic and T. M. Atanackovic, Birkhäuser, Boston, MA, 2004, x+346pp., Price $74.95, ISBN: 0-8176-3399-5

2006 ◽  
Vol 16 (13) ◽  
pp. 637-639
Author(s):  
D. Subbaram Naidu
Keyword(s):  
Optimal Control ◽  
Functional Analysis ◽  
Calculus Of Variations ◽  
Variational Techniques

scholarly journals Optimal Control with Time Delays via the Penalty Method

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Mohammed Benharrat ◽  
Delfim F. M. Torres
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimality Conditions ◽  
Calculus Of Variations ◽  
Convergence Theorem ◽  
Unknown Function ◽  
Time Delays ◽  
Penalty Method ◽  
Necessary Optimality Conditions

We prove necessary optimality conditions of Euler-Lagrange type for a problem of the calculus of variations with time delays, where the delay in the unknown function is different from the delay in its derivative. Then, a more general optimal control problem with time delays is considered. Main result gives a convergence theorem, allowing us to obtain a solution to the delayed optimal control problem by considering a sequence of delayed problems of the calculus of variations.

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