Optimal control with time-delays via the penalty method

Abstract

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 to obtain a solution to the delayed optimal control problem by considering a sequence of delayed problems of the calculus of variations.

This is a preprint of a paper whose final and definite form is: Mathematical Problems in Engineering (ISSN 1024-123X) 2014, Article ID 250419, http://dx.doi.org/10.1155/2014/250419

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