Existence Theorems for Optimal Control and Calculus of Variations Problems Where the States Can Jump

1986 ◽  
Vol 24 (3) ◽  
pp. 412-438 ◽  
Author(s):  
J. M. Murray
Keyword(s):  
Optimal Control ◽  
Calculus Of Variations ◽  
Existence Theorems

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.

A Multiplier Rule for a Functional Subject to Certain Integrodifferential Constraints

1969 ◽  
Vol 91 (2) ◽  
pp. 185-189 ◽  
Author(s):  
M. Wittler ◽  
C. N. Shen
Keyword(s):  
Optimal Control ◽  
Integral Equation ◽  
Calculus Of Variations ◽  
Necessary Conditions ◽  
Inequality Constraint ◽  
Fundamental Lemma ◽  
First Order ◽  
Multiplier Rule ◽  
Nuclear Rocket ◽  
Equation Constraint

A problem in the optimal control of a nuclear rocket requires the minimization of a functional subject to an integral equation constraint and an integrodifferential inequality constraint. A theorem giving first-order necessary conditions is derived for this problem in the form of a multiplier rule. The existence of multipliers and the arbitrariness of certain variations is shown. The fundamental lemma of the calculus of variations is applied. A simple example demonstrates the applicability of the theorem.

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