scholarly journals Necessary Optimality Conditions in Isoperimetric Constrained Optimal Control Problems

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1380
Author(s):  
Silviu-Aurelian Urziceanu
Keyword(s):  
Optimal Control ◽  
Optimality Conditions ◽  
Level Sets ◽  
Optimization Problem ◽  
Optimal Control Problems ◽  
Adjoint Equation ◽  
Necessary Optimality Conditions ◽  
Control Problems ◽  
Constrained Optimal Control ◽  
New Class

In this paper, we focus on a new class of optimal control problems governed by a simple integral cost functional and isoperimetric-type constraints (constant level sets of some simple integral functionals). By using the notions of a variational differential system and adjoint equation, necessary optimality conditions are established for a feasible solution in the considered optimization problem. More precisely, under simplified hypotheses and using a modified Legendrian duality, we establish a maximum principle for the considered optimization problem.

Necessary optimality conditions for bicriterion discrete optimal control problems

1999 ◽  
Vol 40 (3) ◽  
pp. 392-402 ◽  
Author(s):  
X. Q. Yang ◽  
K. L. Teo
Keyword(s):  
Optimal Control ◽  
Optimality Conditions ◽  
Optimal Control Problems ◽  
Adjoint Equation ◽  
Optimization Technique ◽  
Optimal Solution ◽  
Necessary Optimality Conditions ◽  
Control Problems ◽  
Discrete Optimal Control ◽  
Linear State

AbstractIn management science and system engineering, problems with two incommensurate objectives are often detected. Bicriterion optimization finds an optimal solution for the problems. In this paper it is shown that bicriterion discrete optimal control problems can be solved by using a parametric optimization technique with relaxed convexity assumptions. Some necessary optimality conditions for discrete optimal control problems subject to a linear state difference equation are derived. It is shown that in this case no adjoint equation is required.

scholarly journals Necessary optimality conditions for minimax optimal control problems with mixed constraints

2021 ◽  
Author(s):  
Paola Patzi Aquino ◽  
Maria do Rosario de Pinho ◽  
Geraldo Nunes Silva
Keyword(s):  
Optimal Control ◽  
Optimality Conditions ◽  
Optimal Control Problems ◽  
Necessary Optimality Conditions ◽  
Inequality Constraints ◽  
Control Problems ◽  
Parameter Uncertainties ◽  
Minimax Optimal Control ◽  
Minimax Optimal Control Problems ◽  
Equality And Inequality Constraints

A weak maximal principle for minimax optimal control problems with mixed state-control equality and inequality constraints is provided. In the formulation of the minimax control problem we allow for parameter uncertainties in all functions involved: in the cost function, in the dynamical control system and in the equality and inequality constraints. Then a new constraint qualification of Mangassarian-Fromovitz type is introduced which allowed us to prove the necessary conditions of optimality. We also derived the optimality conditions under a full rank conditions type and showed that it is, as usual, a particular case of the Mangassarian-Fromovitz type condition case. Illustrative examples are presented.

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