Müntz–Legendre neural network construction for solving delay optimal control problems of fractional order with equality and inequality constraints

2019 ◽  
Vol 24 (13) ◽  
pp. 9575-9594
Author(s):  
Farzaneh Kheyrinataj ◽  
Alireza Nazemi
Keyword(s):  
Neural Network ◽  
Optimal Control ◽  
Fractional Order ◽  
Optimal Control Problems ◽  
Inequality Constraints ◽  
Control Problems ◽  
Network Construction ◽  
Equality And Inequality Constraints

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.

A Transformation Method With Two Parameters for Constrained Optimal Control Problems

1978 ◽  
Vol 100 (2) ◽  
pp. 124-131 ◽  
Author(s):  
S. Fujii ◽  
H. Fujimoto
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Inequality Constraints ◽  
Inequality Constraint ◽  
Transformation Method ◽  
Control Problems ◽  
Basic Algorithm ◽  
Constrained Optimal Control ◽  
Equality And Inequality Constraints ◽  
Two Parameters

A transformation method with two parameters is described which can be applied to nonconvex optimal control problems with constraints, does not present numerical difficulties, and has a rapid convergence rate. The basic algorithm of the method is summarized for optimal control problems with equality and inequality constraints, the function of the parameters in the method is considered, one modified algorithm is proposed, and its theoretical results are proved. Finally, the method is applied successfully to both convex and nonconvex optimal control problems with a state inequality constraint.

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