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.

scholarly journals Quadratic Cost Minimax Optimal Control Problems for a Semilinear Viscoelastic Equation with Long Memory

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Jin-soo Hwang
Keyword(s):  
Optimal Control ◽  
Long Memory ◽  
Optimal Control Problems ◽  
Necessary Optimality Conditions ◽  
Control Problems ◽  
Minimax Control ◽  
Minimax Optimal Control ◽  
Quadratic Cost ◽  
Minimax Optimal Control Problems ◽  
Viscoelastic Equation

In this paper, we study the quadratic cost minimax optimal control problems for a semilinear viscoelastic equation with long memory. A global well-posedness theorem regarding the solutions to its Cauchy problem is given. We formulate the minimax control problem with bilinear control inputs and corresponding disturbances. Under some assumptions, we prove the existence of optimal pairs and give necessary optimality conditions for optimal pairs in some observation cases.

A weak maximum principle for optimal control problems with mixed constraints under a constant rank condition

2020 ◽  
Vol 37 (3) ◽  
pp. 1021-1047
Author(s):  
Roberto Andreani ◽  
Valeriano Antunes de Oliveira ◽  
Jamielli Tomaz Pereira ◽  
Geraldo Nunes Silva
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problems ◽  
Necessary Optimality Conditions ◽  
Inequality Constraints ◽  
Equality Constraints ◽  
Control Problems ◽  
Constant Rank ◽  
Rank Condition ◽  
Weak Maximum Principle

Abstract Necessary optimality conditions for optimal control problems with mixed state-control equality constraints are obtained. The necessary conditions are given in the form of a weak maximum principle and are obtained under (i) a new regularity condition for problems with mixed linear equality constraints and (ii) a constant rank type condition for the general non-linear case. Some instances of problems with equality and inequality constraints are also covered. Illustrative examples are presented.

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