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.

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 Bilinear Minimax Optimal Control Problems for a von Kárman System with Long Memory

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Jin-soo Hwang
Keyword(s):  
Optimal Control ◽  
Long Memory ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Solution Map ◽  
Minimax Optimal Control ◽  
Minimax Optimal Control Problems ◽  
Von Karman ◽  
Solution Mapping ◽  
Von Kármán

In the present article, we consider a von Kárman equation with long memory. The goal is to study a quadratic cost minimax optimal control problems for the control system governed by the equation. First, we show that the solution map is continuous under a weak assumption on the data. Then, we formulate the minimax optimal control problem. We show the first and twice Fréchet differentiabilities of the nonlinear solution map from a bilinear input term to the weak solution of the equation. With the Fréchet differentiabilities of the control to solution mapping, we prove the uniqueness and existence of an optimal pair and find its necessary optimality condition.

An Approximation Scheme for Uncertain Minimax Optimal Control Problems

2017 ◽  
Vol 26 (4) ◽  
pp. 843-866
Author(s):  
Laura S. Aragone ◽  
Justina Gianatti ◽  
Pablo A. Lotito ◽  
Lisandro A. Parente
Keyword(s):  
Optimal Control ◽  
Approximation Scheme ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Minimax Optimal Control ◽  
Minimax Optimal Control Problems
Sign in / Sign up

Export Citation Format

Share Document