scholarly journals Bilevel Optimal Control: Existence Results and Stationarity Conditions

2020 ◽  
pp. 451-484
Author(s):  
Patrick Mehlitz ◽  
Gerd Wachsmuth
Keyword(s):  
Optimal Control ◽  
Existence Results ◽  
Stationarity Conditions

scholarly journals An Optimal Control Problem Governed by a Kirchhoff-Type Variational Inequality

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Chengfu Wang ◽  
Pengcheng Wu ◽  
Yuying Zhou
Keyword(s):  
Optimal Control ◽  
Variational Inequality ◽  
Optimal Control Problem ◽  
Variational Method ◽  
Control Problem ◽  
Nonlinear Analysis ◽  
Existence Results ◽  
Analysis Techniques ◽  
Kirchhoff Type

This paper is concerned with an optimal control problem governed by a Kirchhoff-type variational inequality. The existence of multiplicity solutions for the Kirchhoff-type variational inequality is established by using some nonlinear analysis techniques and the variational method, and the existence results of an optimal control for the optimal control problem governed by a Kirchhoff-type variational inequality are derived.

scholarly journals Strong Stationarity Conditions for Optimal Control of Hybrid Systems

2017 ◽  
Vol 62 (9) ◽  
pp. 4512-4526 ◽  
Author(s):  
Andreas B. Hempel ◽  
Paul J. Goulart ◽  
John Lygeros
Keyword(s):  
Optimal Control ◽  
Hybrid Systems ◽  
Strong Stationarity ◽  
Stationarity Conditions

A refinement on existence results in nonconvex optimal control

2001 ◽  
Vol 46 (3) ◽  
pp. 381-398 ◽  
Author(s):  
Julio Muñoz ◽  
Pablo Pedregal
Keyword(s):  
Optimal Control ◽  
Existence Results

scholarly journals Optimal control for obstacle problems involving time-dependent variational inequalities with Liouville–Caputo fractional derivative

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Parinya Sa Ngiamsunthorn ◽  
Apassara Suechoei ◽  
Poom Kumam
Keyword(s):  
Optimal Control ◽  
Variational Inequalities ◽  
Obstacle Problem ◽  
Fractional Derivatives ◽  
Necessary Conditions ◽  
Existence Results ◽  
The State ◽  
Time Dependent ◽  
Obstacle Problems ◽  
Caputo Fractional Derivatives

AbstractWe consider an optimal control problem for a time-dependent obstacle variational inequality involving fractional Liouville–Caputo derivative. The obstacle is considered as the control, and the corresponding solution to the obstacle problem is regarded as the state. Our aim is to find the optimal control with the properties that the state is closed to a given target profile and the obstacle is not excessively large in terms of its norm. We prove existence results and establish necessary conditions of obstacle problems via the approximated time fractional-order partial differential equations and their adjoint problems. The result in this paper is a generalization of the obstacle problem for a parabolic variational inequalities as the Liouville–Caputo fractional derivatives were used instead of the classical derivatives.

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