scholarly journals A Priori Error Analysis for an Optimal Control Problem Governed by a Variational Inequality of the Second Kind

2021 ◽  
pp. 1-33
Author(s):  
C. Meyer ◽  
M. Weymuth
Keyword(s):  
Optimal Control ◽  
Variational Inequality ◽  
Optimal Control Problem ◽  
Error Analysis ◽  
Control Problem ◽  
A Priori ◽  
A Priori Error Analysis

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.

Solving the Problem of UAV Air Combat Game Based on Differential Variational Inequality and D-Gap Function

2014 ◽  
Vol 1042 ◽  
pp. 172-177
Author(s):  
Guang Yan Xu ◽  
Ping Li ◽  
Biao Zhou
Keyword(s):  
Optimal Control ◽  
Variational Inequality ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Differential Game ◽  
Numerical Solutions ◽  
Game Problem ◽  
Gap Function ◽  
Differential Variational Inequality ◽  
Air Combat

The strategy of unmanned aerial vehicle air combat can be described as a differential game problem. The analytical solutions for the general differential game problem are usually difficult to obtain. In most cases, we can only get its numerical solutions. In this paper, a Nash differential game problem is converted to the corresponding differential variational inequality problem, and then converted into optimal control problem via D-gap function. The nonlinear continuous optimal control problem is obtained, which is easy to get numerical solutions. Compared with other conversion methods, the specific solving process of this method is more simple, so it has certain validity and feasibility.

scholarly journals Spectral Galerkin Approximation of Space Fractional Optimal Control Problem with Integral State Constraint

2021 ◽  
Vol 5 (3) ◽  
pp. 102
Author(s):  
Fangyuan Wang ◽  
Xiaodi Li ◽  
Zhaojie Zhou
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Jacobi Polynomials ◽  
A Priori ◽  
Galerkin Approximation ◽  
State Constraint ◽  
Diffusion Reaction ◽  
Lagrangian Multiplier ◽  
Adjoint State

In this paper spectral Galerkin approximation of optimal control problem governed by fractional advection diffusion reaction equation with integral state constraint is investigated. First order optimal condition of the control problem is discussed. Weighted Jacobi polynomials are used to approximate the state and adjoint state. A priori error estimates for control, state, adjoint state and Lagrangian multiplier are derived. Numerical experiment is carried out to illustrate the theoretical findings.

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