Direct pseudo-spectral method for optimal control of obstacle problem - an optimal control problem governed by elliptic variational inequality

2017 ◽  
Author(s):  
M. Khaksar-e Oshagh ◽  
M. Shamsi
Keyword(s):  
Optimal Control ◽  
Variational Inequality ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Spectral Method ◽  
Obstacle Problem ◽  
Elliptic Variational Inequality ◽  
Pseudo Spectral Method ◽  
Pseudo Spectral

scholarly journals Numerical Analysis of a Distributed Optimal Control Problem Governed by an Elliptic Variational Inequality

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Mariela Olguín ◽  
Domingo A. Tarzia
Keyword(s):  
Finite Element Method ◽  
Optimal Control ◽  
Finite Element ◽  
Variational Inequality ◽  
Numerical Analysis ◽  
Optimal Control Problem ◽  
Control Problem ◽  
State System ◽  
The Finite Element Method ◽  
Elliptic Variational Inequality

The objective of this work is to make the numerical analysis, through the finite element method with Lagrange’s triangles of type 1, of a continuous optimal control problem governed by an elliptic variational inequality where the control variable is the internal energyg. The existence and uniqueness of this continuous optimal control problem and its associated state system were proved previously. In this paper, we discretize the elliptic variational inequality which defines the state system and the corresponding cost functional, and we prove that there exist a discrete optimal control and its associated discrete state system for each positiveh(the parameter of the finite element method approximation). Finally, we show that the discrete optimal control and its associated state system converge to the continuous optimal control and its associated state system when the parameterhgoes to zero.

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.

Battery Charge Control With an Electro-Thermal-Aging Coupling

2015 ◽  
Author(s):  
Xiaosong Hu ◽  
Hector E. Perez ◽  
Scott J. Moura
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Thermal Aging ◽  
Large Scale ◽  
Clean Energy ◽  
Battery Charge ◽  
Charge Control ◽  
Highly Nonlinear ◽  
Pseudo Spectral Method

Efficient and safe battery charge control is an important prerequisite for large-scale deployment of clean energy systems. This paper proposes an innovative approach to devising optimally health-conscious fast-safe charge protocols. A multi-objective optimal control problem is mathematically formulated via a coupled electro-thermal-aging battery model, where electrical and aging sub-models depend upon the core temperature captured by a two-state thermal sub-model. The Legendre-Gauss-Radau (LGR) pseudo-spectral method with adaptive multi-mesh-interval collocation is employed to solve the resulting highly nonlinear six-state optimal control problem. Charge time and health degradation are therefore optimally traded off, subject to both electrical and thermal constraints. Minimum-time, minimum-aging, and balanced charge scenarios are examined in detail. The implications of the upper voltage bound, ambient temperature, and cooling convection resistance to the optimization outcome are investigated as well.

Sign in / Sign up

Export Citation Format

Share Document