Quasi-boundary value methods for regularizing the backward parabolic equation under the optimal control framework

2019 ◽  
Vol 35 (12) ◽  
pp. 124003
Author(s):  
Jun Liu ◽  
Mingqing Xiao
Keyword(s):  
Optimal Control ◽  
Parabolic Equation ◽  
Boundary Value ◽  
Boundary Value Methods ◽  
Control Framework

scholarly journals Regularized Asymptotics of the Solution of the Singularly Perturbed First Boundary Value Problem on the Semiaxis for a Parabolic Equation with a Rational “Simple” Turning Point

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 405
Author(s):  
Alexander Yeliseev ◽  
Tatiana Ratnikova ◽  
Daria Shaposhnikova
Keyword(s):  
Parabolic Equation ◽  
Maximum Principle ◽  
Boundary Value Problem ◽  
Regularization Method ◽  
Turning Point ◽  
Boundary Value ◽  
Singularly Perturbed ◽  
Asymptotic Convergence ◽  
The Maximum Principle ◽  
Regularized Asymptotics

The aim of this study is to develop a regularization method for boundary value problems for a parabolic equation. A singularly perturbed boundary value problem on the semiaxis is considered in the case of a “simple” rational turning point. To prove the asymptotic convergence of the series, the maximum principle is used.

Boundary value methods based on Adams-type methods

1995 ◽  
Vol 18 (1-3) ◽  
pp. 23-35 ◽  
Author(s):  
P. Amodio ◽  
F. Mazzia
Keyword(s):  
Boundary Value ◽  
Boundary Value Methods

An Economic Model Predictive Control Approach for Wind Power Smoothing and Tower Load Mitigation

2018 ◽  
Author(s):  
Mohamed M. Alhneaish ◽  
Mohamed L. Shaltout ◽  
Sayed M. Metwalli
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Model Predictive Control ◽  
Wind Power ◽  
Predictive Control ◽  
Economic Model ◽  
Control Algorithm ◽  
Fatigue Load ◽  
Economic Model Predictive Control ◽  
Control Framework

An economic model predictive control framework is presented in this study for an integrated wind turbine and flywheel energy storage system. The control objective is to smooth wind power output and mitigate tower fatigue load. The optimal control problem within the model predictive control framework has been formulated as a convex optimal control problem with linear dynamics and convex constraints that can be solved globally. The performance of the proposed control algorithm is compared to that of a standard wind turbine controller. The effect of the proposed control actions on the fatigue loads acting on the tower and blades is studied. The simulation results, with various wind scenarios, showed the ability of the proposed control algorithm to achieve the aforementioned objectives in terms of smoothing output power and mitigating tower fatigue load at the cost of a minimal reduction of the wind energy harvested.

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