Optimized Schwarz Methods for the Optimal Control of Systems Governed by Elliptic Partial Differential Equations

Xu, Yufeng; Chen, Xin

doi:10.1007/s10915-018-0886-4

Cited by 6 publications

(5 citation statements)

References 34 publications

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“…However, there are many shortcomings in standard GA, such as poor local search ability, low optimization accuracy, and premature convergence. In order to improve the performance of GA, researchers put forward many improvement measures from different angles, such as dynamic coding technology, niche clustering technology, adaptive GA, and other improvement measures for genetic operators [10][11][12].…”

Section: Wncs Optimal Controlmentioning

confidence: 99%

“…It has strong adaptive and learning functions and is also applicable to distributed inventory problems. The introduction of the network into the control system not only gains many benefits but also makes the analysis of its structure and mathematical model relatively difficult [ 12 ]. This is because the control system with network modules has to face many problems existing in the network itself.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Control of Whole Network Control System Using Improved Genetic Algorithm and Information Integrity Scale

2022

Computational Intelligence and Neuroscience

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WNCS (Whole network control system) is a network-based distributed control system. The control loop formed by the serial network usually includes several subcontrol systems. WNCS optimal control is a complex and multiparameter coupled highly nonlinear system. Combining the advantages of GA (genetic algorithm), neural network, and fuzzy control, a WNCS optimal control method based on improved GA is proposed. This scheme has both the strong global searching ability of GA and the robustness and self-learning ability of neural network. The simulation results show that the algorithm can keep the diversity of population genes and effectively restrain the premature convergence of the algorithm. On this basis, the optimal control problem of WNCS with short time delay with information integrity scale is studied. The model transformation is used to transform the long time-delay system into a formal nondelay nonlinear system, and then the transformed nondelay nonlinear system obtains the optimal control law that meets the infinite time-domain quadratic performance index without considering packet loss by successive approximation method. The simulation results verify the effectiveness and correctness of the compensation algorithm for nonlinear WNCS.

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Section: Wncs Optimal Controlmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal Control of Whole Network Control System Using Improved Genetic Algorithm and Information Integrity Scale

2022

Computational Intelligence and Neuroscience

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“…In Section 5, we describe the problems to which our analysis should extend. For a study of the elliptic control problem see [44]. To help the reader, a glossary (see Table 5.1) containing the references and definitions of the main objects used in the text can be found at the end of the article.…”

Section: B Alternation (Theorem and Definition 32)mentioning

confidence: 99%

A Complex Homographic Best Approximation Problem. Application to Optimized Robin--Schwarz Algorithms, and Optimal Control Problems

Delourme¹,

Halpern²

2021

SIAM J. Numer. Anal.

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“…30 Finally, the fractal oscillators are also a hot topic in mathematics and engineering. 31,32 The traditional optimization theory [33][34][35][36] is used to couple, for the first time ever, the two-scale fractal calculus in this paper, improving its applicability in engineering. For example, we can use a flexible temperature sensor immersed in a cloth to guarantee an optimal temperature during the working time, yet the air conditioning would maintain the maximum energy efficiency.…”

Section: Introductionmentioning

confidence: 99%

Fractal variational principle for an optimal control problem

2022

Journal of Low Frequency Noise, Vibration and Active Control

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The optimal control of a system governed by an elliptic equation has been widely applied in engineering, and it requires twice differentiability. Furthermore, the optimal control cannot effectively deal with unsmooth boundaries. Now, the condition will not be maintained for a long time because this paper suggests a fractal optimal control of a system governed by a fractal variational principle to deal with unsmooth boundaries. The new optimal theory has obvious advantages in low differentiability for an unsmooth boundary problem. The air conditioning in a room is used as an example to show how to maintain maximum comfortableness of the workplace and maximum efficiency of energy saving.

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Optimized Schwarz Methods for the Optimal Control of Systems Governed by Elliptic Partial Differential Equations

Cited by 6 publications

References 34 publications

Optimal Control of Whole Network Control System Using Improved Genetic Algorithm and Information Integrity Scale

Optimal Control of Whole Network Control System Using Improved Genetic Algorithm and Information Integrity Scale

A Complex Homographic Best Approximation Problem. Application to Optimized Robin--Schwarz Algorithms, and Optimal Control Problems

Fractal variational principle for an optimal control problem

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