Symmetry

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16 pages, 289 KiB

Open AccessArticle

Generalized Forward–Backward Methods and Splitting Operators for a Sum of Maximal Monotone Operators

by Hongying Xiao, Zhaofeng Li, Yuanyuan Zhang and Xiaoyou Liu

Symmetry 2024, 16(7), 880; https://doi.org/10.3390/sym16070880 - 11 Jul 2024

Viewed by 822

Abstract

Suppose each of

A_{1}, \dots, A_{n}

is a maximal monotone, and

β B

is firmly nonexpansive with

β > 0

. In this paper, we have two purposes: the first is finding the zeros of [...] Read more.

Suppose each of

A_{1}, \dots, A_{n}

is a maximal monotone, and

β B

is firmly nonexpansive with

β > 0

. In this paper, we have two purposes: the first is finding the zeros of

\sum_{j = 1}^{n} A_{j} + B

, and the second is finding the zeros of

\sum_{j = 1}^{n} A_{j}

. To address the first problem, we produce fixed-point equations on the original Hilbert space as well as on the product space and find that these equations associate with crucial operators which are called generalized forward–backward splitting operators. To tackle the second problem, we point out that it can be reduced to a special instance of

n = 2

by defining new operators on the product space. Iterative schemes are given, which produce convergent sequences and these sequences ultimately lead to solutions for the last two problems. Full article

(This article belongs to the Special Issue Advanced Symmetry Methods for Dynamics, Control, Optimization and Applications in 2023)

18 pages, 3022 KiB

Open AccessArticle

Improvement and Application of Hale’s Dynamic Time Warping Algorithm

by Hairong Wang and Qiufang Zheng

Symmetry 2024, 16(6), 645; https://doi.org/10.3390/sym16060645 - 23 May 2024

Viewed by 602

Abstract

Due to the different generation and propagation mechanisms of P- and S-waves, there may be significant differences in the seismic data collected by the two, which poses a great obstacle to the time domain matching of P- and S-waves in multiwave exploration. Furthermore, [...] Read more.

Due to the different generation and propagation mechanisms of P- and S-waves, there may be significant differences in the seismic data collected by the two, which poses a great obstacle to the time domain matching of P- and S-waves in multiwave exploration. Furthermore, the quality and accuracy of the matching effect will directly affect the subsequent multiwave joint inversion and interpretation effect. Therefore, the study of P and S-wave-matching methods plays a crucial role in seismic exploration. In 2013, Hale improved the classical Dynamic Time Warping (DTW) algorithm applied to solve the problem of speech recognition, and obtained the DTW algorithm suitable for solving the matching of P-waves and S-waves. The seismic wave-matching results generated by this algorithm are horizontal discontinuous (different trajectories) and need further processing. This study analyses the algorithm based on simulations of seismic waves using Ricker wavelets. In response to existing problems, this paper proposes strategies to improve the DTW algorithm. The algorithm in this study significantly improved the continuity of the registration results of the actual seismic wave data in the horizontal direction (different traces). Full article

(This article belongs to the Special Issue Advanced Symmetry Methods for Dynamics, Control, Optimization and Applications in 2023)

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18 pages, 328 KiB

Open AccessArticle

A Necessary Optimality Condition on the Control of a Charged Particle

by Nigar Yildirim Aksoy, Ercan Celik and Merve Zengin

Symmetry 2024, 16(6), 637; https://doi.org/10.3390/sym16060637 - 21 May 2024

Viewed by 603

Abstract

We consider an optimal control problem with the boundary functional for a Schrödinger equation describing the motion of a charged particle. By using the existence of an optimal solution, we search the necessary optimality conditions for the examined control problem. First, we constitute [...] Read more.

We consider an optimal control problem with the boundary functional for a Schrödinger equation describing the motion of a charged particle. By using the existence of an optimal solution, we search the necessary optimality conditions for the examined control problem. First, we constitute an adjoint problem by a Lagrange multiplier that is related to constraints of theory on symmetries and conservation laws. The adjoint problem obtained is a boundary value problem with a nonhomogeneous boundary condition. We prove the existence and uniqueness of the solution of the adjoint problem. Then, we demonstrate the differentiability of the objective functional in the sense of Frechet and get a formula for its gradient. Finally, we give a necessary optimality condition in the form of a variational inequality. Full article

(This article belongs to the Special Issue Advanced Symmetry Methods for Dynamics, Control, Optimization and Applications in 2023)

35 pages, 542 KiB

Open AccessArticle

An Optimal Control Perspective on Classical and Quantum Physical Systems

by Mauricio Contreras González, Marcelo Villena and Roberto Ortiz Herrera

Symmetry 2023, 15(11), 2033; https://doi.org/10.3390/sym15112033 - 8 Nov 2023

Cited by 1 | Viewed by 1021

Abstract

This paper analyzes classical and quantum physical systems from an optimal control perspective. Specifically, we explore whether their associated dynamics can correspond to an open- or closed-loop feedback evolution of a control problem. Firstly, for the classical regime, when it is viewed in [...] Read more.

This paper analyzes classical and quantum physical systems from an optimal control perspective. Specifically, we explore whether their associated dynamics can correspond to an open- or closed-loop feedback evolution of a control problem. Firstly, for the classical regime, when it is viewed in terms of the theory of canonical transformations, we find that a closed-loop feedback problem can describe it. Secondly, for a quantum physical system, if one realizes that the Heisenberg commutation relations themselves can be considered constraints in a non-commutative space, then the momentum must depend on the position of any generic wave function. That implies the existence of a closed-loop strategy for the quantum case. Thus, closed-loop feedback is a natural phenomenon in the physical world. By way of completeness, we briefly review control theory and the classical mechanics of constrained systems and analyze some examples at the classical and quantum levels. Full article

(This article belongs to the Special Issue Advanced Symmetry Methods for Dynamics, Control, Optimization and Applications in 2023)

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16 pages, 339 KiB

Open AccessArticle

Well-Posedness and Energy Decay Rates for a Timoshenko-Type System with Internal Time-Varying Delay in the Displacement

by Abdelkader Braik, Safa M. Mirgani, Eltigani I. Hassan and Khaled Zennir

Symmetry 2023, 15(10), 1878; https://doi.org/10.3390/sym15101878 - 6 Oct 2023

Viewed by 1064

Abstract

In this work, we consider a Timoshenko-type system in a bounded one-dimensional domain under Dirichlet conditions with time-varying delay and internal friction damping acting in the displacement. First, we show that the system is well-posed using semi-group theory. Then, under appropriate assumptions on [...] Read more.

In this work, we consider a Timoshenko-type system in a bounded one-dimensional domain under Dirichlet conditions with time-varying delay and internal friction damping acting in the displacement. First, we show that the system is well-posed using semi-group theory. Then, under appropriate assumptions on the weights of the delay, the stability of system is obtained via a suitable Lyapunov functional. Full article

(This article belongs to the Special Issue Advanced Symmetry Methods for Dynamics, Control, Optimization and Applications in 2023)

26 pages, 8514 KiB

Open AccessArticle

Symmetric Nonlinear Feedback Control and Machine Learning for Sustainable Spherical Motor Operation

by Marwa Hassan, Eman Beshr, Mahmoud Beshr and Ali M. El-Rifaie

Symmetry 2023, 15(9), 1661; https://doi.org/10.3390/sym15091661 - 28 Aug 2023

Viewed by 1170

Abstract

This paper presents a comprehensive evaluation of a new control technique for the sphere motor system, aimed at achieving accurate tracking, robust and dispersion of vibrations. Control methods include the determination of a nonlinear model and the application of feedback linearization, followed by [...] Read more.

This paper presents a comprehensive evaluation of a new control technique for the sphere motor system, aimed at achieving accurate tracking, robust and dispersion of vibrations. Control methods include the determination of a nonlinear model and the application of feedback linearization, followed by the optimization of the proportional derivative (PD) coefficients through the Adaptive Neuro-Fuzzy Inference System. In addition, the system’s reaction to harsh environments is managed using Long Short-Term Memory. In order to gain a deeper understanding, symmetrical environmental disturbances and trajectories are introduced during the testing phase. The results demonstrate the superior performance of the control strategy, with reduced vibrations, faster recovery and confirmed tracking accuracy. In addition, the control method shows its adaptability and reliability, as evidenced by the significant reduction in CO₂ emissions compared to conventional PD control methods. The use of symmetric trajectories and visualizations further emphasizes the behavior of the system under symmetric conditions, strengthening the effectiveness and applicability of the control strategy in real-world scenarios. Overall, this study presents a promising solution for converting complex systems under different conditions and making them potentially applicable in various industrial contexts. Full article

(This article belongs to the Special Issue Advanced Symmetry Methods for Dynamics, Control, Optimization and Applications in 2023)

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17 pages, 522 KiB

Open AccessArticle

Fuzzy Adaptive Parameter in the Dai–Liao Optimization Method Based on Neutrosophy

by Predrag S. Stanimirović, Branislav D. Ivanov, Dragiša Stanujkić, Lev A. Kazakovtsev, Vladimir N. Krutikov and Darjan Karabašević

Symmetry 2023, 15(6), 1217; https://doi.org/10.3390/sym15061217 - 7 Jun 2023

Viewed by 1161

Abstract

The impact of neutrosophy has increased rapidly in many areas of science and technology in recent years. Furthermore, numerous applications of the neutrosophic theory have become more usual. We aim to use neutrosophy to enhance Dai–Liao conjugate gradient (CG) iterative method. In particular, [...] Read more.

The impact of neutrosophy has increased rapidly in many areas of science and technology in recent years. Furthermore, numerous applications of the neutrosophic theory have become more usual. We aim to use neutrosophy to enhance Dai–Liao conjugate gradient (CG) iterative method. In particular, we suggest and explore a new neutrosophic logic system intended to compute the essential parameter t required in Dai–Liao CG iterations. Theoretical examination and numerical experiments signify the effectiveness of the introduced method for controlling t. By incorporation of the neutrosophy in the Dai–Liao conjugate gradient principle, we established novel Dai–Liao CG iterations for solving large-scale unconstrained optimization problems. Global convergence is proved under standard assumptions and with the use of the inexact line search. Finally, computational evidence shows the computational effectiveness of the proposed fuzzy neutrosophic Dai–Liao CG method. Full article

(This article belongs to the Special Issue Advanced Symmetry Methods for Dynamics, Control, Optimization and Applications in 2023)

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17 pages, 791 KiB

Open AccessArticle

Classical Solutions for the Generalized Kawahara–KdV System

by Svetlin G. Georgiev, A. Boukarou, Keltoum Bouhali, Khaled Zennir, Hatim M. Elkhair, Eltegani I. Hassan, Alnadhief H. A. Alfedeel and Almonther Alarfaj

Symmetry 2023, 15(6), 1159; https://doi.org/10.3390/sym15061159 - 26 May 2023

Cited by 1 | Viewed by 1212

Abstract

In this article, we investigate the generalized Kawahara–KdV system. A new topological approach is applied to prove the existence of at least one classical solution and at least two non-negative classical solutions. The arguments are based upon recent theoretical results. Full article

(This article belongs to the Special Issue Advanced Symmetry Methods for Dynamics, Control, Optimization and Applications in 2023)

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