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Virtual inertia and intelligent control assisted frequency regulation of time-delayed power system under DoS attacks
IF 5.3 1区 数学
Chaos Solitons & Fractals Pub Date : 2024-09-27 DOI: 10.1016/j.chaos.2024.115578
{"title":"Virtual inertia and intelligent control assisted frequency regulation of time-delayed power system under DoS attacks","authors":"","doi":"10.1016/j.chaos.2024.115578","DOIUrl":"10.1016/j.chaos.2024.115578","url":null,"abstract":"<div><div>This work proposes an intelligent fractional order fuzzy-proportional derivative plus fractional order-integral (FOF-PD + FOI) control and virtual inertia (VI) control (VIC) for frequency regulation of renewable penetrated interconnected power system (IPS) under denial of service (DoS) attacks and time delays (TDs). The considered IPS is based on thermal power plants in each area with a wind power plant in area-1 and a solar power plant in area-2, moreover, the impact of DoS attacks is considered in the VIC loop. All the physical constraints and non-linearities are also considered. To harvest the power from solar and wind, a perturb and observe (P&amp;O) maximum power point tracking (MPPT) scheme as well as a variable speed wind turbines' slow dynamic behaviour based MPPT respectively are implemented. To obtain the optimal parameters of the proposed controller, a physics-informed optimization termed Archimedes optimization algorithm (AOA) is used. The proposed FOF-PD + FOI controller's supremacy is tasted over PI, PID and fuzzy-PD + I (F-PD + I) controllers in terms of steady state, dynamic performances and with/without renewable energy sources (RESs) while considering the proposed VIC. To replicate the robust operation of AOA-tuned FOF-PD + FOI controller and VIC, variations in virtual inertia of both areas as well as variations in grid parameters are considered. Furthermore, root locus-based stability evaluation is performed to show the stable operation of the designed control architecture. Finally, the proposed controller is tested over New England IEEE-39 bus-based multi-machine large-scale IPS by considering DoS attacks and TDs.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":null,"pages":null},"PeriodicalIF":5.3,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142327875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Curvature bound for Lp Minkowski problem
IF 1.5 1区 数学
Advances in Mathematics Pub Date : 2024-09-27 DOI: 10.1016/j.aim.2024.109959
{"title":"Curvature bound for Lp Minkowski problem","authors":"","doi":"10.1016/j.aim.2024.109959","DOIUrl":"10.1016/j.aim.2024.109959","url":null,"abstract":"<div><div>We establish curvature estimates for anisotropic Gauss curvature flows. By using this, we show that given a measure <em>μ</em> with a positive smooth density <em>f</em>, any solution to the <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> Minkowski problem in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></math></span> with <span><math><mi>p</mi><mo>≤</mo><mo>−</mo><mi>n</mi><mo>+</mo><mn>2</mn></math></span> is a hypersurface of class <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msup></math></span>. This is a sharp result because for each <span><math><mi>p</mi><mo>∈</mo><mo>[</mo><mo>−</mo><mi>n</mi><mo>+</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span> there exists a convex hypersurface of class <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>n</mi><mo>+</mo><mi>p</mi><mo>−</mo><mn>1</mn></mrow></mfrac></mrow></msup></math></span> which is a solution to the <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> Minkowski problem for a positive smooth density <em>f</em>. In particular, the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msup></math></span> regularity is optimal in the case <span><math><mi>p</mi><mo>=</mo><mo>−</mo><mi>n</mi><mo>+</mo><mn>2</mn></math></span> which includes the logarithmic Minkowski problem in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142328282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Classical System of Matrix Equations Over the Split Quaternion Algebra 分裂四元数代数上的经典矩阵方程组
IF 1.5 2区 数学
Advances in Applied Clifford Algebras Pub Date : 2024-09-27 DOI: 10.1007/s00006-024-01348-5
Kai-Wen Si, Qing-Wen Wang, Lv-Ming Xie
{"title":"A Classical System of Matrix Equations Over the Split Quaternion Algebra","authors":"Kai-Wen Si, Qing-Wen Wang, Lv-Ming Xie","doi":"10.1007/s00006-024-01348-5","DOIUrl":"https://doi.org/10.1007/s00006-024-01348-5","url":null,"abstract":"<p>We design several real representations of split quaternion matrices with the primary objective of establishing both necessary and sufficient conditions for the existence of solutions within a system of split quaternion matrix equations. This includes conditions for the general solution without any constraints, as well as <span>(X=pm X^{eta })</span> solutions and <span>(eta )</span>-(anti-)Hermitian solutions. Furthermore, we derive the expressions for the general solutions when it is solvable. As an application, we investigate the solutions to a system of five split quaternion matrix equations involving <span>(X^star )</span>. Finally, we present several algorithms and numerical examples to demonstrate the results of this paper.</p>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142325447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the two nonzero boundary problems of the AB system with multiple poles
IF 5.3 1区 数学
Chaos Solitons & Fractals Pub Date : 2024-09-27 DOI: 10.1016/j.chaos.2024.115560
{"title":"On the two nonzero boundary problems of the AB system with multiple poles","authors":"","doi":"10.1016/j.chaos.2024.115560","DOIUrl":"10.1016/j.chaos.2024.115560","url":null,"abstract":"<div><div>The Riemann–Hilbert method is used to study AB systems with two nonzero boundary conditions. In order to reconstruct the potentials, spectral analysis of Lax pair and the corresponding Riemann–Hilbert problem are discussed. For these two nonzero boundary problems, we consider the cases where the sectional analytic functions have double and triple poles, respectively. The derived scattering data has multiple zeros or pairs of multiple zeros, from which the relationship between the eigenfunctions at the corresponding poles can be obtained. By solving algebraic equations, we can derive the formulas of <span><math><mi>N</mi></math></span>-order solutions in different cases. As an application, we obtain different types of solitons and breathers in the reflectionless case and the dynamic analysis of these solutions is revealed.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":null,"pages":null},"PeriodicalIF":5.3,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142327872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sobolev instability in the cubic NLS equation with convolution potentials on irrational tori
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2024-09-27 DOI: 10.1016/j.jde.2024.09.044
{"title":"Sobolev instability in the cubic NLS equation with convolution potentials on irrational tori","authors":"","doi":"10.1016/j.jde.2024.09.044","DOIUrl":"10.1016/j.jde.2024.09.044","url":null,"abstract":"<div><div>In this paper we prove the existence of solutions to the cubic NLS equation with convolution potentials on two dimensional irrational tori undergoing an arbitrarily large growth of Sobolev norms as time evolves. Our results apply also to the case of square (and rational) tori. We weaken the regularity assumptions on the convolution potentials, required in a previous work by Guardia (2014) <span><span>[11]</span></span> for the square case, to obtain the <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>s</mi></mrow></msup></math></span>-instability (<span><math><mi>s</mi><mo>&gt;</mo><mn>1</mn></math></span>) of the elliptic equilibrium <span><math><mi>u</mi><mo>=</mo><mn>0</mn></math></span>. We also provide the existence of solutions <span><math><mi>u</mi><mo>(</mo><mi>t</mi><mo>)</mo></math></span> with arbitrarily small <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> norm which achieve a prescribed growth, say <span><math><msub><mrow><mo>‖</mo><mi>u</mi><mo>(</mo><mi>T</mi><mo>)</mo><mo>‖</mo></mrow><mrow><msup><mrow><mi>H</mi></mrow><mrow><mi>s</mi></mrow></msup></mrow></msub><mo>≥</mo><mi>K</mi><msub><mrow><mo>‖</mo><mi>u</mi><mo>(</mo><mn>0</mn><mo>)</mo><mo>‖</mo></mrow><mrow><msup><mrow><mi>H</mi></mrow><mrow><mi>s</mi></mrow></msup></mrow></msub></math></span>, <span><math><mi>K</mi><mo>≫</mo><mn>1</mn></math></span>, within a time <em>T</em> satisfying polynomial estimates, namely <span><math><mn>0</mn><mo>&lt;</mo><mi>T</mi><mo>&lt;</mo><msup><mrow><mi>K</mi></mrow><mrow><mi>c</mi></mrow></msup></math></span> for some <span><math><mi>c</mi><mo>&gt;</mo><mn>0</mn></math></span>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142326436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Flow through a prosthetic mechanical aortic valve: Numerical model and experimental study 流经人工机械主动脉瓣：数值模型和实验研究
IF 2.9 2区 数学
Computers & Mathematics with Applications Pub Date : 2024-09-27 DOI: 10.1016/j.camwa.2024.09.010
{"title":"Flow through a prosthetic mechanical aortic valve: Numerical model and experimental study","authors":"","doi":"10.1016/j.camwa.2024.09.010","DOIUrl":"10.1016/j.camwa.2024.09.010","url":null,"abstract":"<div><div>This research presents a numerical model dedicated for virtual patient diagnostics in the field of synthetic valve implantation. The model operates based on computational fluid dynamics solver with implemented rigid body motion solver. Characteristic indicators related to the prosthetic valve were determined to assess the correctness of cardiac system operation after implantation. A novel approach for dynamic time discretization was developed for reliable and time-efficient calculation. The solver efficiency and computational savings due to application of the developed time-discretization scheme is discussed. Numerical results were validated using experimental data acquired from a test rig, including mass flow meter, pressure transducers, and valve holder designed for this purpose. Multivariant analysis of the model constant was performed towards different levels of the valve resistance to motion. The in-house algorithm was prepared to automatically determine the prosthetic valve position from fast camera images.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142326523","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A hybrid lattice Boltzmann and finite difference method for two-phase flows with soluble surfactants
IF 2.9 2区 数学
Computers & Mathematics with Applications Pub Date : 2024-09-27 DOI: 10.1016/j.camwa.2024.09.022
{"title":"A hybrid lattice Boltzmann and finite difference method for two-phase flows with soluble surfactants","authors":"","doi":"10.1016/j.camwa.2024.09.022","DOIUrl":"10.1016/j.camwa.2024.09.022","url":null,"abstract":"<div><div>A hybrid method is developed to simulate two-phase flows with soluble surfactants. In this method, the interface and bulk surfactant concentration equations of diffuse-interface form, which include source terms to consider surfactant adsorption and desorption dynamics, are solved in the entire fluid domain by the finite difference method, while two-phase flows are solved by a lattice Boltzmann color-gradient model, which can accurately simulate binary fluids with unequal densities. The flow and interface surfactant concentration fields are coupled by a modified Langmuir equation of state, which allows for surfactant concentration beyond critical micelle concentration. The capability and accuracy of the hybrid method are first validated by simulating three numerical examples, including the adsorption of bulk surfactants onto the interface of a stationary droplet, the droplet migration in a constant surfactant gradient, and the deformation of a surfactant-laden droplet in a simple shear flow, in which the numerical results are compared with theoretical solutions and available literature data. Then, the hybrid method is applied to simulate the buoyancy-driven bubble rise in a surfactant solution, in which the influence of surfactants is identified for varying wall confinement, density ratio, Eotvos number and Biot number. It is found that surfactants exhibit a retardation effect on the bubble rise due to the Marangoni stress that resists interface motion, and the retardation effect weakens as the Eotvos or Biot number increases. We further show that the weakened retardation effect at higher Biot numbers is attributed to a decreased non-uniform effect of surfactants at the interface. By comparing with the Cahn-Hilliard phase-field method, we also show that the present method conserves the mass for each fluid, improves numerical stability especially at high density ratio and Eotvos number, and does not need the selection of free parameters, thus breaking the limitations of the existing method.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142327241","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The central limit theorems for integrable Hamiltonian systems perturbed by white noise
IF 2.4 2区 数学
Journal of Differential Equations Pub Date : 2024-09-27 DOI: 10.1016/j.jde.2024.09.047
{"title":"The central limit theorems for integrable Hamiltonian systems perturbed by white noise","authors":"","doi":"10.1016/j.jde.2024.09.047","DOIUrl":"10.1016/j.jde.2024.09.047","url":null,"abstract":"<div><div>In this paper, we consider the dynamics of integrable stochastic Hamiltonian systems. Utilizing the Nagaev-Guivarc'h method, we obtain several generalized results of the central limit theorem. Making use of this technique and the Birkhoff ergodic theorem, we prove that the invariant tori persist under stochastic perturbations. Moreover, they asymptotically follow a Gaussian distribution, which gives a positive answer to the stability of integrable stochastic Hamiltonian systems over time. Our results hold true for both Gaussian and non-Gaussian noises, and their intensities can be not small.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142326437","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fixed-time self-triggered fuzzy adaptive control of N-link robotic manipulators
IF 3.2 1区 数学
Fuzzy Sets and Systems Pub Date : 2024-09-27 DOI: 10.1016/j.fss.2024.109134
{"title":"Fixed-time self-triggered fuzzy adaptive control of N-link robotic manipulators","authors":"","doi":"10.1016/j.fss.2024.109134","DOIUrl":"10.1016/j.fss.2024.109134","url":null,"abstract":"<div><div>This paper studies the fixed-time fuzzy adaptive self-triggered control of <em>n</em>-link robotic manipulators. To achieve fixed-time stability, a fuzzy adaptive fixed-time control algorithm is proposed by reconstructing the self-triggered controller and using the singularity-free function, which avoids the singularity problem and obtains fixed-time stability. Meanwhile, the self-triggered mechanism reduces the communication resources between the actuator and the controller, improving the system's transmission efficiency. Through the above thoughts, a kind of fixed-time fuzzy adaptive controller based on the self-triggered mechanism is designed, which guarantees that the tracking error of each joint converges to the prescribed range within a fixed time. Finally, the effectiveness of the proposed algorithm is verified by a simulation example of the two-link robotic manipulator.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.2,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142326925","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Volume rigidity and algebraic shifting
IF 1.2 1区 数学
Journal of Combinatorial Theory Series B Pub Date : 2024-09-27 DOI: 10.1016/j.jctb.2024.09.002
{"title":"Volume rigidity and algebraic shifting","authors":"","doi":"10.1016/j.jctb.2024.09.002","DOIUrl":"10.1016/j.jctb.2024.09.002","url":null,"abstract":"<div><div>We study the generic volume-rigidity of <span><math><mo>(</mo><mi>d</mi><mo>−</mo><mn>1</mn><mo>)</mo></math></span>-dimensional simplicial complexes in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi><mo>−</mo><mn>1</mn></mrow></msup></math></span>, and show that the volume-rigidity of a complex can be identified in terms of its exterior shifting. In addition, we establish the volume-rigidity of triangulations of several 2-dimensional surfaces and prove that, in all dimensions &gt;1, volume-rigidity is <em>not</em> characterized by a corresponding hypergraph sparsity property.</div></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142328092","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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