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Distributed solving Sylvester equations with fractional order dynamics

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Control Theory and Technology 2021年第2期19卷 249-259页

作者： Songsong Cheng shu liang Yuan Fan Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education School of Electrical Engineering and AutomationAnhui UniversityHefei230601AnhuiChina Key Laboratory of Knowledge Automation for Industrial Processes of Ministry of Education School of Automation and Electrical EngineeringUniversity of Science and Technology BeijingBeijing100083China

This paper addresses distributed computation Sylvester equations of the form AX+XB=C with fractional order *** partitioning parameter matrices A,B and C,we transfer the problem of distributed solving Sylvester equations as two distributed optimization models and design two fractional order continuous-time algorithms,which have more design freedom and have potential to obtain better convergence performance than that of existing first order ***,rewriting distributed algorithms as corresponding frequency distributed models,we design Lyapunov functions and prove that proposed algorithms asymptotically converge to an exact or least squares ***,we validate the effectiveness of proposed algorithms by providing a numerical example.

关键词： Fractional order calculus Distributed optimization Sylvester equation Frequency distributed model Convergence

Hierarchically Distributed Optimization with a Flexible and Complexity-Reducing Algorithm

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Journal of Systems Science & Complexity 2024年第6期37卷 2530-2555页

作者： liang shu ZHANG Lei WEI Yiheng LIU Yemo Department of Control Science and Engineering Tongji UniversityShanghai 200092China Shanghai Research Institute for Intelligent Autonomous Systems Shanghai 200092China School of Mathematics Southeast UniversityNanjing 211189China Beijing Aerospace Automatic Control Institute Beijing 100854China

In this paper,the authors consider distributed convex optimization over hierarchical *** authors exploit the hierarchical architecture to design specialized distributed algorithms so that the complexity can be reduced compared with that of non-hierarchically distributed *** this end,the authors use local agents to process local functions in the same manner as other distributed algorithms that take advantage of multiple agents'computing ***,the authors use pseudocenters to directly integrate lower-level agents'computation results in each iteration step and then share the outcomes through the higher-level network formed by *** authors prove that the complexity of the proposed algorithm exponentially decreases with respect to the total number of *** support the proposed decomposition-composition method for agents and pseudocenters,the authors develop a class of *** operators are generalizations of the widely-used subgradient based operator and the proximal operator and can be used in distributed convex ***,these operators are closed with respect to the addition and composition operations;thus,they are suitable to guide hierarchically distributed design and ***,these operators make the algorithm flexible since agents with different local functions can adopt suitable operators to simplify their ***,numerical examples also illustrate the effectiveness of the method.

关键词： Complexity convergence convex optimization distributed algorithm hierarchical network

A Numerical Study on the Water Impact of the Rigid/Elastic Box-Like Structure

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China Ocean Engineering 2023年第2期37卷 333-342页

作者： YANG Jian SUN Zhao-chen liang shu-xiu State Key Laboratory of Coastal and Offshore Engineering Dalian University of TechnologyDalian 116024China

Recent damages to the box-like structures caused by wave slamming have made it necessary to study the impact problems of this kind of structure. This paper showed findings from numerical simulations of the rigid/elastic structures, aiming to gain insights into the characteristics of the problem. The results of the rigid cases showed the significance of air compressibility during the impact process, while the slamming phenomena became quite different without the effect. In the elastic cases, the trapped air made the structure vibrate at frequencies much smaller than its eigenfrequencies. Besides, the structural deformation made it easy for the trapped air to escape outwards, which weakened the air cushioning effect, especially at high impact velocities. The above analysis gives the results when the structural symmetry axis was vertical to the water(vertical impacts). In addition, the results were given when the axis was oblique to the water(oblique impacts). Compared with the vertical cases, the impact phenomena and structural response showed asymmetry. This work used the computational fluid dynamics(CFD) method to describe fluid motion and the finite element method(FEM) for the deformable structure. A two-way coupling approach was used to deal with the fluid-structure interaction in the elastic cases.

关键词： water impact fluid-structure interaction air compressibility box-like structures two-way coupling

Routh table test for stability of commensurate fractional degree polynomials and their commensurate fractional order systems

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Control Theory and Technology 2019年第3期17卷 297-306页

作者： Sheng-Guo WANG shu liang liang MA Kaixiang PENG College of Engineering and College of Computing and Informatics University of North Carolina at Charlotte NC 28223-0001 U.S.A. School of Automation and Electrical Engineering University of Science and Technology Beijing Beijing 100083 China

A Routh table test for stability of commensurate fractional degree polynomials and their commensurate fractional order systems is presented via an auxiliary integer degree polynomial. The presented Routh test is a classical Routh table test on the auxiliary integer degree polynomial derived from and for the commensurate fractional degree polynomial. The theoretical proof of this proposed approach is provided by utilizing Argument principle and Cauchy index. Illustrative examples show efficiency of the presented approach for stability test of commensurate fractional degree polynomials and commensurate fractional order systems. So far, only one Routh-type test approach [1] is available for the commensurate fractional degree polynomials in the literature. Thus, this classical Routh-type test approach and the one in [1] both can be applied to stability analysis and design for the fractional order systems, while the one presented in this paper is easy for peoples, who are familiar with the classical Routh table test, to use.

关键词： Fractional order systems stability commensurate fractional degree polynomials Routh table test

Spray printing and encapsulated liquid metal as a highly reflective metallic paint for packing products

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Science China(Technological Sciences) 2019年第9期62卷 1577-1584页

作者： liang shu-Ting WANG Hong-Zhang LIU Jing Department of Biomedical Engineering School of MedicineTsinghua UniversityBeijing 100084China College of Materials and Chemical Engineering Chongqing University of Arts and SciencesChongqing 402160China Beijing Key Lab of CryoBiomedical Engineering and Key Lab of Cryogenics Technical Institute of Physics and ChemistryChinese Academy of SciencesBeijing 100190China

In this strategy, liquid metal(LM) with a shiny metallic luster and an excellent optical property, was introduced as a novel metallic paint and coating to packing products and achieved decorative effects. We report a straightforward method via spray printing to fabricate a consecutive ultra-thin LM film on various product substrates. Then, the flexible LM film was coated with a transparent varnish layer, which was rather convenient for the LM paint to be storing, using and transporting. The thicknesses(25 μm) and the shapes of LM paint were well controlled. The flop index(FI=105), and reflectance(R=88.8%) data of the LM metallic paint were characterized. The results indicated that the LM metallic paint could provide a sparkling appearance and an abounding glossy. The deoxidized LM has a pronounced positive influence on the surface roughness, appearance, reflectance,and metallic texture. The LM metallic paint was highly desirable for potential applications in automotive enamel, motorcycle,toy and high-quality industrial coatings in the near future.

关键词： liquid metal packing metallic sparkle paint fine atomization

Rheological Properties of Electrorheological Fluids Beyond and in the Original Transition Zone

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Chinese Physics Letters 2002年第9期19卷 1309-1311页

作者： Fan Zhi-Kang liang shu-Hua Xue Xu School of Material Science and Engineering Xi'an University of Technology Xi'an 710048

We find a nonlinear relationship between the shear stress and shear rate of electrorheological (ER) fluids with aluminosilicate suspension in the original zone corresponding to low shear rates. Beyond the original zon... 详细信息

关键词： Electrorheological fluids

Distributed Nash equilibrium seeking with order-reduced dynamics based on consensus exact penalty

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Control Theory and Technology 2023年第3期21卷 363-373页

作者： shu liang shuyu Liu Yiguang Hong Jie Chen The Department of Control Science and Engineering Tongji UniversityShanghai 201804China Shanghai Research Institute for Intelligent Autonomous Systems Shanghai 201210China

In this paper,we consider a networked game with coupled constraints and focus on variational Nash equilibrium *** distributed algorithm design,we eliminate the coupled constraints by employing local Lagrangian functions and construct exact penalty terms to attain multipliers'optimal consensus,which yields a set of equilibrium conditions without any coupled constraint and consensus ***,these conditions are only based on strategy and multiplier variables,without auxiliary ***,we present a distributed order-reduced dynamics that updates the strategy and multiplier variables with guaranteed *** with many other distributed algorithms,our algorithm contains no auxiliary variable,and therefore,it can save computation and communication.

关键词： Game theory Nash equilibrium seeking Distributed algorithm Coupled constraints Order-reduced dynamics

Study on Energy Spectrum Instability in the Processes of Propagating and Breaking of Focusing Waves

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China Ocean Engineering 2019年第1期33卷 86-93页

作者： ZHANG Yi-hui liang shu-xiu SUN Zhao-chen State Key Laboratory of Lake Science and Environment Nanjing Institute of Geography and LimnologyChinese Academy of Sciences State Key Laboratory of Coastal and Offshore Engineering Dalian University of Technology

Based on phase focusing theory, focusing waves with different spectral types and breaking severities were generated in a wave flume. The time series of surface elevation fluctuation along the flume were obtained by utilizing 22 wave probes mounted along the mid-stream of the flume. Based on the wave spectrum obtained using fast Fourier transform(FFT), the instability characteristics of the energy spectrum were reported in this paper. By analyzing the variation of total spectral energy, the total spectral energy after wave breaking was found to clearly decrease, and the loss value and ratio gradually increased and tended to stabilize with the enhancement of breaking severity for different spectral types. When wave breaking occurred, the energy loss was primarily in a high-frequency range of f/fp>1.0, and energy gain was primarily in a low-frequency range of f/fp<1.0. As the breaking severity increased, the energy gain-loss ratio decreased gradually, which demonstrates that the energy was mostly dissipated. For plunging waves, the energy gain-loss ratio reached 24% for the constant wave steepness(CWS) spectrum, and was slightly larger at approximately 30% for the constant wave amplitude(CWA) spectrum, and was the largest at approximately 42% for the Pierson-Moskowitz(PM) spectrum.

关键词： phase focusing wave breaking wave surface wave steepness

Distributed Optimization and Scaling Design for Solving Sylvester Equations

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Journal of Systems Science & Complexity 2024年第6期37卷 2487-2510页

作者： CHENG Songsong YU Xin ZENG Xianlin liang shu HONG Yiguang Anhui Engineering Laboratory of Human-Robot Integration System and Intelligent Equipment School of Electrical Engineering and AutomationAnhui UniversityHefei 230601China Key Laboratory of Intelligent Control and Decision of Complec Systems School of AutomationBeijing Institute of TechnologyBeijing 100081China Department of Control Science and Engineering Tongji UniversityShanghai 201804China Shanghai Research Institute for Intelligent Autonomous Systems Tongji UniversityShanghai 201210China

This paper develops distributed algorithms for solving Sylvester *** authors transform solving Sylvester equations into a distributed optimization problem,unifying all eight standard distributed matrix *** the authors propose a distributed algorithm to find the least squares solution and achieve an explicit linear convergence *** results are obtained by carefully choosing the step-size of the algorithm,which requires particular information of data and Laplacian *** avoid these centralized quantities,the authors further develop a distributed scaling technique by using local information *** a result,the proposed distributed algorithm along with the distributed scaling design yields a universal method for solving Sylvester equations over a multi-agent network with the constant step-size freely chosen from configurable ***,the authors provide three examples to illustrate the effectiveness of the proposed algorithms.

关键词： Distributed optimization least squares solution linear convergence rate step-size interval Sylvester equation