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Reachable Set Estimation and Safety Verification of Nonlinear Systems via Iterative Sums of Squares Programming

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Journal of Systems Science & Complexity 2022年第3期35卷 1154-1172页

作者： LIN Wang YANG zhengfeng DING Zuohua School of Information Science and Technology Zhejiang Sci-Tech UniversityHangzhou 310018China Shanghai Key Laboratory of Trustworthy Computing East China Normal UniversityShanghai 200062China

In this paper,the problems of forward reachable set estimation and safety verification of uncertain nonlinear systems with polynomial dynamics are ***,an iterative sums of squares(SOS)programming approach is developed for reachable set *** characterizes the over-approximations of the forward reachable sets by sub-level sets of time-varying Lyapunovlike functions that satisfy an invariance condition,and formulates the problem of searching for the Lyapunov-like functions as a bilinear SOS program,which can be solved via an iterative *** make the over-approximation tight,the proposed approach seeks to minimize the volume of the overapproximation set with a desired ***,the reachable set estimation approach is extended for safety verification,via explicitly encoding the safety constraint such that the Lyapunov-like functions guarantee both reaching and *** efficiency of the presented method is illustrated by some numerical examples.

关键词： Computer mathematics reachable set estimation safety verification sums of squares programming

Resultant Elimination via Implicit Equation Interpolation

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Journal of Systems Science & Complexity 2016年第5期29卷 1411-1435页

作者： TANG Min YANG zhengfeng ZENG Zhenbing Shanghai Key Laboratory of Trustworthy Computing East China Normal University Department of Mathematics Shanghai University

It is well known that resultant elimination is an effective method of solving multivariate polynomial equations. In this paper, instead of computing the target resultants via variable by variable elimination, the authors combine multivariate implicit equation interpolation and multivariate resultant elimination to compute the reduced resultants, in which the technique of multivariate implicit equation interpolation is achieved by some high probability algorithms on multivariate polynomial interpolation and univariate rational function interpolation. As an application of resultant elimination, the authors illustrate the proposed algorithm on three well-known unsolved combinatorial geometric optimization problems. The experiments show that the proposed approach of resultant elimination is more efficient than some existing resultant elimination methods on these difficult problems.

关键词： Elimination implicit equations interpolation resultants.

VerifyRealRoots:A Matlab Package for Computing Verified Real Solutions of Polynomials Systems of Equations and Inequalities

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Journal of Systems Science & Complexity 2023年第2期36卷 866-883页

作者： YANG zhengfeng ZHAO Hanrui ZHI Lihong Shanghai Key Laboratory of Trustworthy Computing East China Normal UniversityShanghai 200062China. Key Laboratory of Mathematics Mechanization Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China University of Chinese Academy of Sciences Beijing 100049China

VerifyRealRoots is a Matlab package for computing and verifying real solutions of polynomial systems of equations and *** calls Bertini or MMCRSolver for finding approximate real solutions and then applies AINLSS to verify the existence of a regular solution of a polynomial system or applies AINLSS2(AIVISS)to verify the existence of a double solution(a singular solution of an arbitrary multiplicity)of a slightly perturbed polynomial system.

关键词： Error bounds polynomial system real solutions singular solutions verification

Dynamic analysis of the tethered satellite system considering uncertain but bounded parameters OA

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Defence Technology（防务技术） 2024年第12期42卷 116-124页

作者： Xin Jiang zhengfeng Bai School of Astronautics Harbin Institute of TechnologyHarbin150001China Department of Mechanical Engineering Harbin Institute of TechnologyWeihai264209China

Dynamic analysis of the tethered satellite system(TSS)can provide a fundamental guideline to the evaluation of performance and robust design of the system *** inherited with the parameters would induce unexpected variation of the response and deteriorate the reliability of the *** this work,the effect of uncertain mass of the satellites on the deployment and retrieval dynamics of the TSS is *** the interval mode is employed to take the variation of mass of satellite into account in the processes of deployment and ***,the Chebyshev interval method is used to obtain the lower and upper response bounds of the *** achieve a smooth and reliable implementation of deployment and retrieval,the nonlinear programming based on the Gauss pseudospectral method is adopted to obtain optimal trajectory of tether *** results show that the uncertainties of mass of the satellites have a distinct influence on the response of tether tension in the processes of deployment and retrieval.

关键词： Dynamic analysis Interval uncertainty Tethered satellite Deployment and retrieval

System construction of a four-side primary permanent-magnet linear motor drive mechanical press

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Frontiers of Mechanical Engineering 2020年第4期15卷 600-609页

作者： Jintao LIANG zhengfeng MING Peida LI School of Mechano-Electronic Engineering Xidian UniversityXi’an 710071China

A primary permanent-magnet linear motor (PPMLM) has a robust secondary structure and high force density and is appropriate for direct-drive mechanical press. The structure of a four-side PPMLM drive press is presented based on our previous research. The entire press control system is constructed to realize various flexible forming processes. The control system scheme is determined in accordance with the mathematical model of PPMLM, and active disturbance rejection control is implemented in the servo controller. Field-circuit coupling simulation is applied to estimate the system’s performance. Then, a press prototype with 6 kN nominal force is fabricated, and the hardware platform of the control system is constructed for experimental study. Punch strokes with 0.06 m displacement are implemented at trapezoidal speeds of 0.1 and 0.2 m/s;the dynamic position tracking errors are less than 0.45 and 0.82 mm, respectively. Afterward, continuous reciprocating strokes are performed, and the positioning errors at the bottom dead center are less than 0.015 mm. Complex pulse trajectories are also achieved. The proposed PPMLM drive press exhibits a fast dynamic response and favorable tracking precision and is suitable for various forming processes.

关键词： mechanical press direct drive primary permanent-magnet linear motor(PPMLM) servo system active disturbance rejection control(ADRC) prototype experiment

Wear analysis of revolute joints with clearance in multibody systems

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Science China(Physics,Mechanics & Astronomy) 2013年第8期56卷 1581-1590页

作者： BAI zhengfeng ZHAO Yang WANG XingGui Department of Mechanical Engineering Harbin Institute of Technology (Weihai) Department of Astronautic Engineering Harbin Institute of Technology

In this work, the prediction of wear for revolute joint with clearance in multibody systems is investigated using a computational methodology. The contact model in clearance joint is established using a new hybrid nonlinear contact force model and the friction effect is considered by using a modified Coulomb friction model. The dynamics model of multibody system with clearance is established using dynamic segmentation modeling method and the computational process for wear analysis of clearance joint in multibody systems is presented. The main computational process for wear analysis of clearance joint includes two steps, which are dynamics analysis and wear analysis. The dynamics simulation of multibody system with revolute clearance joint is carried out and the contact forces are drawn and used to calculate the wear amount of revolute clearance joint based on the Archard's wear model. Finally, a four-bar multibody mechanical system with revolute clearance joint is used as numerical example application to perform the simulation and show the dynamics responses and wear characteristics of multibody systems with revolute clearance joint. The main results of this work indicate that the contact between the joint elements is wider and more frequent in some specific regions and the wear phenomenon is not regular around the joint surface, which causes the clearance size increase non-regularly after clearance joint wear. This work presents an effective method to predict wear of revolute joint with clearance in multibody systems.

关键词： clearance joint contact model friction force wear multibody system

Nano-montmorillonite-doped lubricating grease exhibiting excellent insulating and tribological properties

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Friction 2017年第2期5卷 219-230页

作者： zhengfeng CAO Yanqiu XIA Xiang XI School of Energy Power and Mechanical Engineering North China Electric Power University Beijing 102206 China

Three types of nano-montmorillonite were doped as additives to afford lubricating *** physicochemical,insulating,and tribological performances of the obtained lubricating greases were investigated in ***,the tribological action mechanisms were analyzed by high magnification optical microscope,Raman spectroscopy,and energy dispersive X-ray spectroscope (EDS).The results show that the inorganic modification montmorillonite (IOMMT) can significantly increase the number of electron traps in the base grease,leading to excellent insulating ***,IOMMT as a novel lubricant additive (1.5 wt％ in grease) significantly enhances the friction reducing and anti-wear abilities for steel/steel contact that comprises a unique layered structure to prevent friction between the contact pairs and the protective tribofilm generated by physical adsorption and chemical reaction.

关键词： nano-montmorillonite insulation friction and wear

ATTENUATION AND GROUP VELOCITY OF NORMAL MODE IN AN ISO-VELOCITY SHALLOW WATER

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Chinese Journal of Acoustics 1989年第2期8卷 121-132页

作者： Zhang, Renhe Lu, zhengfeng Shanghai Acoustics Lab Shanghai China

Proceeding from the eigenvalue equation of the normal mode in homogeneous shallow water, we derive several formulae calculating the mode attenuation and group velocity, and compare their accuracy by means of numerical results. The paper especially discusses the attenuation and the group velocity of critical mode in a Pekeris channel and shows that in general, the attenuation and the group velocity of the critical mode respectively are less than the absorption and the sound speed in the bot -torn . Therefore, the Kornhauser, Raney, Weston Tindle ' s conclusions are modified that the attenuation and the group velocity of the critical mode are exactly equal to the absorption and the sound speed in the bottom, respectively.

关键词： Acoustic Variables Measurement Wave Velocity Acoustic Waves Attenuation Mathematical Techniques Eigenvalues and Eigenfunctions

GENERATING EXACT NONLINEAR RANKING FUNCTIONS BY SYMBOLIC-NUMERIC HYBRID METHOD

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Journal of Systems Science & Complexity 2013年第2期26卷 291-301页

作者： SHEN Liyong WU Min YANG zhengfeng ZENG Zhenbing School of Mathematical Sciences Graduate University of Chinese Academy of Sciences Shanghai Key Laboratory of Trustworthy Computing East China Normal University

This paper presents a hybrid symbolic-numeric algorithm to compute ranking functions for establishing the termination of loop programs with polynomial guards and polynomial *** authors first transform the problem into a parameterized polynomial optimization problem,and obtain a numerical ranking function using polynomial sum-of-squares relaxation via semidefinite programming(SDP).A rational vector recovery algorithm is deployed to recover a rational polynomial from the numerical ranking function,and some symbolic computation techniques are used to certify that this polynomial is an exact ranking function of the loop *** last,the authors demonstrate on some polynomial loop programs from the literature that our algorithm successfully yields nonlinear ranking functions with rational coefficients.

关键词： Program verification ranking function semidefinite programming symbolic-numeric hybrid method.