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Maneuvering Angle Rigid Formations With global convergence Guarantees

IEEE/CAA Journal of Automatica Sinica 2022年第8期9卷 1464-1475页

作者： Liangming Chen Zhiyun Lin Hector Garcia de Marina Zhiyong Sun Mir Feroskhan School of Mechanical and Aerospace Engineering Nanyang Technological UniversitySingapore 639798Singapore Department of Computer Architecture and Technology and also with CITICUniversity of Granada18014 GranadaSpain Department of Electrical Engineering Eindhoven University of Technology5600 MB Eindhoventhe Netherlands

Angle rigid multi-agent formations can simultaneously undergo translational,rotational,and scaling maneuvering,therefore combining the maneuvering capabilities of both distance and bearing rigid formations.However,maneuvering angle rigid formations in 2D or 3D with global convergence guarantees is shown to be a challenging problem in the existing literature even when relative position measurements are available.Motivated by angle-induced linear equations in 2D triangles and 3D tetrahedra,this paper aims to solve this challenging problem in both 2D and3D under a leader-follower framework.For the 2D case where the leaders have constant velocities,by using local relative position and velocity measurements,a formation maneuvering law is designed for the followers governed by double-integrator dynamics.When the leaders have time-varying velocities,a sliding mode formation maneuvering law is proposed by using the same measurements.For the 3D case,to establish an angle-induced linear equation for each tetrahedron,we assume that all the followers'coordinate frames share a common Z direction.Then,a formation maneuvering law is proposed for the followers to globally maneuver Z-weakly angle rigid formations in 3D.The extension to Lagrangian agent dynamics and the construction of the desired rigid formations by using the minimum number of angle constraints are also discussed.Simulation examples are provided to validate the effectiveness of the proposed algorithms.

关键词： Index Terms—Angle rigid formations formation control formation maneuvering global convergence multi-agent systems

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global convergence of a Modified Limited Memory BFGS Method for Non-convex Minimization

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Acta Mathematicae Applicatae Sinica 2013年第3期29卷 555-566页

作者： Yun-hai XIAO Ting-feng Zeng-xin WEI Department of Mathematics Nanjing University Zhengzhou Technical College College of Mathematics and Information Science Guangxi University

In this paper, a modified limited memory BFGS method for solving large-scale unconstrained optimization problems is proposed. A remarkable feature of the proposed method is that it possesses global convergence property without convexity assumption on the objective function. Under some suitable conditions, the global convergence of the proposed method is proved. Some numerical results are reported which illustrate that the proposed method is efficient.

关键词： Non-convex minimization secant equation limited memory BFGS method global convergence

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global convergence of Conjugate Gradient Methods without Line Search

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Journal of Mathematical Research with Applications 2018年第5期38卷 541-550页

作者： Cuiling CHEN Yu CHEN College of Mathematics and Statistics Guangxi Normal University School of Computing and Information University of Pittsburgh

In this paper, a new steplength formula is proposed for unconstrained optimization,which can determine the step-size only by one step and avoids the line search step. global convergence of the five well-known conjugate gradient methods with this formula is analyzed,and the corresponding results are as follows:（1） The DY method globally converges for a strongly convex LC;objective function;（2） The CD method, the FR method, the PRP method and the LS method globally converge for a general, not necessarily convex, LC;objective function.

关键词： unconstrained optimization conjugate gradient method line search global convergence

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一种修正的HS共轭梯度法及全局收敛性

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高等学校计算数学学报 2010年第2期32卷 150-156页

作者：王开荣刘金魁邹黎敏重庆大学数学与统计学院重庆三峡学院数学与计算机科学学院

1引言考虑无约束极小化问题:（?）,（1）其中f（x）连续可微,其梯度函数用g（x）表示.共轭梯度法求解（1）的常用迭代格式为:x;=x;+α;d;,（2）(?)（3）其中g;=▽f（x;）,α;≥0是由某种线搜索得到的步长因子;d;为搜索方向,β;为标量,β... 详细信息

1引言考虑无约束极小化问题:（?）,（1）其中f（x）连续可微,其梯度函数用g（x）表示.共轭梯度法求解（1）的常用迭代格式为:x;=x;+α;d;,（2）(?)（3）其中g;=▽f（x;）,α;≥0是由某种线搜索得到的步长因子;d;为搜索方向,β;为标量,β;的不同选择产生了不同的共轭梯度法.著名的β;公式有:

关键词： unconstrained optimization conjugate gradient method Hestenes-Stiefel method Wolfe line search global convergence

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global COVERGENCE OF THE NON-QUASI-NEWTON METHOD FOR UNCONSTRAINED OPTIMIZATION PROBLEMS

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Applied Mathematics(A Journal of Chinese Universities) 2006年第3期21卷 276-288页

作者： Liu Hongwei Wang Mingjie Li Jinshan Zhang Xiangsun School of Economics Renmin University of China Beijing 100872 China Department of Mathematics Capital NormaIUniversity Beijing 100037 China Institute of Applied Mathematics Academy of Mathematics ＆ Systems Science Chinese Academy of Sciences Beijing 100080 China

In this paper, the non-quasi-Newton＇s family with inexact line search applied to unconstrained optimization problems is studied. A new update formula for non-quasi-Newton＇s family is proposed. It is proved that the constituted algorithm with either Wolfe-type or Armijotype line search converges globally and Q-superlinearly if the function to be minimized has Lipschitz continuous gradient.

关键词： non-quasi-Newton method inexact line search global convergence unconstrained optimization,superlinear convergence.

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On the global convergence of a Projective Trust Region Algorithm for Nonlinear Equality Constrained Optimization

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Acta Mathematica Sinica,English Series 2018年第12期34卷 1804-1828页

作者： Yong Gang PEI De Tong ZHU Mathematics and Information Science He 'nan Normal University Xinxiang 453007 P. R. China Mathematics and Science College Shanghai Normal University Shanghai 200234 P. R. China

A trust-region sequential quadratic programming （SQP） method is developed and analyzed for the solution of smooth equality constrained optimization problems. The trust-region SQP algorithm is based on filter line search technique and a composite-step approach, which decomposes the overall step as sum of a vertical step and a horizontal step. The algorithm includes critical modifications of horizontal step computation. One orthogonal projective matrix of the Jacobian of constraint functions is employed in trust-region subproblems. The orthogonal projection gives the null space of the trans- position of the Jacobian of the constraint function. Theoretical analysis shows that the new algorithm retains the global convergence to the first-order critical points under rather general conditions. The preliminary numerical results are reported.

关键词： Sequential quadratic programming trust-region filter line search projection global convergence

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global convergence of the Broyden's Class of Quasi-Newton Methods with Nonmonotone Linesearch

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Acta Mathematicae Applicatae Sinica 2003年第1期19卷 19-24页

作者： Da-chuan XuInstitute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China Institute of Applied Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China

Abstract In this paper, the Broyden class of quasi-Newton methods for unconstrained optimization is investigated. Non-monotone linesearch procedure is introduced, which is combined with the Broyden's class. Under the ... 详细信息

关键词： Keywords Quasi-Newton method Broyden class non-monotone linesearch global convergence unconstrained optimization

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global convergence of a Modified Spectral CD Conjugate Gradient Method

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Journal of Mathematical Research and Exposition 2011年第2期31卷 261-268页

作者： Wei CAO Kai Rong WANG Yi Li WANG College of Mathematics and Statistics Chongqing University Chongqing 401331 P. R. China

In this paper,we present a new nonlinear modified spectral CD conjugate gradient method for solving large scale unconstrained optimization problems.The direction generated by the method is a descent direction for the objective function,and this property depends neither on the line search rule,nor on the convexity of the objective function.Moreover,the modified method reduces to the standard CD method if line search is exact.Under some mild conditions,we prove that the modified method with line search is globally convergent even if the objective function is nonconvex.Preliminary numerical results show that the proposed method is very promising.

关键词： unconstrained optimization conjugate gradient method armijo-type line search global convergence

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global convergence of a class of nonlinear dynamical networks

Global convergence of a class of nonlinear dynamical network...

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第26届中国控制与决策会议

作者： Ao Dun Di Liang Haijing Liu Electronic Information and Control Engineering Beijing University of Technology

This paper considers the global convergence of a class of nonlinear dynamical networks, and the subsystems are discrete time pendulum-like systems. Different from most of the existing results, two kinds of interconnections are considered in view of the fact that the subsystems of networks may have more than one kind of interconnection between each other. The Kalman-Yakubovich-Popov（KYP） lemma and the Schur complement formula are applied to get novel criteria, which have the forms of linear matrix inequalities（LMIs）. The Kronecker product is presented which can be used to handle a class of LMI problems. The test of the global convergence of a network of pendulum-like systems is separated into the test of the global convergence of several independent pendulum-like systems. Furthermore, a controller design method based on LMIs is provided. Finally, a numerical example is presented to illustrate the efficiency and applicability of the proposed methods.

关键词： global convergence Nonlinear networks Pendulum-like systems KYP lemma Kronecker product

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global convergence OF A TRUST REGION ALGORITHM USING INEXACT GRADIENT FOR EQUALITY-CONSTRAINED OPTIMIZATION

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Acta Mathematica Scientia 2000年第3期20卷 365-373页

作者：童小娇周叔子 Department of Mathematics Hunan University Changsha 410082 China

A trust-region algorithm is presented for a nonlinear optimization problem of equality-constraints. The characterization of the algorithm is using inexact gradient information. global convergence results are demonstra... 详细信息

关键词： equality constraints trust region method inexact gradient global convergence

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