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TODD LOW-COMPLEXITY ALGORITHM IS A PREDICTOR CORRECTOR path-following method

OPERATIONS RESEARCH LETTERS 1992年第4期11卷 199-207页

作者： TODD, MJ VIAL, JP UNIV GENEVA DEPT ECON COMMERCIALE & INDCH-1211 GENEVA 4SWITZERLAND

We show that Todd's low-complexity algorithm for linear programming takes affine-scaling steps when and only when the current point is nearly centered, and, after such a step, requires at most three more iteration... 详细信息

关键词： LINEAR PROGRAMMING INTERIOR-POINT method path-following method

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On a path-following method for non-linear solid mechanics with applications to structural and cardiac mechanics subject to arbitrary loading scenarios

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INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES 2016年 96卷 181-191页

作者： Skatulla, S. Sansour, C. Univ Cape Town Dept Civil Engn Computat Continuum Mech Grp Cape Town South Africa Univ Cape Town Ctr Res Computat & Appl Mech Cape Town South Africa Univ Nottingham Fac Engn Univ Pk Nottingham NG7 2RD England

In computational solid mechanics path-following methods have been proven useful when dealing with non-monotonously evolving loading magnitudes as encountered e.g. in instability or softening behaviour. The present work derives from a displacement-based method a cavity-volume-based path-following method and considers its application specifically to cardiac mechanics problems. Both methods are able to account for an arbitrary number of simultaneously acting loading conditions. When applied to the Newton-Raphson method, the corresponding loading increments are computed by means of volume increments or point-wise prescribed displacement increments, respectively. No additional variables are required and the physics of the problem at hands is not altered. Both methods are implemented in an inhouse meshfree modelling software and successfully applied to non-linear elastic and inelastic problems in structural mechanics. The cavity-volume control method, in particular, is demonstrated to accurately predict the highly non-linear elastic and anisotropic material behaviour encountered when modelling the heart. Albeit, the proposed methods can be equally used e.g. in finite element methods, they are very well suited for meshfree methods where the Kronecker delta property does not apply. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Cardiac mechanics Volume-control method path-following method Displacement-control method Viscoplasticity Shell buckling

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A path-following method for elasto-plastic solids and structures based on control of plastic dissipation and plastic work

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FINITE ELEMENTS IN ANALYSIS AND DESIGN 2017年 123卷 1-8页

作者： Stanic, Andjelka Brank, Bostjan Univ Ljubljana Fac Civil & Geodet Engn Jamova C 2 Ljubljana 1000 Slovenia

A path-following method that is based on controlling plastic dissipation or plastic work in an inelastic solid or structure is presented. It can be effective for highly nonlinear materially and geometrically problems. In particular, it can be applied for elasto-plastic problems where the standard arc-length methods fail, or to avoid artificial and undesirable elastic unloading of a complete solid or structure during the computation. The essential ingredients, the plastic dissipation and the plastic work based constraint equations, are derived by using either explicit or implicit pseudo-time step integration. These constraint equations am valid for geometrically nonlinear small strain elasto-plasticity with hardening. Their implementation in the framework. of the path-following method is described. Several numerical examples are presented in order to illustrate very satisfying performance of the derived path-following method. It performed very well for some challenging shell problems.

关键词： path-following method Plastic dissipation Constraint equation Elasto-plastic shells

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An improved path-following method for mixed H₂/H_∞ controller design

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2008年第8期53卷 1967-1971页

作者： Ostertag, Eric CNRS ULP UMR 7005 Lab Sci Image Informat TeledetectLSIIT F-67412 Illkirch Graffenstaden France

Among the few methods available to solve bilinear matrix inequalities (BMIs) occurring in control design, the path-following method, published some years ago, appears to be one of the best ones, as far as linearization methods are concerned. However, few details are given in the literature about its implementation and limits. In this technical note, this method is applied to the design of mixed H-2/H-infinity controllers with full details of the algorithm and some improvements over the one which has been published a few years ago. The results obtained with the numerical example given in that same publication, as well as with some other examples, are compared with those given by other methods, including a direct BMI-solving program.

关键词： bilinear matrix inequalities (BMIs) mixed H-2/H-infinity control path-following method

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A differentiable path-following method to compute subgame perfect equilibria in stationary strategies in robust stochastic games and its applications

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2022年第3期298卷 1032-1050页

作者： Cao, Yiyin Dang, Chuangyin Xiao, Zhongdong City Univ Hong Kong Dept Adv Design & Syst Engn Kowloon Hong Kong Peoples R China Xi An Jiao Tong Univ Sch Management Xian Shaanxi Peoples R China

As an effective paradigm to address uncertainty in payoffs and transition probabilities, robust stochastic games have been formulated in the literature. This paper is concerned with the computation of subgame perfect equilibria in stationary strategies (SSPEs) in robust stochastic games. To tackle this problem, we develop in this paper a globally convergent differentiable path-following method by exploiting the structures of the games. Incorporating a logarithmic-barrier term into each player's payoff function with an extra variable between zero and one, we constitute a logarithmic-barrier robust stochastic game in which each player solves in each state a convex optimization problem. An application of the optimality conditions to the barrier game together with a fixed-point argument yields a polynomial equilibrium system for the barrier game. As a result of this system, we establish the existence of a smooth path that starts from an arbitrary mixed strategy profile and ends at an SSPE as the extra variable descends from one to zero. As an alternative scheme, we make up a convex-quadratic-penalty robust stochastic game and attain a globally convergent convex-quadratic-penalty differentiable path-following method for SSPEs in robust stochastic games. Numerical comparisons show that the logarithmic-barrier path-following method significantly outperforms the convex-quadratic-penalty path-following method. To further evince the value of the proposed methods, we apply the logarithmic-barrier path-following method to solve a supply chain configuration problem and a market entry problem from medical waste recycling. (c) 2021 Elsevier B.V. All rights reserved.

关键词： Game theory Robust stochastic game Subgame perfect equilibrium in stationary strategies Logarithmic-barrier differentiable path-following method Convex-quadratic-penalty differentiable

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An improved path-following method for solving static output feedback control problems

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OPTIMAL CONTROL APPLICATIONS & methodS 2016年第6期37卷 1193-1206页

作者： Chen, Jian Lin, Chong Chen, Bing Qingdao Univ Inst Complex Sci Qingdao 266071 Peoples R China Qingdao Univ Technol Coll Automat Engn Qingdao 266555 Peoples R China

This paper studies the static output feedback stabilization problems. An improved path-following method is proposed for continuous-time systems as well as for discrete-time systems. The method has two advantages. Firstly, by virtue of a new linearization approach, the related bilinear matrix inequalities ensuring the stabilization of the systems are expanded and linearized around some points. The initialization methods for both systems are built. Then a wide range perturbation step is added to help the method escape from local optimum. The effectiveness and merits of the proposed method are shown through several examples. Copyright (c) 2015 John Wiley & Sons, Ltd.

关键词： static output feedback bilinear matrix inequalities linear matrix inequalities path-following method

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An infeasible-start path-following method for monotone LCPs

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MATHEMATICAL AND COMPUTER MODELLING 2003年第1-2期38卷 23-31页

作者： Zhang, PI Li, XS Jinan Univ Dept Math Guangzhou 510632 Peoples R China Dalian Univ Technol Dept Appl Math Dalian 116024 Peoples R China Dalian Univ Technol Dept Mech Engn Dalian 116024 Peoples R China

As is known in interior-point methods, algebraically equivalent paths give rise to different trajectories to the optimal set, together with different line search strategies. In this paper, an infeasible-starting path-following method for linear complementarity problems is constructed based on a specific algebraic transformation ln(xs/mu) = 0. The algorithm is given and the global Q-linear convergence is established, under minimal assumptions. Moreover, with properly chosen starting point and properly controlled stepsize, an epsilon-feasible and epsilon-complementary solution of the problem can be obtained in 0(n(2) ln(1/epsilon)) iterations. (C) 2003 Elsevier Science Ltd. All rights reserved.

关键词： LCP interior-point method path-following method algebraically equivalent path

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BMI Optimization Based on Improved path-following method in Control 1

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Chinese Intelligent Automation Conference (CIAC)

作者： Chen, Jian Lin, Chong Qingdao Univ Inst Complex Sci Qingdao 266071 Peoples R China Qingdao Technol Univ Coll Sci Qingdao 266555 Peoples R China

ISBN: (数字)9783662464632

ISBN: (纸本)9783662464632;9783662464625

This paper deals with the optimization of the bilinear matrix inequality problems by using an improved path-following method. First, the existing path-following method is depicted in detail, including its implementation and limit. Then, based on a new linearization method, an improved path-following method is given. In order to enhance the ability of global optimization, a wide range of perturbation steps is added. Both methods are implemented on static output feedback control problems. Finally, a numerical example is presented to show that the convergence and optimization ability of the improved path-following method are better than the existing one.

关键词： Bilinear matrix inequalities Control problem path-following method Convergence

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Design and Development of a DTMF Controlled Room Cleaner Robot with Two path-following method 19

Design and Development of a DTMF Controlled Room Cleaner Rob...

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19th International Conference on Computer and Information Technology (ICCIT)

作者： Rashid, Humayun Mahmood, Akash Shekha, Sarjahan Reza, S. M. Taslim Rasheduzzaman, Md. IIUC Dept Elect & Elect Engn Sitakunda Chittagong Bangladesh

ISBN: (纸本)9781509040902

Automatic control system for robotics is getting popular day by day because of its incredible reliability and especially for the time optimization capability with performance. In this paper, the implementation of a room cleaning robot is presented which has been developed using the Arduino Uno platform with control ability by cell phone from any distance using DTMF technology. It is an electronic device with self-controlled obstacle avoidance capability along with a waste and dust cleaning system. Generally, a vacuum cleaner is an effective technology for household cleaning purpose, but it requires to be operated manually by any person. The main purpose of developing a DTMF-controlled room cleaner robot is to implement an automatic cleaning system which can be operated from any distance by using the cell phone. The robot has been built on microcontroller platform and utilized DTMF technology to develop remote controlling operation. Two effective smart paths following methods have been utilized by the robot for cleaning operation along with upgraded vacuum system with necessary filter and air suction system.

关键词： Room Cleaning Robot DTMF remote control Obstacle avoidance path-following method

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Hybrid path-following method for Solving Static Output Feedback Problems 29

Hybrid Path-following Method for Solving Static Output Feedb...

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第29届中国控制与决策会议

作者： Jian Chen Chong Lin Bing Chen Ying Guo Institute of Complexity Science College of Automation and Electrical EngineeringQingdao University College of Automation Engineering Qingdao Technological University School of mathematics and statistics Zaozhuang University

ISBN: (纸本)9781509046584

This paper studies the path-following method for solving static output feedback（SOF） *** order to find initial values for the method,a new linear matrix inequality（LMI） based iterative algorithm is given by a new stabilization ***,the convergence of the improved path-following method（IPFM） is *** on the above two parts,a hybrid path-following method（HPFM） is proposed and it is extended to solve the SOF H controller design *** effectiveness and merits of the proposed method are shown through several examples.

关键词： static output feedback bilinear matrix inequalities linear matrix inequalities path-following method

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