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Fault-tolerant decentralized H-infinity control for multi-channel systems using homotopy method 被引量:1
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作者 Ning CHEN Weihua GUI Masao IKEDA 《控制理论与应用(英文版)》 EI 2007年第1期77-82,共6页
This paper considers a fault-tolerant decentralized H-infinity control problem for multi-channel linear time-invariant systems. The purpose is to design a decentralized H-infinity output feedback controller to.stabili... This paper considers a fault-tolerant decentralized H-infinity control problem for multi-channel linear time-invariant systems. The purpose is to design a decentralized H-infinity output feedback controller to.stabilize the given system and achieve a certain H-infinity performance requirement both in the normal situation and in the situation where any one of the local controllers fails. The designed problem is reduced to a feasibility problem of a set of bilinear matrix inequalities (BMIs). An algorithm is proposed to solve the BMIs. First, the normal situation is considered where all the local controllers are functioning. The local controllers are obtained from a standard centralized H-infinity controller by using a homotopy method imposing a structural constraint progressively. Secondly, the above case is extended to the one where any one of the local controllers fails. We again use a homotopy method where the coefficient matrices of the failed controller are decreased progressively to zero. The efficiency of the proposed algorithm is demonstrated by an example. 展开更多
关键词 Decentralized control H-infinity control Fault-tolerant Control BMI homotopy method
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A CONTINUATION HOMOTOPY METHOD FOR THE INVERSE PROBLEM OF OPERATOR IDENTIFICATION AND ITS APPLICATION 被引量:1
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作者 韩波 刘家琦 卢惠林 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 1993年第1期69-75,共7页
A new widly convergent method for solving the problem of operator identification is illustrated. Numerical simulations are carried out to test the feasibility and to study the general characteristics of the technique ... A new widly convergent method for solving the problem of operator identification is illustrated. Numerical simulations are carried out to test the feasibility and to study the general characteristics of the technique without the real measurement data. This technique is a direct application of the continuation homo-topy method for solving nonlinear systems of equations. It is found that this method does give excellent results in solving the inverse problem of the elliptic differential equations. 展开更多
关键词 Inverse Problem homotopy method Elliptic Differential Equations.
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Finding Periodic Solutions of Ordinary Differential Equations by the Homotopy Method 被引量:1
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作者 王国铭 吕显瑞 黄庆道 《Northeastern Mathematical Journal》 CSCD 2004年第3期369-378,共10页
As an important aspect of applications, it is discussed how to find periodic solutions for ordinary differential equations. By using the homotopy method, a global method for finding those solutions is proposed.
关键词 homotopy method finding periodic solution global convergence comparison principle
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The Aggregate Homotopy Method for Constrained Sequential Max-min Problems 被引量:1
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作者 于波 刘国新 +1 位作者 冯果忱 李勇 《Northeastern Mathematical Journal》 CSCD 2003年第4期287-290,共4页
关键词 nonsmooth programming aggregate function interior point method homotopy method
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Finding Periodic Solutions of High Order Duffing Equations via Homotopy Method
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作者 YANG XUE Xu Xu 《Communications in Mathematical Research》 CSCD 2009年第3期193-203,共11页
This paper presents a detailed analysis of finding the periodic solutions for the high order Duffing equation x^(2n) + g(x) = e(t) (n ≥ 1). Firstly, we give a constructive proof for the existence of periodi... This paper presents a detailed analysis of finding the periodic solutions for the high order Duffing equation x^(2n) + g(x) = e(t) (n ≥ 1). Firstly, we give a constructive proof for the existence of periodic solutions via the homotopy method. Then we establish an efficient and global convergence method to find periodic solutions numerically. 展开更多
关键词 high order Duffing equation periodic solution homotopy method
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Solving Fixed Point Problems in More General Nonconvex Sets Via an Interior Point Homotopy Method
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作者 SU Meng-long LIU Mai-xue 《Chinese Quarterly Journal of Mathematics》 CSCD 2012年第1期74-78,共5页
In this paper,we are mainly devoted to solving fixed point problems in more general nonconvex sets via an interior point homotopy method.Under suitable conditions,a constructive proof is given to prove the existence o... In this paper,we are mainly devoted to solving fixed point problems in more general nonconvex sets via an interior point homotopy method.Under suitable conditions,a constructive proof is given to prove the existence of fixed points,which can lead to an implementable globally convergent algorithm. 展开更多
关键词 nonconvex sets interior point homotopy method
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Modified Homotopy Method for a Class of Brouwer Fixed-point Problems
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作者 苏孟龙 吕显瑞 《Northeastern Mathematical Journal》 CSCD 2007年第1期35-42,共8页
In this paper, we modify the homotopy method (proposed by Yu and Lin, Appl. Math. Comput., 74(1996), 65) and hence make the modified method be able to solve Brouwer fixed-point problems in a broader class of nonco... In this paper, we modify the homotopy method (proposed by Yu and Lin, Appl. Math. Comput., 74(1996), 65) and hence make the modified method be able to solve Brouwer fixed-point problems in a broader class of nonconvex subsets in Rn. In addition, a simple example is given to show the effectiveness of the modified method. 展开更多
关键词 homotopy method Brouwer fixed-point problem nonconvex subset
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Solving a Class of Brouwer Fixed-point Problems via a Modified Aggregate Constraint Homotopy Method
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作者 苏孟龙 吕显瑞 《Northeastern Mathematical Journal》 CSCD 2007年第5期377-385,共9页
In this paper, we provide an aggregate function homotopy interior point method to solve a class of Brouwer fixed-point problems. Compared with the homotopy method (proposed by Yu and Lin, Appl. Math. Comput., 74(199... In this paper, we provide an aggregate function homotopy interior point method to solve a class of Brouwer fixed-point problems. Compared with the homotopy method (proposed by Yu and Lin, Appl. Math. Comput., 74(1996), 65), the main adavantages of this method are as foUows: on the one hand, it can solve the Brouwer fixed-point problems in a broader class of nonconvex subsets Ω in R^n (in this paper, we let Ω={x∈ R^n : gi(x) ≤0, i= 1,... , m}); on the other hand, it can also deal with the subsets Ω with larger amount of constraints more effectively. 展开更多
关键词 homotopy method Brouwer fixed-point problem nonconvex subset
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Finding Solutions to the Picard Boundary Value Problem via Homotopy Method
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作者 李兰 徐旭 《Northeastern Mathematical Journal》 CSCD 2008年第6期545-557,共13页
This paper deals with the problem of finding solutions to the Picard boundary problem. In our approacn, by means of the homotopy method, the equation considered is linked to a simpler equation by introducing a paramet... This paper deals with the problem of finding solutions to the Picard boundary problem. In our approacn, by means of the homotopy method, the equation considered is linked to a simpler equation by introducing a parameter. We first find the solutions of the simpler equation, and give a priori estimates of the equation we considered, and then one can obtain the solutions of Picard boundary problem by following the path of solutions of Cauchy problem. 展开更多
关键词 Picard boundary problem homotopy method path solution
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Existence of Periodic Solutions for Odd Order Ordinary Differential Equations via the Homotopy Method
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作者 刘停战 于波 《Northeastern Mathematical Journal》 CSCD 2004年第2期135-138,共4页
This paper deals with the problems of finding periodic solutions for the third order ordinary differential equations of the form (1) where T is a fixed positive number and f satisfies some additional conditions which ... This paper deals with the problems of finding periodic solutions for the third order ordinary differential equations of the form (1) where T is a fixed positive number and f satisfies some additional conditions which will be stated later.The periodicity problem has been one of main topics in the qualitative theory of ordinary 展开更多
关键词 homotopy method finding periodic solution odd order ordinary differential equations global convergence
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Numerical investigation on MHD Jeffery-Hamel nanofluid flow with different nanoparticles using fuzzy extension of generalized dual parametric homotopy algorithm
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作者 LALCHAND Verma RAMAKANTA Meher 《Journal of Central South University》 SCIE EI CAS CSCD 2024年第6期1915-1930,共16页
This study considers an MHD Jeffery-Hamel nanofluid flow with distinct nanoparticles such as copper,Al_(2)O_(3)and SiO_(2)between two rigid non-parallel plane walls with the fuzzy extension of the generalized dual par... This study considers an MHD Jeffery-Hamel nanofluid flow with distinct nanoparticles such as copper,Al_(2)O_(3)and SiO_(2)between two rigid non-parallel plane walls with the fuzzy extension of the generalized dual parametric homotopy algorithm.The nanofluids have been formulated to enhance the thermophysical characteristics of fluids,including thermal diffusivity,conductivity,convective heat transfer coefficients and viscosity.Due to the presence of distinct nanofluids,a change in the value of volume fraction occurs that influences the velocity profiles of the flow.The short value of nanoparticles volume fraction is considered an uncertain parameter and represented in a triangular fuzzy number range among[0.0,0.1,0.2].A novel generalized dual parametric homotopy algorithm with fuzzy extension is used here to study the fuzzy velocities at various channel positions.Finally,the effectiveness of the proposed approach has been demonstrated through a comparison with the available results in the crisp case. 展开更多
关键词 fuzzy number Jeffery-Hamel(J-H)flow NANOFLUID homotopy analysis method
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A Combined Homotopy Interior Point Method for Nonconvex Programming with Pseudo Cone Condition 被引量:13
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作者 于波 刘庆怀 +1 位作者 冯果忱 孙以丰 《Northeastern Mathematical Journal》 CSCD 2000年第4期383-386,共4页
关键词 nonconvex programming interior point method homotopy method
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A Combined Homotopy Infeasible Interior-Point Method for Convex Nonlinear Programming 被引量:3
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作者 杨轶华 吕显瑞 刘庆怀 《Northeastern Mathematical Journal》 CSCD 2006年第2期188-192,共5页
In this paper, on the basis of the logarithmic barrier function and KKT conditions, we propose a combined homotopy infeasible interior-point method (CHIIP) for convex nonlinear programming problems. For any convex n... In this paper, on the basis of the logarithmic barrier function and KKT conditions, we propose a combined homotopy infeasible interior-point method (CHIIP) for convex nonlinear programming problems. For any convex nonlinear programming, without strict convexity for the logarithmic barrier function, we get different solutions of the convex programming in different cases by CHIIP method. 展开更多
关键词 convex nonlinear programming infeasible interior point method homotopy method global convergence
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Iteratively weighted thresholding homotopy method for the sparse solution of underdetermined linear equations 被引量:1
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作者 Wenxing Zhu Zilin Huang +1 位作者 Jianli Chen Zheng Peng 《Science China Mathematics》 SCIE CSCD 2021年第3期639-664,共26页
Recently, iteratively reweighted methods have attracted much interest in compressed sensing, outperforming their unweighted counterparts in most cases. In these methods, decision variables and weights are optimized al... Recently, iteratively reweighted methods have attracted much interest in compressed sensing, outperforming their unweighted counterparts in most cases. In these methods, decision variables and weights are optimized alternatingly, or decision variables are optimized under heuristically chosen weights. In this paper,we present a novel weighted l1-norm minimization problem for the sparsest solution of underdetermined linear equations. We propose an iteratively weighted thresholding method for this problem, wherein decision variables and weights are optimized simultaneously. Furthermore, we prove that the iteration process will converge eventually. Using the homotopy technique, we enhance the performance of the iteratively weighted thresholding method. Finally, extensive computational experiments show that our method performs better in terms of both running time and recovery accuracy compared with some state-of-the-art methods. 展开更多
关键词 sparse optimization weighted thresholding method homotopy method
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A GEOMETRICAL INTERPRETATION OF THE WITHOUT-EXCEPTION FEASIBILITY OF PL HOMOTOPY METHODS
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作者 王则柯 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 1989年第4期310-317,共8页
PL homotopy metheds are effective methods to locate zerces(or fixed points) of highly nonlinearmappirgs. Due to the Jexicographical system, the methods are feasible without exceptions Thispaper presents a geemetrical ... PL homotopy metheds are effective methods to locate zerces(or fixed points) of highly nonlinearmappirgs. Due to the Jexicographical system, the methods are feasible without exceptions Thispaper presents a geemetrical interpretation of the without-exception feasibility. 展开更多
关键词 Th Pi PL A GEOMETRICAL INTERPRETATION OF THE WITHOUT-EXCEPTION FEASIBILITY OF PL homotopy methodS line node 立切 二七 七印
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Computation of Load Flow Problems with Homotopy Methods
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作者 陈玉荣 蔡大用 《Tsinghua Science and Technology》 SCIE EI CAS 2001年第4期340-343,共4页
Load flow computations are the basis for voltage security assessments in power systems. All of the flow equation solutions must be computed to explore the mechanisms of voltage instability and voltage collapse. Conv... Load flow computations are the basis for voltage security assessments in power systems. All of the flow equation solutions must be computed to explore the mechanisms of voltage instability and voltage collapse. Conventional algorithms, such as Newton's methods and its variations, are not very desirable because they can not be easily used to find all of the solutions. This paper investigates homotopy methods which can be used for numerically computing the set of all isolated solutions of multivariate polynomial systems resulting from load flow computations. The results significantly reduce the number of paths being followed. 展开更多
关键词 load flow computations homotopy methods Bezout number Bernshtein Khoranski Kushnirenko (BKK) bound
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A FINITE-DIFFERENCE RELAXATION SCHEME BASED ON BOTH MULTIGRID TECHNIQUES AND HOMOTOPY METHOD FOR 2D STEADY-STATE NAVIER-STOKES EQUATIONS
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作者 Liao Shi-jun, Zhu Ji-maoDepartment of Naval Architecture & Ocean Engineering, Shanghai Jiao Tang University,Shanghai 200030, P. R. China 《Journal of Hydrodynamics》 SCIE EI CSCD 1997年第1期42-55,共14页
In this paper, multigrid techniques together with homotopy method are applied to propose a kind of finite-difference relaxation scheme for 2D steady-state Navier-Stokes equations. The proposed numerical scheme can giv... In this paper, multigrid techniques together with homotopy method are applied to propose a kind of finite-difference relaxation scheme for 2D steady-state Navier-Stokes equations. The proposed numerical scheme can give convergent results for viscous flows with high Reynolds number. As an example, the results of shear-driven cavity flow with high Reynolds number up to 25000 on fine grid 257×257 are given. 展开更多
关键词 2D Navier-Stokes equations multigrid techniques homotopy method shear-driven cavity flow
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A HOMOTOPY METHOD OF SWITCHING SOLUTION BRANCHES AT THE PITCHFORK BIFURCATION POINT
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作者 Cong, Y.-H. Zhu, Z.-Y. 《Journal of Computational Mathematics》 SCIE EI CSCD 2001年第3期299-308,共10页
Provides information on a study which proposed a continuation method for switching solution branches at a pitchfork point. Problem of the standard pitchfork; Information on the systems of equations; Numerical examples... Provides information on a study which proposed a continuation method for switching solution branches at a pitchfork point. Problem of the standard pitchfork; Information on the systems of equations; Numerical examples of the efficiency of the proposed switching method. 展开更多
关键词 homotopy method switching solution branches pitchfork point
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Homotopy Continuation Method for Linear Complementarity Problems
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作者 刘国新 于波 《Northeastern Mathematical Journal》 CSCD 2004年第3期309-316,共8页
It is well known that a linear complementarity problem (LCP) can be formulated as a system of nonsmooth equations F(x) = 0, where F is a map from Rninto itself. Using the aggregate function, we construct a smooth Newt... It is well known that a linear complementarity problem (LCP) can be formulated as a system of nonsmooth equations F(x) = 0, where F is a map from Rninto itself. Using the aggregate function, we construct a smooth Newton homotopy H(x,t) = 0. Under certain assumptions, we prove the existence of a smooth path defined by the Newton homotopy which leads to a solution of the original problem, and study limiting properties of the homotopy path. 展开更多
关键词 linear complementarity aggregate function homotopy method
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Nonlinear oscillations with parametric excitation solved by homotopy analysis method 被引量:5
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作者 Jianmin Wen Zhengcai Cao 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2008年第3期325-329,共5页
An analytical technique, namely the homotopy analysis method (HAM), is used to solve problems of nonlinear oscillations with parametric excitation. Unlike perturbation methods, HAM is not dependent on any small phys... An analytical technique, namely the homotopy analysis method (HAM), is used to solve problems of nonlinear oscillations with parametric excitation. Unlike perturbation methods, HAM is not dependent on any small physical parameters at all, and thus valid for both weakly and strongly nonlinear problems. In addition, HAM is different from all other analytic techniques in providing a simple way to adjust and control convergence region of the series solution by means of an auxiliary parameter h. In the present paper, a periodic analytic approximations for nonlinear oscillations with parametric excitation are obtained by using HAM, and the results are validated by numerical simulations. 展开更多
关键词 Nonlinear oscillation Parametric excitation Series solutions homotopy analysis method
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