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iterative algorithms for solving a class of complex conjugate and transpose matrix equations

APPLIED MATHEMATICS AND COMPUTATION 2011年第21期217卷 8343-8353页

作者： Wu, Ai-Guo Lv, Lingling Duan, Guang-Ren Shenzhen Grad Sch Harbin Inst Technol Shenzhen 518055 Peoples R China N China Inst Water Conservancy & Hydroelect Power Inst Elect Power Zhengzhou 450011 Peoples R China Harbin Inst Technol Ctr Control Theory & Guidance Technol Harbin 150001 Peoples R China

This paper is concerned with iterative solutions to a class of complex matrix equations, which include some previously investigated matrix equations as special cases. By applying the hierarchical identification principle, an iterative algorithm is constructed to solve this class of matrix equations. A sufficient condition is presented to guarantee that the proposed algorithm is convergent for an arbitrary initial matrix with a real representation of a complex matrix as tools. By using some properties of the real representation, a convergence condition that is easier to compute is also given in terms of original coefficient matrices. A numerical example is employed to illustrate the effectiveness of the proposed methods. (C) 2011 Elsevier Inc. All rights reserved.

关键词： iterative algorithm Conjugate Transpose Complex matrix equations Real representation 2-Norm

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An iterative Interference Alignment Scheme for the SISO Interference Channel

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WIRELESS PERSONAL COMMUNICATIONS 2012年第3期67卷 707-720页

作者： Shen, Hui Li, Bin Huawei Technol Dept Corp Res Shenzhen Peoples R China Huawei Technol Wireless Res Dept Shenzhen Peoples R China

In this paper, we propose a novel iterative interference alignment (IA) scheme for the single-input single-output (SISO) interference channel system using minimum total mean square error criterion under the individual transmitter power constraints. We show that interference alignment under such criterion could be realized through an iterative algorithm. The convergence of the proposed algorithm is discussed. We also proposed a robust MMSE-based iterative design with imperfect channel state information. Simulation results, compared with several existing IA schemes, have shown that the proposed method could effectively improve the BER performance of the SISO interference channel system while maintaining the same degree of freedom as Cadambe-Jafar scheme. The proposed robust MMSE-based iterative interference alignment scheme is shown to be less sensitive to channel estimation error.

关键词： SISO interference channel Interference alignment iterative algorithm Robust

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Tangent Orbital Rendezvous with the Same Direction of Terminal Velocities

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2012年第1期35卷 335-340页

作者： Zhang, Gang Zhou, Di Bai, Xiaoli Harbin Inst Technol Dept Control Sci & Engn Harbin 150001 Peoples R China Texas A&M Univ Dept Aerosp Engn College Stn TX 77843 USA

This Note studies the tangent orbit rendezvous technique, which requires that two cooperative spacecraft arrive at an assigned point with the same velocity direction after the same transfer time. The transfer time for fixed initial and final points is a function only of the initial flight-path angle. Then, the solutions can be obtained by setting two transfer times equal. There are many solutions for the multiple-revolution case, whereas for two given revolution numbers of the chief's and chaser's orbits, there can be zero, one, or two solutions. Although its energy consumption is not optimal, tangent orbit rendezvous process can be easily controlled for a manned spacecraft rendezvous problem. This proposed technique can be used in some special rendezvous and docking problems with simple controls.

关键词： Spacecraft Rendezvous Terminal Velocity Flight Path Angle Elliptical Transfer Orbit Earth Centered Inertial Apogee Altitude Energy Consumption Secant Method iterative algorithm Kepler's Equation

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Process conditions optimization in Al-Cu alloy matrix composites

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POWDER TECHNOLOGY 2012年 225卷 101-106页

作者： Mazahery, Ali Shabani, Mohsen Ostad Islamic Azad Univ Lenjan Branch Dept Mat Sci Esfahan Iran

Based on the idea of survival of the fittest and natural selection. a class of parallel iterative algorithm with specific learning ability was introduced to find the optimal solidification conditions and produce 2024 Al alloy with minimum wear and maximum strength. This novel algorithm repeats evaluation, selection, crossover and mutation after initialization until the stopping condition is satisfied. Mechanical and wear properties of unreinforced 2024 Al alloy and composites with different vol.% of coated boron carbide particles were also experimentally investigated. It is seen that incorporation of hard particles to 2024 aluminum alloy contributes to the improvement of the mechanical properties and wear resistance of the base alloy to a great extent. (C) 2012 Elsevier B.V. All rights reserved.

关键词： Aluminum matrix iterative algorithm Analytical methods

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Precoding scheme for space-time-coded multiple-input-multiple-output system with estimation error and feedback delay in Rayleigh fading channel

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IET COMMUNICATIONS 2012年第16期6卷 2525-2533页

作者： Yu, X. Yin, X. Leung, S. H. Rui, Y. Nanjing Univ Aeronaut & Astronaut Dept Elect Engn Nanjing Jiangsu Peoples R China City Univ Hong Kong Dept Elect Engn Hong Kong Hong Kong Peoples R China Chinese Acad Sci Shanghai Adv Res Inst Shanghai Peoples R China

In this study, a precoding scheme for minimising bit error rate (BER) subject to a power constraint for space-time-coded multiple-input-multiple-output systems over flat Rayleigh fading channel in the presence of channel estimation error and feedback delay is presented, it includes the precoding with estimation error or feedback delay only as its special cases. With this scheme, an algorithm for attaining the optimal power allocation across multiple beams is developed. It is shown that the Lagrange multiplier for the constrained optimisation does exist and is unique. A practical iterative algorithm based on Newton's method for finding the Lagrange multiplier is proposed. Generally, the optimal power control may result in negative power allocation to some beams. A necessary and sufficient condition for the beams having positive power control is developed that simplifies the optimisation procedure. Simulation results show that the developed precoding scheme can provide BER lower than the equal power allocation scheme and the existing precoding scheme, but has performance degradation when compared with the precoding scheme with estimation error or feedback delay only.

关键词： negative power allocation bit error rate error statistics space-time codes Codes precoding channel estimation optimal power control feedback delay space-time-coded multiple-input-multiple-output system Lagrange multiplier iterative algorithm flat Rayleigh fading channel MIMO system estimation theory precoding scheme positive power control multiple beams channel estimation error constrained optimisation Newton method Interpolation and function approximation (numerical analysis) BER Radio links and equipment Communication channel equalisation and identification Rayleigh channels MIMO communication Other topics in statistics

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iterative Narrowband-Based Graph Cuts Optimization for Geodesic Active Contours With Region Forces (GACWRF)

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IEEE TRANSACTIONS ON IMAGE PROCESSING 2012年第1期21卷 284-296页

作者： Tao, Wenbing Huazhong Univ Sci & Technol Inst Pattern Recognit & Artificial Intelligence Wuhan 430074 Peoples R China Huazhong Univ Sci & Technol State Key Lab Multispectral Informat Proc Technol Wuhan 430074 Peoples R China

In this paper, an iterative narrow-band-based graph cuts (INBBGC) method is proposed to optimize the geodesic active contours with region forces (GACWRF) model for interactive object segmentation. Based on cut metric on graphs proposed by Boykov and Kolmogorov, an NBBGC method is devised to compute the local minimization of GAC. An extension to an iterative manner, namely, INBBGC, is developed for less sensitivity to the initial curve. The INBBGC method is similar to graph-cuts-based active contour (GCBAC) presented by Xu et al., and their differences have been analyzed and discussed. We then integrate the region force into GAC. An improved INBBGC (IINBBGC) method is proposed to optimize the GACWRF model, thus can effectively deal with the concave region and complicated real-world images segmentation. Two region force models such as mean and probability models are studied. Therefore, the GCBAC method can be regarded as the special case of our proposed IINBBGC method without region force. Our proposed algorithm has been also analyzed to be similar to the Grabcut method when the Gaussian mixture model region force is adopted, and the band region is extended to the whole image. Thus, our proposed IINBBGC method can be regarded as narrow-band-based Grabcut method or GCBAC with region force method. We apply our proposed IINBBGC algorithm on synthetic and real-world images to emphasize its performance, compared with other segmentation methods, such as GCBAC and Grabcut methods.

关键词： Geodesic active contours (GAC) graph cuts iterative algorithm narrowband region forces

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Solving periodic Lyapunov matrix equations via finite steps iteration

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IET CONTROL THEORY AND APPLICATIONS 2012年第13期6卷 2111-2119页

作者： Cai, G. -B. Hu, C. -H. Xian Res Inst High Tech Dept Automat Xian 710025 Shaanxi Peoples R China

Periodic Lyapunov matrix equations play important roles in stability analysis and stabilisation of discrete-time periodic systems. In this paper, an iterative algorithm for solving periodic Lyapunov matrix equations is established. It is shown that the proposed iteration converges to the unique solution of the considered matrix equations at finite steps with arbitrary initial condition despite the stability of the associated discrete-time periodic linear systems. Both the reverse-time and forward-time discrete-time periodic Lyapunov matrix equations are considered. Numerical examples are worked out to illustrate the effectiveness of the proposed algorithm.

关键词： reverse-time discrete-time periodic Lyapunov matrix equations Time-varying control systems stability Stability in control theory stability analysis iteration convergence Lyapunov matrix equations linear systems discrete-time periodic linear system Linear algebra (numerical analysis) convergence arbitrary initial condition Interpolation and function approximation (numerical analysis) forward-time discrete-time periodic Lyapunov matrix equations discrete-time periodic system Optimal control iterative methods Discrete control systems stabilisation iterative algorithm finite steps iteration numerical example discrete time systems periodic control

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Noniterative Instantaneous Impact Point Prediction Allgorithm for Launch Operations

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2012年第2期35卷 645-648页

作者： Ahn, Jaemyung Roh, Woong-Rae Korea Adv Inst Sci & Technol Dept Aerosp Engn Taejon 305701 South Korea Korea Aerosp Res Inst Mission Design Dept Taejon 305333 South Korea

The instantaneous impact point (DP) in launch operations is defined as the touchdown point of a rocket with an assumption of an immediate end of the propelled flight [1-3]. The IIP is very important information to judge whether the flight is normal or not, and it should be continuously monitored during the whole flight so that proper actions be taken in an emergency to protect human life and property. Therefore, the real-time prediction and monitoring of the IIP is one of the key safety requirements.

关键词： Prediction algorithms Rocket Trajectories Earth Earth Centered Inertial Earth Centered Earth Fixed Flight Path Angle Sun Synchronous Orbit iterative algorithm Federal Aviation Administration Numerical Integration

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On the generalized reflexive and anti-reflexive solutions to a system of matrix equations

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LINEAR ALGEBRA AND ITS APPLICATIONS 2012年第11期437卷 2793-2812页

作者： Dehghan, Mehdi Hajarian, Masoud Shahid Beheshti Univ Fac Math Sci Dept Math GC Tehran 19839 Iran Amirkabir Univ Technol Fac Math & Comp Sci Dept Appl Math Tehran 15914 Iran

Let P and Q be two generalized reflection matrices, i.e., P = P-H, P-2 = I and Q = Q(H), Q(2) = I. An n x n matrix A is said to be generalized reflexive (generalized anti-reflexive) with respect to the matrix pair (P: Q) if A = PAQ (A = -PAQ). It is obvious that any n x m matrix is also a generalized reflexive with respect to the matrix pair (I-n: I-m). By extending the conjugate gradient least square (CGLS) approach, the present paper treats two iterative algorithms to solve the system of matrix equations {F-1(X) = A(1), F-2(X) = A(2), . . . . . . . . . F-m(X) = A(m), (including the Sylvester and Lyapunov matrix equations as special cases) over the generalized reflexive and anti-reflexive matrices, where F-1, F-2, . . . , F-m are the linear operators from C-nxn onto C-rixSi and A(i) is an element of C-rixSi for i = 1, 2, . . . . m. When this system is consistent over the generalized reflexive (generalized anti-reflexive) matrix, it is proved that the first (second) iterative algorithm converges to a generalized reflexive (generalized anti-reflexive) solution for any initial generalized reflexive (generalized anti-reflexive) matrix. Also the first (second) iterative algorithm can obtain the least Frobenius norm generalized reflexive (generalized anti-reflexive) solution for special initial generalized reflexive (generalized anti-reflexive) matrix. Furthermore, the optimal approximation generalized reflexive (generalized anti-reflexive) solution to a given generalized reflexive (generalized anti-reflexive) matrix can be derived by finding the least Frobenius norm generalized reflexive (generalized anti-reflexive) solution of a new system of matrix equations. Finally, we test the proposed iterative algorithms and show their effectiveness using numerical examples. (c) 2012 Elsevier Inc. All rights reserved.

关键词： Generalized reflexive matrix Generalized anti-reflexive matrix iterative algorithm System of matrix equations

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Reward-Lifetime Scheduling Approach to the Autonomous Spacecraft Power Management Problem

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JOURNAL OF AEROSPACE COMPUTING INFORMATION AND COMMUNICATION 2012年第2期9卷 58-67页

作者： Shriver, Patrick M. Palo, Scott E. Zenick, Raymond G. Balas, Mark J. Metatech Corp Albuquerque NM 87106 USA Univ Colorado Dept Aerosp Engn Sci Boulder CO 80309 USA AeroAstro Inc Power & Commun Grp Ashburn VA 20147 USA Univ Wyoming Dept Elect & Comp Engn Laramie WY 82071 USA

A high-level characterization of spacecraft operations and subsystems is used to formally define the spacecraft power management problem. Two objectives of maximizing the payload reward and minimizing the battery discharge are optimized in the Pareto-optimal sense. These objectives are subject to one constraint of maintaining a minimum battery voltage. Even with simplifying assumptions, this formulation is shown to be computationally intractable. Nonetheless, a formal proof of optimal substructure is used to develop an optimal dynamic programming solution. This algorithm is intended to reduce the labor-intensive operations problem of manually generating a 'good enough' schedule to one of selecting an optimal schedule.

关键词： Spacecraft Performance Spacecraft Subsystem Eclipses Los Alamos National Laboratories Pareto Optimality Ground Station Telemetry Automated Planning and Scheduling Secondary Batteries iterative algorithm

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