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Bounds for Input- and State-to-Output Properties of Uncertain Linear Systems ∗

IFAC-PapersOnLine 2015年第14期48卷 1-6页

作者： Giorgio Valmorbida Dhruva Raman James Anderson Department of Engineering Science University of Oxford 17 Parks Road OX1 3PJ Oxford UK

We consider the effect of parametric uncertainty on properties of Linear Time Invariant systems. Traditional approaches to this problem determine the worst-case gains of the system over the uncertainty set. Whilst such approaches are computationally tractable, the upper bound obtained is not necessarily informative in terms of assessing the influence of the parameters on the system performance. We present theoretical results that lead to simple, convex algorithms producing parametric bounds on the ℒ 2 -induced input-to-output and state-to-output gains as a function of the uncertain parameters. These bounds provide quantitative information about how the uncertainty affects the system.

关键词： Robust control Uncertainty analysis Linear systems semi-definite programming

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Probabilistic Control of Uncertain Linear Systems Using Stochastic Reachability

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IFAC-PapersOnLine 2015年第14期48卷 167-173页

作者： Leonhard Asselborn Olaf Stursberg Control and System Theory EECS University of Kassel Germany

This paper proposes an approach to algorithmically synthesize control strategies for set-to-set transitions of discrete-time uncertain systems based on reachable set computations in a stochastic setting. For given Gaussian distributions of the initial states and disturbances, state sets wich are reachable to a chosen confidence level under the effect of time-variant control laws are computed by using principles of the ellipsoidal calculus. The proposed algorithm iterates over LMI-constrained semi-definite programming problems to compute probabilistically stabilizing controllers, while ellipsoidal input constraints are considered. An example for illustration is included.

关键词： Ellipsoidal calculus discrete time systems uncertain dynamics stochastic reachability linear matrix inequalities semi-definite programming stochastic stability

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Output Feedback Controller Sparsification via H 2 -Approximation ∗

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IFAC-PapersOnLine 2015年第22期48卷 112-117页

作者： R. Arastoo M. Bahavarnia M.V. Kothare N. Motee Department of Mechanical Engineering and Mechanics Packard Lab. Lehigh University Bethlehem PA Department of Chemical and Biomolecular Engineering Iaccoca Hall Lehigh University Bethlehem PA

The problem of optimal sparse output feedback control design for continuous linear time invariant systems is considered. This work adopts the concept of % p -approximation to develop an optimization algorithm capable of synthesizing a structured sparse static controller gain for which the overall closed loop system exhibits empirical frequency characteristics resembling that of the system controlled with a pre-designed centralized controller. We, moreover, modify our optimization problem so that the control signal generated by the sparse controller falls into the vicinity of the centralized control input, in the sense of L norm. Furthermore, we show that our optimization problem can be equivalently reformulated into a rank constrained problem for which we propose to use a tailored version of Alternating Direction Method of Multipliers (ADMM) as a computationally efficient algorithm to sub-optimally solve it. Finally, we illuminate the effectiveness of our proposed method by testing it on randomly generated sample network models.

关键词： Sparsity Promoting Control H p -approximation Weighted l 1 minimization Alternating Direction Method of Multipliers semi-definite programming

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semi-definite programming APPROACH TO SENSOR NETWORK NODE LOCALIZATION WITH ANCHOR POSITION UNCERTAINTY

SEMI-DEFINITE PROGRAMMING APPROACH TO SENSOR NETWORK NODE LO...

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IEEE International Conference on Acoustics, Speech and Signal Processing

作者： Lui, Kenneth W. K. Ma, W-K. So, H. C. Chan, Frankie K. W. City Univ Hong Kong Dept Elect Engn Tat Chee Ave Kowloon Hong Kong Peoples R China Chinese Univ Hong Kong Dept Elect Engn Shatin Peoples R China

ISBN: (纸本)9781424423538

The problem of node localization in a wireless sensor network (WSN) with the use of the incomplete and noisy distance measurements between nodes as well as anchor position information is currently an an important yet challenging research topic. Most WSN localization studies at present have assumed that the anchor positions are perfectly known which is not valid in the underwater and underground scenarios. In this paper, semi-definite programming (SDP) algorithms are devised for finding the localizations of unknown-position nodes in the presence of anchor position uncertainty. Computer simulations are included to contrast the performance of the proposed algorithms with the conventional SDP method and Cramer-Rao lower bound.

关键词： sensor networks node localization range measurements semi-definite programming

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Parameter estimation of brushless doubly-fed induction generator based on steady experimental results

Parameter estimation of brushless doubly-fed induction gener...

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IEEE Energy Conversion Congress and Exposition

作者： J. Su Y. Chen L. Sun X. Liu Y. Kang State Key Lab. of Adv. Electromagn. Eng. & Technol. Huazhong Univ. of Sci. & Technol. Wuhan China

ISBN: (纸本)9781467371520

The brushless doubly-fed induction generator (BDFIG) cancels brushes on the basis of the doubly-fed induction generator by adding a set of stator and rotor windings to guarantee higher reliability. However this also leads to more complicated coupling and more difficulties of parameter measurement. This paper proposes a new and experiment-based method for BDFIG parameter estimation. With this method, currents and voltages under several simple and stable conditions are measured and the parameters required for modeling and control can be calculated. This paper discusses the basic principles and the estimation process of the proposed method in detail. A group of experiment data from a 64kW BDFIG is also used to illustrate the estimation procedure. The estimated parameters are then substituted into the mathematical simulation model and compared with the experimental results. Both steady and dynamic waveforms are well matched, which implies the accuracy of the estimated parameters. The proposed method could also be applied to other types of machines to achieve better control.

关键词： brushless doubly-fed induction generator experiment-based parameter estimation semi-definite programming

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A convex relaxation framework for a class of semi-supervised learning methods and its application in pattern recognition

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ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE 2014年 35卷 335-344页

作者： Yang, Liming Wang, Laisheng Gao, Yongping Sun, Qun Zhao, Tengyang China Agr Univ Coll Sci Beijing 100083 Peoples R China Capital Normal Univ Beijing 100048 Peoples R China China Agr Univ Coll Biotechnol Beijing 100193 Peoples R China Univ London Imperial Coll Sci Technol & Med London SW7 2AZ England

semi-supervised learning has been an attractive research tool for using unlabeled data in pattern recognition. Applying a novel semi-definite programming (SDP) relaxation strategy to a class of continuous semi-supervised support vector machines ((SVMs)-V-3), a new convex relaxation framework for the (SVMs)-V-3 is proposed based on SDP. Compared with other SDP relaxations for (SVMs)-V-3, the proposed methods only require solving the primal problems and can implement L-1-norm regularization. Furthermore, the proposed technique is applied directly to recognize the purity of hybrid maize seeds using near-infrared spectral data, from which we find that the proposed method achieves equivalent performance to the exact solution algorithm for solving the (SVM)-V-3 in different spectral regions. Experiments on several benchmark data sets demonstrate that the proposed convex technique is competitive with other SDP relaxation methods for solving semi-supervised SVMs in generalization. (c) 2014 Elsevier Ltd. All rights reserved.

关键词： semi-supervised learning Support vector machine semi-definite programming Purity of hybrid seeds

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New reformulations for probabilistically constrained quadratic programs

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2014年第3期233卷 550-556页

作者： Hsia, Yong Wu, Baiyi Li, Duan Beihang Univ Sch Math & Syst Sci Minist Educ State Key Lab Software Dev EnvironmLMIB Beijing 100191 Peoples R China Chinese Univ Hong Kong Dept Syst Engn & Engn Management Shatin Hong Kong Peoples R China

The mixed integer quadratic programming (MIQP) reformulation by Zheng, Sun, Li, and Cui (2012) for probabilistically constrained quadratic programs (PCQP) recently published in EJOR significantly dominates the standard MIQP formulation (Ruszczynski, 2002: Benati & Rizzi, 2007) which has been widely adopted in the literature. Stimulated by the dimensionality problem which Zheng et al. (2012) acknowledge themselves for their reformulations, we study further the characteristics of PCQP and develop new MIQP reformulations for PCQP with fewer variables and constraints. The results from numerical tests demonstrate that our reformulations clearly outperform the state-of-the-art MIQP in Zheng et al. (2012). (C) 2013 Elsevier B.V. All rights reserved.

关键词： Quadratic programming Probabilistic constraint semi-definite programming Mixed-integer quadratic program Value-at-risk/variance portfolio selection

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Wireless capacity with arbitrary gain matrix

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THEORETICAL COMPUTER SCIENCE 2014年第0期553卷 57-63页

作者： Halldorsson, Magnus M. Mitra, Pradipta Reykjavik Univ Sch Comp Sci ICE TCS IS-101 Reykjavik Iceland

Given a set of wireless links, a fundamental problem is to find the largest subset that can transmit simultaneously, within the SINR model of interference. Significant progress on this problem has been made in recent years. In this note, we study the problem in the setting where we are given a fixed set of arbitrary powers each sender must use, and an arbitrary gain matrix defining how signals fade. This variation of the problem appears immune to most algorithmic approaches studied in the literature. Indeed it is very hard to approximate since it generalizes the max independent set problem. Here, we propose a simple semi-definite programming approach to the problem that yields constant factor approximation, if the optimal solution is strictly larger than half of the input size. (C) 2013 Published by Elsevier B.V.

关键词： Wireless networks SINR model semi-definite programming

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Algorithms for Secrecy Guarantee With Null Space Beamforming in Two-Way Relay Networks

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2014年第8期62卷 2111-2126页

作者： Yang, Yunchuan Sun, Cong Zhao, Hui Long, Hang Wang, Wenbo Beijing Univ Posts & Telecommun Minist Educ Wireless Signal Proc & Network Lab Key Lab Universal Wireless Commun Beijing 100088 Peoples R China Beijing Univ Posts & Telecommun Sch Sci Beijing 100876 Peoples R China

In this paper, we consider a two-way relay network with two sources and multiple cooperative relays in the presence of an eavesdropper. To guarantee the secrecy, a null space beamforming scheme is applied, where the relay beamforming vector lies in the nullspace of the equivalent channel of relay link from two sources to the eavesdropper. Our goal is to obtain the optimal beamforming vector as well as two sources' transmit power subject to various criteria. We propose three different approaches and solve them in an alternating iterative way, where subproblems for solving beamforming and sources' power are formulated in each iteration, respectively. First, we minimize the total transmit power under secrecy rate constraint at two sources. For beamforming vector subproblem, two different methods, semi-definite programming (SDP) and sequential quadratic programming (SQP), are proposed, where we analyze and verify SQP has lower complexity than SDP. Second, we maximize the secrecy sum rate, subject to total transmit power constraint. The beamforming vector subproblem is equivalent to a generalized Rayleigh quotient problem with rank constraint. Third, the problem of minimum per-user secrecy rate maximization under the total power constraint is investigated for user fairness. An iterative procedure utilizing the SDP with bisection search method is proposed to solve beamforming subproblem. In each approach the subproblem with two sources' power is formulated as a single variable problem and solved by Newton's method with line search. Simulation results demonstrate the validity of proposed approaches and algorithms for both symmetric and asymmetric scenarios.

关键词： Null space beamforming physical layer security semi-definite programming sequential quadratic programming

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Calibrating low-rank correlation matrix problem: an SCA-based approach

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OPTIMIZATION METHODS & SOFTWARE 2014年第3期29卷 561-582页

作者： Wang, Bo Zhang, Liwei Dalian Univ Technol Sch Math Sci Dalian 116023 Peoples R China

Rank-constrained nearest correlation matrix problems, weighted or not, are reformulated into difference of convex (DC) functions constrained optimization problems. A general sequential convex approximation (SCA) approach for a DC-constrained optimization problem is developed. To overcome difficulties encountered in solving the convex approximation subproblems in the SCA approach, an SCA-based nonsmooth equation approach is proposed to solve the specific rank-constrained problem. In this approach, we use a simple iteration scheme for updating the multiplier variable corresponding to the rank constraint, and an inexact smoothing Newton method for calculating the primal variable and the multiplier variable corresponding to the linear constraint. Numerical experiments are reported and they illustrate the efficiency of our approach.

关键词： DC programming correlation matrix low rank semi-definite programming H-weighted SCA

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