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7th World Congress on Intelligent Control and Automation

作者： Zhang, Xuelian Hu, Lisheng Cao, Guangyi Shanghai Jiao Tong Univ Dept Automat Shanghai Peoples R China

ISBN: (纸本)9781424421138

The constraints make a process nonlinear even for a linear system in process control. A robust model predictive control (MPC) algorithm for the linear systems with disturbance by explicitly considering the constraints is proposed in this paper. By introducing an auxiliary system to the uncertain MPC system, the robust H-2 problem is converted to an LQ problem. Then the constraint can be exploited explicitly. Based on polynomial matrix description of the plant, the robust MPC algorithm is formulated as an optimization problem of a semi-definite programming. The utility of the proposed algorithm is demonstrated through a numerical example.

关键词： Model predictive control Youla-Ku era parametrization polynomial matrix fraction semi-definite programming linear system

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Non-negative Sparse Principal Component Analysis for Multidimensional Constrained Optimization

Non-negative Sparse Principal Component Analysis for Multidi...

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10th Pacific Rim International Conference on Artificial Intelligence (PRICAI 2008)

作者： Duong, Thanh D. X. Duong, Vu N. Ton Duc Thang Univ Ho Chi Minh City Vietnam Univ Sci VNU HCM Ho Chi Minh City Vietnam EUROCONTROL Experimental Ctr Bois France

ISBN: (纸本)9783540891963

One classic problem in air traffic management (ATM) has been the problem of detection and resolution of conflicts between aircraft. Traditionally, a conflict between two aircraft is detected whenever the two protective cylinders surrounding the aircraft intersect. In Trajectory-based Air Traffic Management, a baseline for the next generation of air traffic management system, we suggest that these protective cylinders be deformable volumes induced by variations in weather information such as wind speed and directions subjected to uncertainties of future states of trajectory controls. Using contact constraints oil deforming parametric surfaces of these protective volumes, a constrained minimization algorithm is proposed to compute collision between two deformable bodies, and a differential optimization scheme is proposed to resolve detected conflicts. Given the covariance matrix representing the state of aircraft trajectory and its control and objective functions, we consider the problem of maximizing the variance explained by a particular linear combination of the input variables where the coefficients in this combination are required to be non-negative, and the number of non-zero coefficients is constrained (e.g. state of trajectory and estimated time of arrival over one change point). Using convex relaxation and re-weighted l(1) technique, we reduce the problem to solving some semi-definite programming ones, and reinforce the non-negative principal components that satisfy the sparsity constraints. Numerical results show that the method presented in this paper is efficient and reliable in practice. Since the proposed method can be applied to a wide range of dynamic modeling problems such as collision avoidance in dynamic autonomous robots environments, dynamic interactions with 4D computer animation scenes, financial asset trading, or autonomous intelligent vehicles, we also attempt to keep all descriptions as general as possible.

关键词： principal component analysis semi-definite relaxation semi-definite programming l(1)-minimization iterative reweighting

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Distributed peer-to-peer multiplexing using ad hoc relay networks

Distributed peer-to-peer multiplexing using ad hoc relay net...

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33rd IEEE International Conference on Acoustics, Speech and Signal Processing

作者： Fazeli-Dehkordy, Siavash Gazor, Saeed Shahbazpanahi, Shahram Queens Univ Dept Elect & Comp Eng Walter Light Hall Kingston ON K7L 3N6 Canada Univ Ontario Inst Technol Fac Engn & Appl Sci London ON LIH 7K4 Canada

ISBN: (纸本)9781424414833

We consider an ad hoc network consisting of d source-destination pairs and R relaying nodes. Each source wishes to transmit its data to its corresponding destination through the relay network. Each relay in the network transmits a properly scaled version of its received signal thereby cooperating with other relays to deliver each source's data to the corresponding destination. Assuming a minimal cooperation among the relaying nodes, we design a distributed beamformer such that the total relay transmit power dissipated by all relays is minimized while, at the same time, the quality of services at all destinations are guaranteed to be above certain pre-defined thresholds. We show that using a semi-definite relaxation approach, the power minimization problem can be turned into a semi-definite programming (SDP) optimization, and therefore, it can be solved efficiently using interior point methods. Our results show that the distributed relay multiplexing is possible and may be beneficial depending on the channel conditions.

关键词： distributed beamforming relay networks semi-definite programming convex feasibility problem distributed signal processing

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Robust adaptive beamforming for general-rank signal models using positive semi-definite covariance constraint

Robust adaptive beamforming for general-rank signal models u...

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33rd IEEE International Conference on Acoustics, Speech and Signal Processing

作者： Chen, Haihua Gershman, Alex B. Tech Univ Darmstadt Commun Syst Grp D-64283 Darmstadt Germany

ISBN: (纸本)9781424414833

In this paper, we develop an improved approach to the worst-case robust adaptive beamforming for general-rank signal models by means of taking into account the positive semi-definite constraint for the mismatched signal covariance matrix. The resulting robust adaptive beamforming problem is solved in an iterative way using semi-definite programming (SDP) at each iteration. Simulation results show that the proposed technique achieves a substantially improved performance as compared to the current robust adaptive beamforming techniques developed for the general-rank signal environments.

关键词： robust adaptive beamforming semi-definite programming worst-case performance optimization

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Per-Antenna Power Constrained MIMO Transceivers Optimized for BER

Per-Antenna Power Constrained MIMO Transceivers Optimized fo...

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42nd Asilomar Conference on Signals, Systems and Computers

作者： Weng, Chin-Chih Vaidyanathan, P. P. CALTECH Dept Elect Engn Pasadena CA 91125 USA

ISBN: (纸本)9781424429400

This paper considers the linear transceiver optimization problem for multi-carrier multiple-input multiple-output (MIMO) channels with per-antenna power constraints. Because in practical implementations each antenna is limited individually by its equipped power amplifier, this paper adopts the more realistic per-antenna power constraints, in contrast to the conventional sum-power constraint on the transmitter antennas. Assuming perfect channel knowledge both at the transmitter and the receiver, the optimization problem can be transformed into a semi-definite program (SDP), which can be solved by convex optimization tools. Furthermore, several objective functions of the MIMO system,, including average bit error rate, can also be optimized by the introduction of the majorization theory.

关键词： Per-antenna Constraints BER Optimization Schur Convexity semi-definite programming MIMO Transceivers

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Unsupervised Support Vector Machines with Perturbations

Unsupervised Support Vector Machines with Perturbations

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2nd International Symposium on Intelligent Information Technology Application

作者： Kong, Xiangwei Zhao, Kun Deng, Naiyang China Agr Univ Coll Sci Beijing Peoples R China Beijing Jiaotong Univ Sch Econ & Management Beijing Peoples R China Beihang Wuzi Univ Logist Sch Beijing Area Logist Syst & Technol Major Lab Beijing 100191 Peoples R China

ISBN: (纸本)9780769534978

Support Vector Machines (SVMs) have been dominant learning techniques for almost ten years, and mostly applied to supervised learning problems. Recently nice results are obtained by two-class unsupervised and semi-supervised classification algorithms where the optimization problems based on Bounded C-SVMs, Bounded nu-SVMs and Lagrangian SVMs respectively are relaxed to semi-definite programming (SDP). These support vector methods implicitly assume, that training data in the optimization problems are known exactly. But in practice, the training data are usually subjected to measurement noise. Zhao et al proposed robust version to unsupervised and semi-supervised classification problems based on Bounded C-SVMs, which need to find the dual problem twice. In this paper we propose unsupervised classification algorithm based on primal problem of standard SVMs with perturbations, which directly relaxes it with label variables to a semi-definite programming;Numerical results confirm the robustness of the proposed method.

关键词： Support Vector Machines semi-definite programming unsupervised learning robust

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EVERY 2-CSP ALLOWS NONTRIVIAL APPROXIMATION

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COMPUTATIONAL COMPLEXITY 2008年第4期17卷 549-566页

作者： Hastad, Johan Royal Inst Technol Sch Comp Sci & Commun S-10044 Stockholm Sweden

We use semidefinite programming to prove that any constraint satisfaction problem in two variables over any domain allows an efficient approximation algorithm that does better than picking a random assignment. Specifically we consider the case when each variable can take values in [d] and that each constraint rejects t out of the d(2) possible input pairs. Then, for some universal constant c, we can, in probabilistic polynomial time, find an assignment whose objective value is, in expectation, within a factor 1 - t/d(2) + ct/d(4) log d of optimal, improving on the trivial bound of 1 - t/d(2).

关键词： semi-definite programming constraint satisfaction approximation algorithms

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Quantum operation quantum Fourier transform and semi-definite programming

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PHYSICS LETTERS A 2004年第1-2期323卷 48-56页

作者： Duan, RY Ji, ZF Feng, Y Ying, MS Tsinghua Univ State Key Lab Intelligent Technol & Syst Dept Comp Sci & Technol Beijing 100084 Peoples R China

We analyze a class of quantum operations based on a geometrical representation of d-level quantum system (or qudit for short). A sufficient and necessary condition of complete positivity, expressed in terms of the quantum Fourier transform, is found for this class of operations. A more general class of operations on qudits is also considered and its completely positive condition is reduced to the well-known seriti-definite programming problem. (C) 2004 Elsevier B.V. All rights reserved.

关键词： quantum operation complete positivity quantum Fourier transform semi-definite programming

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Discretization method for semi-definite programming

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2004年第12期48卷 1937-1945页

作者： Yang, QZ Yu, H Nankai Univ Sch Math Tianjin 300071 Peoples R China Nankai Univ LPMC Tianjin 300071 Peoples R China

semi-definite programs are convex optimization problems arising in a wide variety of applications and the extension of linear programming. Most methods for linear programming have been generalized to semi-definite programs. This paper discusses the discretization method in semi-definite programming. The convergence and the convergent rate of error between the optimal value of the semi-definite programming problems and the optimal value of the discretized problems are obtained. An approximately optimal division is given under certain assumptions. With the significance of the convergence property, the duality result in semi-definite programs is proved in a simple way which is different from the other common proofs. (C) 2004 Elsevier Ltd. All rights reserved.

关键词： semi-definite programming duality semi-infinite programming optimal division

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Finite quantum tomography and semidefinite programming

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INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS 2007年第6期46卷 1471-1494页

作者： Mirzaee, M. Rezaee, M. Jafarizadeh, M. A. Arak Univ Dept Phys Arak Iran Tabriz Univ Dept Theoret Phys & Astrophys Tabriz Iran

Using the convex semidefinite programming method and superoperator formalism we obtain the finite quantum tomography of some mixed quantum states such as: truncated coherent states tomography, phase tomography and coherent spin state tomography, qudit tomography, N-qubit tomography, where that obtained results are in agreement with those of References (Buzek et al., Chaos, Solitons and Fractals 10 (1999) 981;Schack and Caves, Separable states of N quantum bits. In: Proceedings of the X. International Symposium on Theoretical Electrical Engineering, 73. W. Mathis and T. Schindler, eds. Otto-von-Guericke University of Magdeburg, Germany (1999);Pegg and Barnett Physical Review A 39 (1989) 1665;Barnett and Pegg Journal of Modern Optics 36 (1989) 7;St. Weigert Acta Physica Slov. 4 (1999) 613).

关键词： finite quantum tomograpy semi-definite programming superoperator formalism truncated coherent states qudit quantum tomography and truncation

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