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Sparsity Promotion in State Feedback Controller Design

IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2017年第8期62卷 4066-4072页

作者： Babazadeh, Maryam Nobakhti, Amin Sharif Univ Technol Dept Elect Engn Tehran Iran

A globally convergent algorithm for synthesis of sparse optimal state feedback (SOSF) control of linear time-invariant (LTI) systems is proposed. This problem is known to be NP-hard due to its combinatorial nature. A structured H-2 norm controller design problem is intrinsically non-convex, even if a fixed structure is known in advance. The proposed algorithm minimizes the H-2 norm performance index, and simultaneously regularizes the sparsity of the control structure using the l(1) norm. It guarantees that the solution converges to a stationary point of the original problem. The algorithm is implemented using Linear Matrix Inequalities (LMIs) which are efficient, reliable and extendable to other control problems. The performance of the proposed algorithm is illustrated with application to several examples. The results are also compared with Alternating Direction Method of Multiplier (ADMM) for sparse LQR design (as a special case of the H-2 norm problem). In most instances, the appropriate selection of the control structure leads to a near optimal performance index with a substantially reduced number of communication links.

关键词： Control structure selection H-2 performance index l(1) norm semi-definite programming sparse optimal control

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Amortization does not enhance the max-Rains information of a quantum channel

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NEW JOURNAL OF PHYSICS 2018年第5期20卷 053044-053044页

作者： Berta, Mario Wilde, Mark M. Imperial Coll London Dept Comp London SW7 2AZ England CALTECH Inst Quantum Informat & Matter Pasadena CA 91125 USA Louisiana State Univ Ctr Computat & Technol Dept Phys & Astron Hearne Inst Theoret Phys Baton Rouge LA 70803 USA

Given an entanglement measure E, the entanglement of a quantum channel is defined as the largest amount of entanglement E that can be generated from the channel, if the sender and receiver are not allowed to share a quantum state before using the channel. The amortized entanglement of a quantum channel is defined as the largest net amount of entanglement E. that can be generated from the channel, if the sender and receiver are allowed to share an arbitrary state before using the channel. Our main technical result is that amortization does not enhance the entanglement of an arbitrary quantum channel, when entanglement is quantified by the max-Rains relative entropy. We prove this statement by employing semi-definite programming (SDP). duality and SDP. formulations for the max-Rains relative entropy and a channel's max-Rains information, found recently in Wang et al (arXiv: 1709. 00200). The main application of our result is a single-letter, strong converse, and efficiently computable upper bound on the capacity of a quantum channel for transmitting qubits when assisted by positive-partial-transpose preserving (PPT-P) channels between every use of the channel. As the class of local operations and classical communication (LOCC) is contained in PPT-P, our result establishes a benchmark for the LOCC-assisted quantum capacity of an arbitrary quantum channel, which is relevant in the context of distributed quantum computation and quantum key distribution.

关键词： max-Rains information LOCC-assisted quantum capacity semi-definite programming

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Downlink Beamforming for SWIPT Multi-User MISO Underlay Cognitive Radio Networks

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IEEE COMMUNICATIONS LETTERS 2017年第2期21卷 434-437页

作者： Mohjazi, Lina Ahmed, Imtiaz Muhaidat, Sami Dianati, Mehrdad Al-Qutayri, Mahmoud Univ Surrey Inst Commun Syst Dept Elect Engn Surrey GU2 7XH England McGill Univ Dept Elect & Comp Engn Montreal H3A 0E9 PQ Canada Khalifa Univ Dept Elect & Comp Engn Abu Dhabi 127788 U Arab Emirates

This letter investigates downlink beamforming for simultaneous wireless information and power transfer in multi-user multi-input single-output underlay cognitive radio networks. Under the assumption of the integrated power splitting (PS) receiver architecture at the secondary receivers, we aim to minimize the total transmission power from the secondary base station by jointly optimizing the beamforming vectors and the PS ratios. We first exploit the structure of the relaxed problem to provide a closed form expression for the optimal solution. Since the underlying optimization problem is non-convex, we resort to semidefinite programming relaxation and we analytically prove that the relaxation is in fact tight and yields optimal beamforming solution.

关键词： Downlink beamforming wireless power transfer cognitive radio semi-definite programming

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Quantum coherence via conditional entropy

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JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 2018年第41期51卷 414018-414018页

作者： Liu, Yunchao Zhao, Qi Yuan, Xiao Tsinghua Univ Ctr Quantum Informat Inst Interdisciplinary Informat Sci Beijing 100084 Peoples R China Univ Oxford Dept Mat Pk Rd Oxford OX1 3PH England

Quantum coherence characterizes the non-classical feature of a single party system with respect to a local basis. Based on a recently introduced resource framework, coherence can be regarded as a resource and be systematically manipulated and quantified. Operationally, coherence quantifies the intrinsic randomness of the outcome of the projective measurement in the system's computational basis. However, such a relation is only proven when randomness is characterized by the von Neumann entropy. In this work, we consider several recently proposed coherence measures and relate them to the general uncertainties of the projective measurement outcome conditioned on all the other systems. Our work thus provides a unified framework for redefining several coherence measures via general conditional entropies. Based on the relation, we numerically calculate the coherence measures via semi-definite programming. Furthermore, we discuss the operational meaning of the unified definition. Our result highlights the close relation between single partite coherence and bipartite quantum correlation.

关键词： quantum coherence conditional entropy semi-definite programming

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Barrier certificates revisited

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JOURNAL OF SYMBOLIC COMPUTATION 2017年第Part1期80卷 62-86页

作者： Dai, Liyun Gan, Ting Xia, Bican Zhan, Naijun Peking Univ LMAM Beijing Peoples R China Peking Univ Sch Math Sci Beijing Peoples R China Chinese Acad Sci Inst Software State Key Lab Comp Sci Beijing 100864 Peoples R China

A barrier certificate can separate the state space of a considered hybrid system (HS) into safe and unsafe parts according to the safety property to be verified. Therefore this notion has been widely used in the verification of HSs. A stronger condition on barrier certificates (BCs) means that fewer BCs can be synthesized, as the expressiveness of synthesized BCs is weaker. On the other hand, synthesizing more expressive BCs normally means higher complexity. Kong et al. (2013a) investigated how to relax the condition of BCs while still keeping their convexity so that one can synthesize more expressive BCs efficiently using semi-definite programming (SDP). In this paper, we first discuss how to relax the condition of BCs in a general way, while still keeping their convexity. Thus, one can utilize different weaker conditions flexibly to synthesize different kinds of BCs with more expressiveness efficiently using SDP, which gives more opportunities to verify the considered system. We also show how to combine two functions together to form a combined BC in order to prove a safety property under consideration, whereas neither of them may be a BC separately. In fact, the notion of combined BCs is strictly more expressive than that of BCs, so it further brings more chances to verify a considered system. Another contribution of this paper is to investigate how to avoid the unsoundness of SDP based approaches caused by numerical error through symbolic checking. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Hybrid system Barrier certificate Formal verification Invariant Nonlinear system semi-definite programming Sum of squares

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LOW-COMPLEXITY OPTIMIZATION FOR TWO-DIMENSIONAL DIRECTION-OF-ARRIVAL ESTIMATION VIA DECOUPLED ATOMIC NORM MINIMIZATION

LOW-COMPLEXITY OPTIMIZATION FOR TWO-DIMENSIONAL DIRECTION-OF...

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IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Tian, Zhi Zhang, Zhe Wang, Yue George Mason Univ Dept Elect & Comp Engn Fairfax VA 22030 USA George Washington Univ Sch Engn & Appl Sci Washington DC 20052 USA

ISBN: (纸本)9781509041176

This paper presents an efficient optimization technique for super-resolution two-dimensional (2D) direction of arrival (DOA) estimation by introducing a new formulation of atomic norm minimization (ANM). ANM allows grid less angle estimation for correlated sources even when the number of snapshots is far less than the antenna size, yet it incurs huge computational cost in 2D processing. This paper introduces a novel formulation of ANM via semi-definite programming, which expresses the original high-dimensional problem by two decoupled Toeplitz matrices in one dimension, followed by ID angle estimation with automatic angle pairing. Compared with the state-of-the-art 2D ANM, the proposed technique reduces the computational complexity by several orders of magnitude with respect to the antenna size, while retaining the benefits of ANM in terms of super-resolution performance with use of a small number of measurements, and robustness to source correlation and noise. The complexity benefits are particularly attractive for large-scale antenna systems such as massive MIMO and radio astronomy.

关键词： Two-dimensional DOA atomic norm minimization semi-definite programming decoupled Toeplitz

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Optimization under non-convex Quadratic Matrix Inequality constraints with application to design of optimal sparse controller

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IFAC-PapersOnLine 2017年第1期50卷 10754-10759页

作者： Shishkin S.L. United Technologies Research Center 411 Silver Lane MS 129-15 East Hartford CT 06447 United States

Matrix optimization problems that contain one or more non-convex quadratic matrix constraints are considered. An iterative solving method is proposed; at each iteration convex matrix subproblem is formulated and solved using standard Convex Optimization algorithms. Global convergence of the method is proven. Implementation of the method is especially simple if non-convex matrix constraints are concave. The method is applied for solving long-standing problem of the H∞ design with additional sparsity constraint or objective on the controller. © 2017

关键词： H∞ control Non-convex optimization semi-definite programming Sparsity

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Optimum UAV Positioning for Better Coverage-Connectivity Tradeoff 28

Optimum UAV Positioning for Better Coverage-Connectivity Tra...

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28th Annual IEEE International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC)

作者： Abdel-Malek, Mai A. Ibrahim, Ahmed S. Mokhtar, Mohamed Florida Int Univ Dept Elect & Comp Engn Miami FL 33199 USA

ISBN: (纸本)9781538635315

Unmanned aerial vehicle (UAV) plays prominent role in enhancing backhaul connectivity and providing extended coverage areas due to its mobility and flexible deployment. To realize these objectives simultaneously, we present a new framework for positioning the UAV to maximize the small-cells backhaul network connectivity characterized by its Fiedler value, the second smallest eigenvalue of the Laplacian matrix representing the network graph, while maintaining particular signal-to-noise ratio constraint for each individual user equipment. Moreover, we show that the localization problem can be approximated by a low complexity convex semi-definite programming optimization problem. Finally, our extensive simulations verify the approximation validity and demonstrate the potential gain of UAV deployment.

关键词： connectivity coverage 3D positioning semi-definite programming unmanned aerial vehicle

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Optimization under non-convex Quadratic Matrix Inequality constraints with application to design of optimal sparse controller

Optimization under non-convex Quadratic Matrix Inequality co...

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20th World Congress of the International-Federation-of-Automatic-Control (IFAC)

作者： Shishkin, Serge L. United Technol Res Ctr 411 Silver LaneMS 129-15 E Hartford CT 06447 USA

Matrix optimization problems that contain one or more non-convex quadratic matrix constraints are considered. An iterative solving method is proposed;at each iteration convex matrix subproblem is formulated and solved using standard Convex Optimization algorithms. Global convergence of the method is proven. Implementation of the method is especially simple if non-convex matrix constraints are concave. The method is applied for solving long-standing problem of the H-infinity design with additional sparsity constraint or objective on the controller. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： Non-convex optimization semi-definite programming H-infinity control Sparsity

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Optimal Energy Consensus Control for Linear Multi-Agent Systems 36

Optimal Energy Consensus Control for Linear Multi-Agent Syst...

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第36届中国控制会议

作者： Han Zhang Xiaoming Hu Department of Mathematics KTH Royal Institute of Technology

ISBN: (纸本)9781538629185

In this paper, an optimal energy cost controller for linear multi-agent systems’ consensus is proposed. It is assumed that the topology among the agents is fixed and the agents are connected through an edge-weighted graph. The controller only uses relative information between agents. Due to the difficulty of finding the controller gain, we focus on finding the optimal controller among a sub-family whose design is based on Algebraic Riccati Equation（ARE） and guarantee consensus. It is found that the energy cost for such controllers is bounded by an interval and hence we minimize the upper bound. To do that, the control gain and the edge weights are optimized separately. The control gain is optimized by choosing Q = 0 in the ARE;the edge weights are optimized under the assumption that there is limited communication resources in the network. Negative edge weights are allowed, and the problem is formulated as a semi-definite programming（SDP） problem. The controller coincides with the optimal control in [8] when the graph is complete. Furthermore, two sufficient conditions for the existence of negative optimal edge weights realization are given.

关键词： Consensus Control Multi-Agent Systems Optimal Control semi-definite programming Synchronizability

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