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Internal Quadratic Invariance and Decentralized Control

Internal Quadratic Invariance and Decentralized Control

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American Control Conference

作者： Laurent Lessard Sanjay Lall Department of Aeronautics and Astronautics at Stanford University Stanford CA 94305 USA Department of Electrical Engineering and Aeronautics and Astronautics at Stanford University Stanford CA 94305 USA

ISBN: (纸本)9781424474264

For decentralized control systems with quadratically invariant information constraints, the set of achievable closed-loop maps is affine, and thus the associated minimum-norm controller synthesis problem is amenable to a convex programming approach. In this paper, we show that a strictly broader class of problems we call internally quadratically invariant, also yields an affine set of achievable closed-loop maps. We treat systems represented by rational as well as proper rational transfer functions and present an illustrative example.

关键词： decentralised control In-law Rational number TRANSFER FUNCTIONS invariance Affine Distributed control systems realizable Invariant Quadratic maps convex programming

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A Distributed Algorithm with Event-Triggered Communication for Resource Allocation Problem

A Distributed Algorithm with Event-Triggered Communication f...

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American Control Conference

作者： Xiasheng Shi Ronghao Zheng Tao Yang Zhiyun Lin Gangfeng Yan College of Electrical Engineering Zhejiang University Hangzhou China University of North Texas Denton USA School of Automation Hangzhou Dianzi University Hangzhou China Colleg

ISBN: (纸本)9781538679012;9781538679265

This paper focuses on the distributed resource allocation problem in continuous-time multi-agent systems over undirected networks, in which each agent has a local convex cost function only known by itself and all agents are required to converge to the global optimizer of the sum of the local cost functions under constraints. A gradient-based distributed algorithm is proposed for solving the problem. Furthermore, the step-size of gradient is a constant. A sufficient condition is given which guarantees that the proposed algorithm can achieve the global optimization. Moreover, in order to avoid continuous communication, an event-triggered communication control strategy is designed. Finally, an example of the economic dispatch problem in smart grid is presented to validate and illustrate the feasibility of the proposed algorithm.

关键词： continuous time systems convex programming distributed algorithms gradient methods multi-agent systems power engineering computing power generation dispatch resource allocation smart power grids

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Optimization, Learning, and Games with Predictable Sequences 13

Optimization, Learning, and Games with Predictable Sequences

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Annual Conference on Neural Information Processing Systems

作者： Alexander Rakhlin Karthik Sridharan University of Pennsylvania

ISBN: (纸本)9781632660244

We provide several applications of Optimistic Mirror Descent, an online learning algorithm based on the idea of predictable sequences. First, we recover the Mirror Prox algorithm for offline optimization, prove an extension to Holder-smooth functions, and apply the results to saddle-point type problems. Next, we prove that a version of Optimistic Mirror Descent (which has a close relation to the Exponential Weights algorithm) can be used by two strongly-uncoupled players in a finite zero-sum matrix game to converge to the minimax equilibrium at the rate of O((log T)/T). This addresses a question of Daskalakis et al. Further, we consider a partial information version of the problem. We then apply the results to convex programming and exhibit a simple algorithm for the approximate Max Flow problem.

关键词： convex programming Game theory Mirrors learning algorithms algorithms Maximum Flow descent PDHX gene

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The Sum-Rate Maximization Precoding for Multiuser MIMO SWIPT Systems

The Sum-Rate Maximization Precoding for Multiuser MIMO SWIPT...

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IEEE Vehicular Technology Conference

作者： Zhaohui Yue Hui Gao Ruohan Cao Tiejun Lv Key Laboratory of Trustworthy Distributed Computing and Service Ministry of Education School of Information and Communication Engineering Beijing University of Posts and Telecommunications

ISBN: (纸本)9781479980895

This paper proposes a linear precoding that aims at maximizing the sum-rate in a multiuser multiple-input multiple-output (MU-MIMO) simultaneous wireless information and power transfer (SWIPT) system. In this scenario some receivers harvest energy while the others decode information at the same time. The sum-rate for information decoding users is considered as the optimization policy where the transmit power constraint and power harvesting per user constraints are taken into account. Since the objective function of the sum-rate maximization problem is non-convex, it is difficult to find the optimal solution. Thus, we propose an iterative algorithm to find a locally optimal design based on a sequential convex approximation (SCA) method. In this way, the non-convex optimization problem is approximated by a convex program at each iteration. Finally, with the aid of the concept of the Rate-Energy (R-E) region simulation results show that the proposed scheme achieves significant improvement compared to existing works.

关键词： Non-convex prediction coding multiple input multiple output systems Transmitter power convex programming Optimal design DECODING Iterative algorithms Objective function convexity

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From weak to strong LP gaps for all CSPs 17

From weak to strong LP gaps for all CSPs

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Proceedings of the 32nd Computational Complexity Conference

作者： Mrinalkanti Ghosh Madhur Tulsiani Toyota Technological Institute at Chicago

ISBN: (纸本)9783959770408

We study the approximability of constraint satisfaction problems (CSPs) by linear programming (LP) relaxations. We show that for every CSP, the approximation obtained by a basic LP relaxation, is no weaker than the approximation obtained using relaxations given by [EQUATION] levels of the Sherali-Adams hierarchy on instances of size *** was proved by Chan et al. [FOCS 2013] (and recently strengthened by Kothari et al. [STOC 2017]) that for CSPs, any polynomial size LP extended formulation is no stronger than relaxations obtained by a super-constant levels of the Sherali-Adams hierarchy. Combining this with our result also implies that any polynomial size LP extended formulation is no stronger than simply the basic LP, which can be thought of as the base level of the Sherali-Adams hierarchy. This essentially gives a dichotomy result for approximation of CSPs by polynomial size LP extended *** our techniques, we also simplify and strengthen the result by Khot et al. [STOC 2014] on (strong) approximation resistance for LPs. They provided a necessary and sufficient condition under which Ω(log log n) levels of the Sherali-Adams hierarchy cannot achieve an approximation better than a random assignment. We simplify their proof and strengthen the bound to [EQUATION] levels.

关键词： linear programming hierarchy integrality gap convex programming constraint satisfaction problem

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Robust Classification using Structured Sparse Representation

Robust Classification using Structured Sparse Representation

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IEEE Conference on Computer Vision and Pattern Recognition

作者： Ehsan Elhamifar Rene Vidal Center for Imaging Science Johns Hopkins University

ISBN: (纸本)9781457703942

In many problems in computer vision, data in multiple classes lie in multiple low-dimensional subspaces of a high-dimensional ambient space. However, most of the existing classification methods do not explicitly take this structure into account. In this paper, we consider the problem of classification in the multi-subspace setting using sparse representation techniques. We exploit the fact that the dictionary of all the training data has a block structure where the training data in each class form few blocks of the dictionary. We cast the classification as a structured sparse recovery problem where our goal is to find a representation of a test example that uses the minimum number of blocks from the dictionary. We formulate this problem using two different classes of non-convex optimization programs. We propose convex relaxations for these two non-convex programs and study conditions under which the relaxations are equivalent to the original problems. In addition, we show that the proposed optimization programs can be modified properly to also deal with corrupted data. To evaluate the proposed algorithms, we consider the problem of automatic face recognition. We show that casting the face recognition problem as a structured sparse recovery problem can improve the results of the state-of-the-art face recognition algorithms, especially when we have relatively small number of training data for each class. In particular, we show that the new class of convex programs can improve the state-of-the-art face recognition results by 10% with only 25% of the training data. In addition, we show that the algorithms are robust to occlusion, corruption, and disguise.

关键词： Facial Recognition Dictionaries as Topic sparse representation Training data face recognition algorithm Masonry construction Classification Methods convex programming Non-convex

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Generalized Hessian approximations via Stein's lemma for constrained minimization

Generalized Hessian approximations via Stein's lemma for con...

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Information Theory and Applications Workshop, ITA

作者： Murat A. Erdogdu Department of Statistics Stanford University Stanford CA USA

ISBN: (纸本)9781509052943

We consider the problem of convex constrained minimization of an average of n functions, where the parameter and the features are related through inner products. We focus on second order batch updates, where the curvature matrix is obtained by assuming random design and by applying the celebrated Stein's lemma together with subsampling techniques. The proposed algorithm enjoys fast convergence rates similar to the Newton method, yet the per-iteration cost has the same order of magnitude as the gradient descent. We demonstrate its performance on well-known optimization problems where Stein's lemma is not directly applicable, such as M-estimation for robust statistics, and inequality form linear/quadratic programming etc. Under certain assumptions, we show that the constrained optimization algorithm attains a composite convergence rate that is initially quadratic and asymptotically linear. We validate its performance through widely encountered optimization tasks on several real and synthetic datasets by comparing it to classical optimization algorithms.

关键词： convergence convex programming gradient methods Hessian matrices minimisation Hessian matrix convex programming gradient methods Optimization algorithms Converge Lemma Hessian

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Continuous and Discrete Sum-Rate Maximization for Multiuser MIMO-OFDM Systems with CoMP

Continuous and Discrete Sum-Rate Maximization for Multiuser ...

引用

IEEE Global Communications Conference

作者： Chih-yu Hsu Meng Wang Phee Lep Yeoh Brian S. Krongold Dept. of Electr. & Electron. Eng. Univ. of Melbourne Melbourne VIC Australia

ISBN: (纸本)9781479935130

In this paper, we propose two efficient and practical resource allocation algorithms to maximize the weighted sum-rate of coordinated multipoint (CoMP) transmission with joint processing in multiuser multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems subject to per-antenna power constraints. We first propose a continuous-rate algorithm that utilizes successive convex approximation (SCA) to dynamically allocate the transmit powers of multiple CoMP base stations (BSs) transmitting to multiple co-channel user terminals (UTs). Next, we propose a discrete-rate algorithm that takes the continuous-rate result as a starting point and redistributes the transmit powers to obtain a discrete solution. Simulation results are provided to benchmark our continuous-rate algorithm with two alternative approaches: iterative waterfilling (IWF), and zero-forcing beamforming (ZFB). Results show that SCA provides significant sum-rate improvements over IWF in medium to high interference scenarios, and outperforms ZFB in low to medium interference scenarios. Moreover, our proposed discrete rate algorithm produces a higher discrete sum-rate with much lower computational complexity compared to existing algorithms.

关键词： MIMO communication OFDM modulation antennas approximation theory array signal processing convex programming iterative methods multiuser channels radiofrequency interference resource allocation IWF SCA ZFB computational complexity continuous sum-rate maximization continuous-rate algorithm coordinated multipoint transmission maximization weighted sum-rate discrete sum-rate maximization iterative waterfilling medium-to-high interference scenarios multiple CoMP base stations multiple co-channel user terminals multiuser MIMO-OFDM systems multiuser multiple-input multiple-output systems orthogonal frequency-division multiplexing systems per-antenna power constraints resource allocation algorithms successive convex approximation zero-forcing beamforming Interference OFDM Optimization Resource management Signal to noise ratio Transmitting antennas Orthogonal frequency division multiplexing management of resources multiuser channels transmitting antennas signal to noise ratios MIMO communication Radiofrequency interference convex programming array signal processing Approximation Theory Resource utilization iterative methods complexity classes ANTENNA Allocation Algorithm

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Price sensitivity based demand function for power flow in congested transmission lines

Price sensitivity based demand function for power flow in co...

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Michael Faraday IET International Summit 2020 (MFIIS 2020)

作者： P. Saha S. Banerjee B. Paul C. Kumar Chanda Narula Institute of Technology Agarpara Kolkata India Gargi Memorial Institute of Technology Baruipur Kolkata India Indian Institute of Engineering Science and Technology Shibpur Howrah India

In an open power market having elastic loads the remote generators needed to compete with local generators to provide power at a competitive price. The price for transmission of power depends upon the LMP (Locational Marginal Price) of each generator located within the network. Price sensitivity represented by LMP is of utmost importance to maintain the proper functionality of the power market. convex quadratic function for the amount of power transmitted is used by transition owners. These obtained revenues marks up the price that both the power produces and power users needed to pay for using the power network. In this paper a five bus system is considered, the LMPs at each busses are calculated correspondingly demand functions for each of the transmission has been obtained which computes the revenue obtained at maximum point for maintain the optimal transmission capacity in the system.

关键词： power transmission economics pricing power markets load flow convex programming quadratic programming power generation economics power transmission lines

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Optimal battery sizing for a distribution network in Austria to maximise profits and reliability

Optimal battery sizing for a distribution network in Austria...

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CIRED 2020 Berlin Workshop (CIRED 2020)

作者： Da Huo Marcos V. Santos David M. Greenwood Neal S. Wade Markus P. Resch School of Engineering Newcastle University Newcastle upon Tyne NE1 7RU UK Energie Güssing GmbH Wiener Straße 23 7540 Güssing Austria

Energy storage systems (ESSs) can benefit distribution networks by providing multiple services to the distribution system operator and contributing to system reliability. Given the high capital costs of ESS, it is beneficial to optimally design them for their intended applications; however, this can be computationally expensive due to the non-convex formulation of the AC power flow, the complexity of business use cases and the simulation of multi-period operations. This study develops a comprehensive model to size the ESS to minimise the system lifetime costs and maximise reliability. The non-convex AC power flow model is modified using a convex relaxation, which yields efficient and globally optimal results. The battery degradation is simulated by a global wear coefficient considering the effect of depth of discharge. The sizing study is implemented to fulfil multiple applications on the Güssing distribution network in Austria.

关键词： distribution networks profitability reliability energy storage power system reliability load flow convex programming concave programming battery storage plants power distribution economics

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