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First Order Methods For Globally Optimal Distributed Controllers Beyond Quadratic Invariance

First Order Methods For Globally Optimal Distributed Control...

引用

American Control Conference

作者： Luca Furieri Maryam Kamgarpour Automatic Control Laboratory ETH Zurich Switzerland

ISBN: (数字)9781538682661

ISBN: (纸本)9781538682678

We study the distributed Linear Quadratic Gaussian (LQG) control problem in discrete-time and finite-horizon, where the controller depends linearly on the history of the outputs and it is required to lie in a given subspace, e.g. to possess a certain sparsity pattern. It is well-known that this problem can be solved with convex programming within the Youla domain if and only if a condition known as Quadratic Invariance (QI) holds. In this paper, we first show that given QI sparsity constraints, one can directly descend the gradient of the cost function within the domain of output-feedback controllers and converge to a global optimum. Note that convergence is guaranteed despite non-convexity of the cost function. Second, we characterize a class of Uniquely Stationary (US) problems, for which first-order methods are guaranteed to converge to a global optimum. We show that the class of US problems is strictly larger than that of strongly QI problems and that it is not included in that of QI problems. We refer to Figure 1 for details. Finally, we propose a tractable test for the US property.

关键词： Cost functions global optimum Converge Controllers feedback controller invariance convex programming Quadratic discrete-time linear quadratic Gaussian control

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Identification of Structured LTI MIMO State-Space Models

Identification of Structured LTI MIMO State-Space Models

引用

IEEE Annual Conference on Decision and Control

作者： Chengpu Yu Michel Verhaegen Shahar Kovalsky Ronen Basri Delft Center for Systems and Control Delft University Delft 2628CD Netherlands Weizmann Institute of Science Department of Computer Science and Applied Mathematics

ISBN: (纸本)9781479978878

The identification of structured state-space model has been intensively studied for a long time but still has not been adequately addressed. The main challenge is that the involved estimation problem is a non-convex (or bilinear) optimization problem. This paper is devoted to developing an identification method which aims to find the global optimal solution under mild computational burden. Key to the developed identification algorithm is to transform a bilinear estimation to a rank constrained optimization problem and further a difference of convex programming (DCP) problem. The initial condition for the DCP problem is obtained by solving its convex part of the optimization problem which happens to be a nuclear norm regularized optimization problem. Since the nuclear norm regularized optimization is the closest convex form of the low-rank constrained estimation problem, the obtained initial condition is always of high quality which provides the DCP problem a good starting point. The DCP problem is then solved by the sequential convex programming method. Finally, numerical examples are included to show the effectiveness of the developed identification algorithm.

关键词： Identification methods Non-convex convex programming LTI INITIAL CONDITIONS Authentication bilinearity

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OPTIMUM TIME COORDINATION OF DIRECTIONAL OVERCURRENT RELAYS USING CVX, GAMS AND GENETIC ALGORITHM

OPTIMUM TIME COORDINATION OF DIRECTIONAL OVERCURRENT RELAYS ...

引用

The 10th International Conference on Power Electronics, Machines and Drives (PEMD 2020)

作者： R. Dawood M. Al-Greer A. Gailani G. Pillai Electrical Transmission Projects (ETP) Ministry of Electricity Baghdad Iraq School of Computing Engineering and Digital Technologies Teesside University Middlesbrough UK

This paper proposes new optimization techniques to obtain optimal values of Time Multiplier Setting (TMS) for directional overcurrent relays (DOCRs) in a protection scheme. General Algebraic Modelling System (GAMS) and CVX modelling system for convex optimization are the new techniques proposed. TMS of DOCRs needs to be accurately determined in order to coordinate the operating time and avert the mal-operation of the backup relays in the transmission and distribution network. Without optimum coordination of the action of relays, fault conditions will trip healthy transmission lines and might lead to a total shut down of the grid. The time coordination of relays in a network is an extremely constrained optimization function which identified as a linear programming problem (LPP). Of late, the use of genetic algorithm (GA) for DOCRs coordination have become increasingly prominent. Therefore, the proposed CVX and GAMS techniques are compared with conventional GA scheme. Results show that an accurate optimization solution for directional overcurrent relay coordination can be achieved using both GAMS and CVX methods in comparison to GA based method with GAMS providing a more accurate solution.

关键词： overcurrent protection linear programming relay protection genetic algorithms power distribution faults power transmission faults convex programming power transmission lines power transmission protection power distribution protection

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Optimal Focused Electromagnetic Hyperthermia Treatment of Breast Cancer

Optimal Focused Electromagnetic Hyperthermia Treatment of Br...

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European Conference on Antennas and Propagation

作者： Domenica A. M. Iero Lorenzo Crocco Tommaso Isernia Erdal Korkmaz Dipartimento di Inforinatica Matematica Elettronica e Trasporti (DIIES) Università Mediterranea di Reggio Calabria Reggio Calabria Italy Istituto per il Rilevamento Elettromagnetico dell'Ambiente (IREA) Consiglio Nazionale delle Ricerche (CNR) Napoli Italy Department of Electrical and Electronics Engineering Fatih University Istanbul Turkey

ISBN: (纸本)9781509022342

In this communication, two novel focusing methods are introduced and assessed in designing a pre-clinic applicator for hyperthermia treatment. The first method is an optimized version of the well known Time Reversal approach, which preserves the method's original simplicity and effectiveness. The second one pursues the focusing task in highly controlled way, by exploiting the convexity of the problem with respect to part of the unknowns (the array's excitations). In particular, it takes advantage of a constrained optimization framework, by imposing proper bounds on the power deposition in healthy tissues.

关键词： Hyperthermia Focusing convex programming Time Reversal Phase Conjugation Array Synthesis Phased Arrays

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Optimal Energy-Efficient Transmission for Fading Channels with an Energy Harvesting Transmitter

Optimal Energy-Efficient Transmission for Fading Channels wi...

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IEEE Global Communications Conference

作者： Qingqing Wu Meixia Tao Wen Chen Jinsong Wu Department of Electronic Engineering Shanghai Jiao Tong University Bell Laboratories Alcatel-Lucent

ISBN: (纸本)9781479935130

This paper investigates the optimal energy-efficient transmission policy of multi-channels in energy harvesting systems. We configure the transmitter with the active mode in which the energy cost includes the basic operation cost and transmission cost and signal processing cost, while with the sleep mode only counting the basic operation cost. Then the energy efficiency maximization problem of joint transmission time and power allocation is formulated and studied in the offline manner. Based on the fractional optimization theory, we transform the original fractional optimization problem into a series of subtractive-form optimization problems which are then further transformed into convex optimization problems. Then characteristics of the optimal solution are described based on the analysis of transmission time and power allocation. Finally, a special case without considering the basic operation cost as previous works assumed is studied. We find that the optimal policy results a best subchannel scheduling which can be viewed as the peaky transmission. Through this, the energy cost of the sleep mode in previous case can be interpreted as the switching operation cost.

关键词： convex programming energy conservation energy harvesting fading channels radio transmitters telecommunication scheduling convex optimization problem energy costing energy efficiency maximization problem energy harvesting transmitter fading channel fractional optimization theory multichannel policy operation costing optimal energy-efficient transmission policy power allocation signal processing costing subchannel scheduling subtractive-form optimization problem time allocation transmission costing Energy consumption Energy harvesting Fading Resource management Transmitters Wireless communication

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Computational Convergence Analysis of Distributed Gradient Tracking for Smooth convex Optimization Using Dissipativity Theory

Computational Convergence Analysis of Distributed Gradient T...

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American Control Conference

作者： Shuo Han University of Illinois Chicago IL 60607

ISBN: (纸本)9781538679012;9781538679265

We present a computational analysis that establishes the O(1/K) convergence of the distributed gradient tracking method when the objective function is smooth and convex but not strongly convex. The analysis is inspired by recent work on applying dissipativity theory to the analysis of centralized optimization algorithms, in which convergence is proved by searching for a numerical certificate consisting of a storage function and a supply rate. We derive a base supply rate that can be used to analyze distributed optimization with non-strongly convex objective functions. The base supply rate is then used to create a class of supply rates by combining with integral quadratic constraints. Provided that the class of supply rates is rich enough, a numerical certificate of convergence can be automatically generated following a standard procedure that involves solving a linear matrix inequality. Our computational analysis is found capable of certifying convergence under a broader range of step sizes than what is given by the original analytic result.

关键词： computational complexity convergence of numerical methods convex programming gradient methods linear matrix inequalities

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Cognitive Radio Enabled Transmission for State Estimation in Industrial Cyber-physical Systems

Cognitive Radio Enabled Transmission for State Estimation in...

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IEEE Global Communications Conference

作者： Ling Lyu Cailian Chen Yao Li Feilong Lin Lingya Liu Xinping Guan Department of Automation Shanghai Jiao Tong University

ISBN: (纸本)9781479959532

State estimation, which computes the best possible approximation for the system state based on the perceived information transmitted from sensors to the estimators, is vital for control system performance in industrial cyber-physical systems (ICPSs) with the integrated techniques of control, communication and computing. Thus the performance of state estimation relies on the communication reliability. In order to improve the reliability, redundant channels/slots are reserved for the data transmission in industrial wireless techniques, such as WirelessHART. However, the redundancy scheme burdens the increasingly over-crowded ISM spectrum band due to the envisioned emerging ubiquitous industrial wireless monitoring in the architecture of ICPS in the near future. The cognitive radio (CR) technology can intelligently explore the available spectrum opportunities on licensed channels, and it motivates this paper to consider the redundant transmission through the opportunistically available licensed channels to guarantee the transmission reliability for state estimation. Unfortunately, spectrum sensing takes extra energy consumption, thus it is necessary to take into account the energy efficiency for the battery-powered IWSN. Then a CR enabled energy-efficiency maximization problem is formulated by regarding the convergence of state estimation as a constraint of the resource allocation problem. In order to solve the non-convex and mixed integer programming, the Dinkelbach and Lagrangian relaxation techniques are adopted to transform the problem into a convex programming and furthermore reduce the computational complexity. Numerical results demonstrate that the CR technology can significantly release the spectrum for the redundancy design from the ISM band while guarantee the reliability for the effective state estimation.

关键词： State estimation Cognitive radio communication reliability ISM band power transmission reliability Energy efficiency convex programming data transmission Spectra Wireless monitoring energy consumption Industrial Resource utilization chromium Non-convex

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Efficient description of the design space of analog circuits 03

Efficient description of the design space of analog circuits

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Proceedings of the 40th annual Design Automation Conference

作者： Maria del Mar Hershenson Barcelona Design Inc. Newark CA

ISBN: (纸本)9781581136883

In this paper we present a method for determining the feasible set of analog design problems and we propose an efficient method for their verification. The verification method presented relies on the formulation of the analog circuit design problem as a convex optimization problem in both the design variables and the performance specifications. Since the design is convex not only in the design variables but also in the specification parameters, we observe that the feasible sets are convex and points at the boundary can be found by solving a single convex optimization problem. We also show that feasible sets can be very well approximated with a polyhedron and therefore defined by a finite set of points. The implication of the latter is that new verifications do not need to be run for every new instantiation of a synthesized analog cell.

关键词： convex programming analog synthesis geometric program circuits verification optimization

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Distributed Coordination for Separable convex Optimization with Coupling Constraints

Distributed Coordination for Separable Convex Optimization w...

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IEEE Annual Conference on Decision and Control

作者： Simon K. Niederlander Jorge Cortes Institute for Systems Theory and Automatic Control University of Stuttgart Germany Department of Mechanical and Aerospace Engineering University of California San Diego United States

ISBN: (纸本)9781479978878

This paper considers a network of agents described by an undirected graph that seek to solve a convex optimization problem with separable objective function and coupling equality and inequality constraints. Both the objective function and the inequality constraints are Lipschitz continuous. We assume that the constraints are compatible with the network topology in the sense that, if the state of an agent is involved in the evaluation of any given local constraint, this agent is able to fully evaluate it with the information provided by its neighbors. Building on the saddle-point dynamics of an augmented Lagrangian function, we develop provably correct distributed continuous-time coordination algorithms that allow each agent to find their component of the optimal solution vector along with the optimal Lagrange multipliers for the equality constraints in which the agent is involved. Our technical approach combines notions and tools from nonsmooth analysis, set-valued and projected dynamical systems, viability theory and convex programming.

关键词： Agents inequality constraint Network topology Separable Objective function undirected graph convex programming Lagrange multipliers Constraint Equality convex function Distribute

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The Finite Convergence of the Relaxation Method for Solving Systems of Inequalities

The Finite Convergence of the Relaxation Method for Solving ...

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作者： Goffin, J. L California Univ Berkeley Operations Research Center Office of Naval Research Mathematical Sciences Division Arlington VA OFFICE OF NAVAL RESEARCH ARLINGTON VA

The main concern of this work is to rejuvenate the relaxation method for solving linear inequalities, which uses as primitive the notion of hyperplanes, instead of the more derived concept of vertices or bases. The main result is that the method converges finitely for a wide range of values of the relaxation parameter. The smooth enough property is defined, and it delineates a class of problems where the method works particularly well. It is hoped that the relaxation method might become a powerful alternative to the decomposition, or column generation, techniques for large scale programs in which the theoretical finiteness of the simplex method breaks down to a practical transfiniteness.

关键词： Linear programming Simplex method convex bodies convex sets Engineering Real numbers Algorithms California Computational science New york Operations research Optimization Universities Bodies convex programming Theorems Topology

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