Results 1  10
of
43
Zero Duality Gap in Optimal Power Flow Problem
, 2012
"... The optimal power flow (OPF) problem is nonconvex and generally hard to solve. In this paper, we propose a semidefinite programming (SDP) optimization, which is the dual of an equivalent form of the OPF problem. A global optimum solution to the OPF problem can be retrieved from a solution of this co ..."
Abstract

Cited by 115 (27 self)
 Add to MetaCart
The optimal power flow (OPF) problem is nonconvex and generally hard to solve. In this paper, we propose a semidefinite programming (SDP) optimization, which is the dual of an equivalent form of the OPF problem. A global optimum solution to the OPF problem can be retrieved from a solution of this convex dual problem whenever the duality gap is zero. A necessary and sufficient condition is provided in this paper to guarantee the existence of no duality gap for the OPF problem. This condition is satisfied by the standard IEEE benchmark systems with 14, 30, 57, 118 and 300 buses as well as several randomly generated systems. Since this condition is hard to study, a sufficient zerodualitygap condition is also derived. This sufficient condition holds for IEEE systems after small resistance (10 −5 per unit) is added to every transformer that originally assumes zero resistance. We investigate this sufficient condition and justify that it holds widely in practice. The main underlying reason for the successful convexification of the OPF problem can be traced back to the modeling of transformers and transmission lines as well as the nonnegativity of physical quantities such as resistance and inductance.
Finding globally optimum solutions in antenna optimization problems
 IEEE International Symposium on Antennas and Propagation
, 2010
"... During the last decade, the unprecedented increase in the affordable computational power has strongly supported the development of optimization techniques for designing antennas. Among these techniques, genetic algorithm [1] and particle swarm optimization [2] could be mentioned. Most of these techn ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
During the last decade, the unprecedented increase in the affordable computational power has strongly supported the development of optimization techniques for designing antennas. Among these techniques, genetic algorithm [1] and particle swarm optimization [2] could be mentioned. Most of these techniques use physical dimensions of an antenna
Programmable antenna design using convex optimization
 19th International Symposium on Mathematical Theory of Networks and Systems
, 2010
"... Abstract—This work presents an application of convex optimization and algebraic geometry in devising secure, powerefficient, beamsteerable, and onchip transmission systems for wireless networks. First, we introduce a passively controllable smart (PCS) antenna system that can be programmed to gen ..."
Abstract

Cited by 3 (3 self)
 Add to MetaCart
Abstract—This work presents an application of convex optimization and algebraic geometry in devising secure, powerefficient, beamsteerable, and onchip transmission systems for wireless networks. First, we introduce a passively controllable smart (PCS) antenna system that can be programmed to generate different radiation patterns in far field by adjusting its variable passive controller at every signal transmission. To study the programming capability of a PCS antenna system, we consider a PCS antenna transmitting data in z directions, where some voltages v1, v2,..., vz are induced in different directions in far field. The objective of this paper is to study the set of all feasible vectors (v1, v2,..., vz) that can be generated by a passive control of the PCS antenna system. To this end, it is shown that all feasible vectors (v1, v2,..., vz) form a convex semialgebraic set parameterized by a linear matrix inequality (LMI). Later on, this LMI condition is further studied and it is proven that the geometry of the set of all feasible voltages (v1, v2,..., vz) is simply an ellipsoid. This significant result makes it possible to compute the feasibility set online to decide how the PCS antenna must be programmed for either directional or simultaneous data transmission. Unlike the existing smart antennas whose programming leads to an NPhard problem or are made of many active elements, the PCS antenna proposed in the present work has a lowcomplex programming capability and consists of only one active element. I.
Solving largescale linear circuit problems via convex optimization
, 2009
"... Abstract — A broad class of problems in circuits, electromagnetics, and optics can be expressed as finding some parameters of a linear system with a specific type. This paper is concerned with studying this type of circuit using the available control techniques. It is shown that the underlying prob ..."
Abstract

Cited by 5 (4 self)
 Add to MetaCart
Abstract — A broad class of problems in circuits, electromagnetics, and optics can be expressed as finding some parameters of a linear system with a specific type. This paper is concerned with studying this type of circuit using the available control techniques. It is shown that the underlying problem can be recast as a rank minimization problem that is NPhard in general. In order to circumvent this difficulty, the circuit problem is slightly modified so that the resulting optimization becomes convex. This interesting result is achieved at the cost of complicating the structure of the circuit, which introduces a tradeoff between the design simplicity and the implementation complexity. When it is strictly required to solve the original circuit problem, the elegant structure of the proposed rank minimization problem allows for employing a celebrated heuristic method to solve it efficiently. I.
Passively Controllable Smart Antennas
 in IEEE Global Communications Conference 2010 (GLOBECOM
, 2010
"... Abstract — We recently introduced passively controllable smart (PCS) antenna systems for efficient wireless transmission, with direct applications in wireless sensor networks. A PCS antenna system is accompanied by a tunable passive controller whose adjustment at every signal transmission generates ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Abstract — We recently introduced passively controllable smart (PCS) antenna systems for efficient wireless transmission, with direct applications in wireless sensor networks. A PCS antenna system is accompanied by a tunable passive controller whose adjustment at every signal transmission generates a specific radiation pattern. To reduce cochannel interference and optimize the transmitted power, this antenna can be programmed to transmit data in a desired direction in such a way that no signal is transmitted (to the far field) at prespecified undesired directions. The controller of a PCS antenna was assumed to be centralized in our previous work, which was an impediment to its implementation. In this work, we study the design of PCS antenna systems under decentralized controllers, which are both practically implementable and cost efficient. The PCS antenna proposed here is made of one active element and its programming needs solving secondordercone optimizations. These properties differentiate a PCS antenna from the existing smart antennas, and make it possible to implement a PCS antenna on a smallsized, lowpower silicon chip. I.
Message passing for dynamic network energy management
, 2012
"... We consider a network of devices, such as generators, fixed loads, deferrable loads, and storage devices, each with its own dynamic constraints and objective, connected by lossy capacitated lines. The problem is to minimize the total network objective subject to the device and line constraints, over ..."
Abstract

Cited by 15 (0 self)
 Add to MetaCart
We consider a network of devices, such as generators, fixed loads, deferrable loads, and storage devices, each with its own dynamic constraints and objective, connected by lossy capacitated lines. The problem is to minimize the total network objective subject to the device and line constraints, over a given time horizon. This is a large optimization problem, with variables for consumption or generation in each time period for each device. In this paper we develop a decentralized method for solving this problem. The method is iterative: At each step, each device exchanges simple messages with its neighbors in the network and then solves its own optimization problem, minimizing its own objective function, augmented by a term determined by the messages it has received. We show that this message passing method converges to a solution when the device objective and constraints are convex. The method is completely decentralized, and needs no global coordination other than synchronizing iterations; the problems to be solved by each device can typically be solved extremely efficiently and in parallel. The method is fast enough that even a serial implementation can solve substantial problems
CONFIDENTIAL. Limited circulation. For review only. Solving LargeScale Linear Circuit Problems via Convex Optimization
"... Abstract — A broad class of problems in circuits, electromagnetics, and optics can be expressed as finding some parameters of a linear system with a specific type. This paper is concerned with studying this type of circuit using the available control techniques. It is shown that the underlying probl ..."
Abstract
 Add to MetaCart
Abstract — A broad class of problems in circuits, electromagnetics, and optics can be expressed as finding some parameters of a linear system with a specific type. This paper is concerned with studying this type of circuit using the available control techniques. It is shown that the underlying problem can be recast as a rank minimization problem that is NPhard in general. In order to circumvent this difficulty, the circuit problem is slightly modified so that the resulting optimization becomes convex. This interesting result is achieved at the cost of complicating the structure of the circuit, which introduces a tradeoff between the design simplicity and the implementation complexity. When it is strictly required to solve the original circuit problem, the elegant structure of the proposed rank minimization problem allows to employ a celebrated heuristic method to solve it efficiently. I.
Controllability and Observability of Uncertain Systems: A Robust Measure
"... Abstract—This paper deals with the class of polynomially uncertain continuoustime linear timeinvariant (LTI) systems whose uncertainties belong to a semialgebraic set. The objective is to determine the minimum of the smallest singular value of the controllability or observability Gramian over th ..."
Abstract
 Add to MetaCart
Abstract—This paper deals with the class of polynomially uncertain continuoustime linear timeinvariant (LTI) systems whose uncertainties belong to a semialgebraic set. The objective is to determine the minimum of the smallest singular value of the controllability or observability Gramian over the uncertainty region. This provides a quantitative measure for the robust controllability or observability degree of the system. To this end, it is shown that the problem can be recast as a sumofsquares (SOS) problem. In the special case when the uncertainty region is polytopic, the corresponding SOS formulation can be simplified significantly. One can apply the proposed method to any largescale interconnected system to identify those inputs and outputs that are more effective in controlling the system. This enables the designer to simplify the control structure by ignoring those inputs and outputs whose contribution to the overall control operation is relatively weak. A numerical example is presented to demonstrate the efficacy of the results. I.
Results 1  10
of
43