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88
Guaranteed minimumrank solutions of linear matrix equations via nuclear norm minimization
, 2007
"... The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding, and collaborative ..."
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Cited by 570 (23 self)
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The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding, and collaborative filtering. Although specific instances can often be solved with specialized algorithms, the general affine rank minimization problem is NPhard, because it contains vector cardinality minimization as a special case. In this paper, we show that if a certain restricted isometry property holds for the linear transformation defining the constraints, the minimum rank solution can be recovered by solving a convex optimization problem, namely the minimization of the nuclear norm over the given affine space. We present several random ensembles of equations where the restricted isometry property holds with overwhelming probability, provided the codimension of the subspace is sufficiently large. The techniques used in our analysis have strong parallels in the compressed sensing framework. We discuss how affine rank minimization generalizes this preexisting concept and outline a dictionary relating concepts from cardinality minimization to those of rank minimization. We also discuss several algorithmic approaches to solving the norm minimization relaxations, and illustrate our results with numerical examples.
A survey of recent results in networked control systems
 PROCEEDINGS OF THE IEEE
, 2007
"... Networked Control Systems (NCSs) are spatially distributed systems for which the communication between sensors, actuators, and controllers is supported by a shared communication network. In this paper we review several recent results on estimation, analysis, and controller synthesis for NCSs. The re ..."
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Cited by 281 (11 self)
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Networked Control Systems (NCSs) are spatially distributed systems for which the communication between sensors, actuators, and controllers is supported by a shared communication network. In this paper we review several recent results on estimation, analysis, and controller synthesis for NCSs. The results surveyed address channel limitations in terms of packetrates, sampling, network delay and packet dropouts. The results are presented in a tutorial fashion, comparing alternative methodologies.
Rank minimization and applications in system theory
 In American Control Conference
, 2004
"... AbstractIn this tutorial paper, we consider the problem Of minimizing the rank of a matrix over a convex set. The Rank Minimization Problem (RMP) arises in diverse areas such as control, system identification, statistics and signal processing, and is known to be computationally NPhard. We give an ..."
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Cited by 49 (0 self)
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AbstractIn this tutorial paper, we consider the problem Of minimizing the rank of a matrix over a convex set. The Rank Minimization Problem (RMP) arises in diverse areas such as control, system identification, statistics and signal processing, and is known to be computationally NPhard. We give an overview of the problem, its interpretations, applications, and solution methods. In particular, we focus on how convex optimization can he used to develop heuristic methods for this problem.
Exponential stability of impulsive systems with application to uncertain sampleddata systems
 SYSTEMS & CONTROL LETTERS
, 2007
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Algorithms for leader selection in large dynamical networks: Noisefree leaders
 in Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference
, 2011
"... Abstract — We examine the leader selection problem in multiagent dynamical networks where leaders, in addition to relative information from their neighbors, also have access to their own states. We are interested in selecting an a priori specified number of agents as leaders in order to minimize th ..."
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Cited by 22 (8 self)
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Abstract — We examine the leader selection problem in multiagent dynamical networks where leaders, in addition to relative information from their neighbors, also have access to their own states. We are interested in selecting an a priori specified number of agents as leaders in order to minimize the total variance of the stochastically forced network. Combinatorial nature of this optimal control problem makes computation of the global minimum difficult. We propose a convex relaxation to obtain a lower bound on the global optimal value, and use simple but efficient greedy algorithms to obtain an upper bound. Furthermore, we employ the alternating direction method of multipliers to search for a local minimum. Two examples are provided to illustrate the effectiveness of the developed methods. Index Terms — Alternating direction method of multipliers, consensus, convex optimization/relaxation, greedy algorithm, leader selection, performance bounds, variance amplification. I.
Rank minimization approach for solving BMI problems with random search
 in Proceedings American Control Conference, 2001
"... t omizuka~me, berkeley, edu This paper presents the rank minimization approach to solve general bilinear matrix inequality (BMI) problems. Due to the NPhardness of BMI problems, no proposed algorithm that globally solves general BMI problems is a polynomialtime algorithm. We present a local search ..."
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Cited by 14 (0 self)
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t omizuka~me, berkeley, edu This paper presents the rank minimization approach to solve general bilinear matrix inequality (BMI) problems. Due to the NPhardness of BMI problems, no proposed algorithm that globally solves general BMI problems is a polynomialtime algorithm. We present a local search algorithm based on the semidefinite programming (SDP) relaxation approach to indefinite quadratic programming, which is analogous to the wellknown relaxation method for a certain class of combinatorial problems. Instead of applying the branch and bound (BB) method for global search, a linearizationbased local search algorithm is employed to reduce the relaxation gap. Furthermore, a random search approach is introduced along with the deterministic approach. Four numerical experiments are presented to show the search performance of the proposed approach. 1
A nonlinear SDP algorithm for static output feedback problems in COMPlib. LAASCNRS research report no. 04508
, 2004
"... Abstract: We present an algorithm for the solution of static output feedback problems formulated as semidefinite programs with bilinear matrix inequality constraints and collected in the library COMPleib. The algorithm, based on the generalized augmented Lagrangian technique, is implemented in the p ..."
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Cited by 13 (4 self)
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Abstract: We present an algorithm for the solution of static output feedback problems formulated as semidefinite programs with bilinear matrix inequality constraints and collected in the library COMPleib. The algorithm, based on the generalized augmented Lagrangian technique, is implemented in the publicly available general purpose software PENBMI. Numerical results demonstrate the behavior of the code.
Anticipative and Nonanticipative Controller Design for Network Control Systems
 In Panos J. Antsaklis, Paulo Tabuada, Networked Embedded Sensing and Control, volume 331 of Lect. Notes in Contr. and Inform. Sci
, 2006
"... Summary. We propose a numerical procedure to design a linear outputfeedback controller for a remote linear plant in which the loop is closed through a network. The controller stabilizes the plant in the presence of delays, sampling, and packet dropouts in the (sensor) measurement and actuation chan ..."
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Cited by 11 (1 self)
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Summary. We propose a numerical procedure to design a linear outputfeedback controller for a remote linear plant in which the loop is closed through a network. The controller stabilizes the plant in the presence of delays, sampling, and packet dropouts in the (sensor) measurement and actuation channels. We consider two types of control units: anticipative and nonanticipative. In both cases the closedloop system with delays, sampling, and packet dropouts can be modeled as delay differential equations. Our method of designing the controller parameters is based on the LyapunovKrasovskii theorem and a linear cone complementarity algorithm. Numerical examples show that the proposed design method is significantly better than the existing ones. 1
other authors
 Biocontrol Sci Technol
, 1999
"... Differential effects of salen and manganesesalen complex (EUK8) on the regulation of cellular cadmium uptake and toxicity ..."
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Cited by 8 (1 self)
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Differential effects of salen and manganesesalen complex (EUK8) on the regulation of cellular cadmium uptake and toxicity