Results 1  10
of
15
Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones
, 1998
"... SeDuMi is an addon for MATLAB, that lets you solve optimization problems with linear, quadratic and semidefiniteness constraints. It is possible to have complex valued data and variables in SeDuMi. Moreover, large scale optimization problems are solved efficiently, by exploiting sparsity. This pape ..."
Abstract

Cited by 736 (3 self)
 Add to MetaCart
SeDuMi is an addon for MATLAB, that lets you solve optimization problems with linear, quadratic and semidefiniteness constraints. It is possible to have complex valued data and variables in SeDuMi. Moreover, large scale optimization problems are solved efficiently, by exploiting sparsity. This paper describes how to work with this toolbox.
Robust Solutions To LeastSquares Problems With Uncertain Data
, 1997
"... . We consider leastsquares problems where the coefficient matrices A; b are unknownbutbounded. We minimize the worstcase residual error using (convex) secondorder cone programming, yielding an algorithm with complexity similar to one singular value decomposition of A. The method can be interpret ..."
Abstract

Cited by 149 (13 self)
 Add to MetaCart
. We consider leastsquares problems where the coefficient matrices A; b are unknownbutbounded. We minimize the worstcase residual error using (convex) secondorder cone programming, yielding an algorithm with complexity similar to one singular value decomposition of A. The method can be interpreted as a Tikhonov regularization procedure, with the advantage that it provides an exact bound on the robustness of solution, and a rigorous way to compute the regularization parameter. When the perturbation has a known (e.g., Toeplitz) structure, the same problem can be solved in polynomialtime using semidefinite programming (SDP). We also consider the case when A; b are rational functions of an unknownbutbounded perturbation vector. We show how to minimize (via SDP) upper bounds on the optimal worstcase residual. We provide numerical examples, including one from robust identification and one from robust interpolation. Key Words. Leastsquares, uncertainty, robustness, secondorder cone...
sdpsol: A Parser/Solver for Semidefinite Programs with Matrix Structure
 In Recent advances in LMI methods for control
, 1995
"... . A variety of analysis and design problems in control, communication and information theory, statistics, combinatorial optimization, computational geometry, circuit design, and other fields can be expressed as semidefinite programming problems (SDPs) or determinant maximization problems (maxdet pr ..."
Abstract

Cited by 46 (19 self)
 Add to MetaCart
. A variety of analysis and design problems in control, communication and information theory, statistics, combinatorial optimization, computational geometry, circuit design, and other fields can be expressed as semidefinite programming problems (SDPs) or determinant maximization problems (maxdet problems). These problems often have matrix structure, i.e., some of the optimization variables are matrices. This matrix structure has two important practical ramifications: first, it makes the job of translating the problem into a standard SDP or maxdet format tedious, and, second, it opens the possibility of exploiting the structure to speed up the computation. In this paper we describe the design and implementation of sdpsol, a parser/solver for SDPs and maxdet problems. sdpsol allows problems with matrix structure to be described in a simple, natural, and convenient way. Although the current implementation of sdpsol does not exploit matrix structure in the solution algorithm, the languag...
A cone Complementarity Linearization Algorithm for Static OutputFeedback and Related Problems
 IEEE Transaction on Automatic Control
, 1997
"... Abstract—This paper describes a linear matrix inequality (LMI)based algorithm for the static and reducedorder outputfeedback synthesis problems of nthorder linear timeinvariant (LTI) systems with nu (respectively, ny) independent inputs (respectively, outputs). The algorithm is based on a “cone ..."
Abstract

Cited by 30 (0 self)
 Add to MetaCart
Abstract—This paper describes a linear matrix inequality (LMI)based algorithm for the static and reducedorder outputfeedback synthesis problems of nthorder linear timeinvariant (LTI) systems with nu (respectively, ny) independent inputs (respectively, outputs). The algorithm is based on a “cone complementarity ” formulation of the problem and is guaranteed to produce a stabilizing controller of order m n 0 max(nu;ny), matching a generic stabilizability result of Davison and Chatterjee [7]. Extensive numerical experiments indicate that the algorithm finds a controller with order less than or equal to that predicted by Kimura’s generic stabilizability result (m n0nu0ny+1). A similar algorithm can be applied to a variety of control problems, including robust control synthesis. Index Terms — Complementarity problem, linear matrix inequality, reducedorder stabilization, static output feedback. I.
Optimizing dominant time constant in RC circuits
, 1996
"... We propose to use the dominant time constant of a resistorcapacitor (RC) circuit as a measure of the signal propagation delay through the circuit. We show that the dominant time constant is a quasiconvex function of the conductances and capacitances, and use this property to cast several interestin ..."
Abstract

Cited by 16 (8 self)
 Add to MetaCart
We propose to use the dominant time constant of a resistorcapacitor (RC) circuit as a measure of the signal propagation delay through the circuit. We show that the dominant time constant is a quasiconvex function of the conductances and capacitances, and use this property to cast several interesting design problems as convex optimization problems, specifically, semidefinite programs (SDPs). For example, assuming that the conductances and capacitances are affine functions of the design parameters (which is a common model in transistor or interconnect wire sizing), one can minimize the power consumption or the area subject to an upper bound on the dominant time constant, or compute the optimal tradeoff surface between power, dominant time constant, and area. We will also note that, to a certain extent, convex optimization can be used to design the topology of the interconnect wires. This approach has two advantages over methods based on Elmore delay optimization. First, it handles a far wider class of circuits, e.g., those with nongrounded capacitors. Second, it always results in convex optimization problems for which very efficient interiorpoint methods have recently been developed. We illustrate the method, and extensions, with several examples involving optimal wire and transistor sizing.
Multiobjective Robust Control of LTI Systems Subject to Unstructured Perturbations
 Sys. Contr. Letter
, 1996
"... We consider a multiobjective robust controller synthesis problem for an LTI system subject to unstructured perturbations. Our design specifications include robust stability, robust performance (H 2 norm) bounds and timedomain bounds (output and command input peak). We derive sufficient conditions, ..."
Abstract

Cited by 11 (3 self)
 Add to MetaCart
We consider a multiobjective robust controller synthesis problem for an LTI system subject to unstructured perturbations. Our design specifications include robust stability, robust performance (H 2 norm) bounds and timedomain bounds (output and command input peak). We derive sufficient conditions, based on a single quadratic Lyapunov function, for the existence of an LTI controller such that the closedloop system satisfies all specifications simultaneously. These conditions can be numerically checked using finitedimensional, convex optimization over LMIs, associated with a twodimensional search. When considering only a subset of the specifications, we recover previous results from the literature, such as those obtained in mixed H 2 /H1 control. Keywords: Multiobjective robust control, mixed H 2 /H1 , timedomain specification, unstructured perturbation, quadratic Lyapunov function, linear matrix inequality. 1 Introduction In a multiobjective robust control problem, one seeks a co...
Inversion Error, Condition Number, And Approximate Inverses Of Uncertain Matrices
 Inverses of Uncertain Matrices. Linear Algebra and its Applications
, 2000
"... The classical condition number is a very rough measure of the effect of perturbations on the inverse of a square matrix. First, it assumes the perturbation is infinitesimally small. Second, it does not take into account the perturbation structure (e.g., Vandermonde). Similarly, the classical notion ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
The classical condition number is a very rough measure of the effect of perturbations on the inverse of a square matrix. First, it assumes the perturbation is infinitesimally small. Second, it does not take into account the perturbation structure (e.g., Vandermonde). Similarly, the classical notion of inverse of a matrix neglects the possibility of large, structured perturbations. We define a new quantity, the structured maximal inversion error, that takes into account both structure and non necessarily small perturbation size. When the perturbation is infinitesimal, we obtain a "structured condition number". We introduce the notion of approximate inverse, as a matrix that best approximates the inverse of a matrix with structured perturbations, when the perturbation varies in a given range. For a wide class of perturbation structures, we show how to use (convex) semidefinite programming to compute bounds on on the structured maximal inversion error and structured condition number, and compute an approximate inverse. The results are exact when the perturbation is "unstructured"we then obtain an analytic expression for the approximate inverse. When the perturbation is unstructured and additive, we recover the classical condition number; the approximate inverse is the operator related to the Total Least Squares (orthogonal regression) problem.
Applications of Semidefinite Programming
, 1998
"... A wide variety of nonlinear convex optimization problems can be cast as problems involving linear matrix inequalities (LMIs), and hence efficiently solved using recently developed interiorpoint methods. In this paper, we will consider two classes of optimization problems with LMI constraints: ffl ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
A wide variety of nonlinear convex optimization problems can be cast as problems involving linear matrix inequalities (LMIs), and hence efficiently solved using recently developed interiorpoint methods. In this paper, we will consider two classes of optimization problems with LMI constraints: ffl The semidefinite programming problem, i.e., the problem of minimizing a linear function subject to a linear matrix inequality. Semidefinite programming is an important numerical tool for analysis and synthesis in systems and control theory. It has also been recognized in combinatorial optimization as a valuable technique for obtaining bounds on the solution of NPhard problems.
Algorithms and Software for LMI Problems in Control
 IEEE Control Systems Magazine
, 1997
"... this article is to provide an overview of the state of the art of ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
this article is to provide an overview of the state of the art of