Results 1  10
of
10
CSDP, a C library for semidefinite programming.
, 1997
"... this paper is organized as follows. First, we discuss the formulation of the semidefinite programming problem used by CSDP. We then describe the predictor corrector algorithm used by CSDP to solve the SDP. We discuss the storage requirements of the algorithm as well as its computational complexity. ..."
Abstract

Cited by 144 (1 self)
 Add to MetaCart
this paper is organized as follows. First, we discuss the formulation of the semidefinite programming problem used by CSDP. We then describe the predictor corrector algorithm used by CSDP to solve the SDP. We discuss the storage requirements of the algorithm as well as its computational complexity. Finally, we present results from the solution of a number of test problems. 2 The SDP Problem We consider semidefinite programming problems of the form max tr (CX)
Optimal Wire and Transistor Sizing for Circuits with NonTree Topology
 in Proc. Int. Conf. on Computer Aided Design
, 1997
"... Conventional methods for optimal sizing of wires and transistors use linear RC circuit models and the Elmore delay as a measure of signal delay. If the RC circuit has a tree topology the sizing problem reduces to a convex optimization problem which can be solved using geometric programming. The tree ..."
Abstract

Cited by 28 (11 self)
 Add to MetaCart
Conventional methods for optimal sizing of wires and transistors use linear RC circuit models and the Elmore delay as a measure of signal delay. If the RC circuit has a tree topology the sizing problem reduces to a convex optimization problem which can be solved using geometric programming. The tree topology restriction precludes the use of these methods in several sizing problems of significant importance to highperformance deep submicron design including, for example, circuits with loops of resistors, e.g., clock distribution meshes, and circuits with coupling capacitors, e.g., buses with crosstalk between the lines. The paper proposes a new optimization method which can be used to address these problems. The method uses the dominant time constant as a measure of signal propagation delay in an RC circuit, instead of Elmore delay. Using this measure, sizing of any RC circuit can be cast as a convex optimization problem which can be solved using the recently developed efficient interi...
FIR Filter Design via Semidefinite Programming and Spectral Factorization
, 1996
"... We present a new semidefinite programming approach to FIR lter design with arbitrary upper and lower bounds on the frequency response magnitude. It is shown that the constraints can be expressed as linear matrix inequalities (LMIs), and hence they can be easily handled by recent interiorpoint metho ..."
Abstract

Cited by 15 (6 self)
 Add to MetaCart
We present a new semidefinite programming approach to FIR lter design with arbitrary upper and lower bounds on the frequency response magnitude. It is shown that the constraints can be expressed as linear matrix inequalities (LMIs), and hence they can be easily handled by recent interiorpoint methods. Using this LMI formulation, we can cast several interesting filter design problems as convex or quasiconvex optimization problems, e.g., minimizing the length of the FIR filter and computing the Chebychev approximation of a desired power spectrum or a desired frequency response magnitude on a logarithmic scale.
Control applications of nonlinear convex programming
 the 1997 IFAC Conference on Advanced Process Control
, 1998
"... Since 1984 there has been a concentrated e ort to develop e cient interiorpoint methods for linear programming (LP). In the last few years researchers have begun to appreciate a very important property of these interiorpoint methods (beyond their e ciency for LP): they extend gracefully to nonline ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
Since 1984 there has been a concentrated e ort to develop e cient interiorpoint methods for linear programming (LP). In the last few years researchers have begun to appreciate a very important property of these interiorpoint methods (beyond their e ciency for LP): they extend gracefully to nonlinear convex optimization problems. New interiorpoint algorithms for problem classes such as semide nite programming (SDP) or secondorder cone programming (SOCP) are now approaching the extreme e ciency of modern linear programming codes. In this paper we discuss three examples of areas of control where our ability to e ciently solve nonlinear convex optimization problems opens up new applications. In the rst example we show how SOCP can be used to solve robust openloop optimal control problems. In the second example, we show how SOCP can be used to simultaneously design the setpoint and feedback gains for a controller, and compare this method with the more standard approach. Our nal application concerns analysis and synthesis via linear matrix inequalities and SDP. Submitted to a special issue of Journal of Process Control, edited by Y. Arkun & S. Shah, for papers presented at the 1997 IFAC Conference onAdvanced Process Control, June 1997, Ban. This and related papers available via anonymous FTP at
LMI Synthesis of Parametric Robust H1 Controllers
 in Proc. American Control Conf
, 1997
"... This paper presents a new algorithm for designing full order LTI controllers for systems with real parametric uncertainty. The approach is based on the robust L2 gain analysis of the Lur'e system using Popov analysis and multipliers. The core algorithm, previously applied to the robust H2 performanc ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
This paper presents a new algorithm for designing full order LTI controllers for systems with real parametric uncertainty. The approach is based on the robust L2 gain analysis of the Lur'e system using Popov analysis and multipliers. The core algorithm, previously applied to the robust H2 performance synthesis problem, is shown to be applicable to the robust controller design with the H1 cost. Although the performance metrics are di erent, we demonstrate that the same solution algorithm based on LMI synthesis leads to a very effective and e cient technique for real parametric robust H1 control design. Furthermore, it is di cult to compare robust H2 controllers to =Km designs, but in this work we provide insights into the issue of conservatism for various robust H1 control approaches, in particular, the Popov controller synthesis, the robust H1 design, and the =Km synthesis. The detailed analysis of these approaches is demonstrated on a exible structure benchmark problem. Keywords: Lur'e system, real parametric uncertainty; L2 gain; Popov controller synthesis; bilinear matrix inequality; linear matrix inequality. 1
Parametric robust H_2 control design with generalized multipliers via LMI Synthesis
, 1998
"... ..."
Design and Implementation of a Parser/Solver for SDPs with Matrix Structure
"... A wide variety of analysis and design problems arising in control, communication and information theory, statistics, computational geometry and many other fields can be expressed as semidefinite programming problems (SDPs) or determinant maximization problems (maxdetproblems). In engineering applic ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
A wide variety of analysis and design problems arising in control, communication and information theory, statistics, computational geometry and many other fields can be expressed as semidefinite programming problems (SDPs) or determinant maximization problems (maxdetproblems). In engineering applications these problems usually have matrix structure, i.e., the optimization variables are matrices. Recent interiorpoint methods can exploit such structure to gain huge efficiency. In this paper, we describe the design and implementation of a parser/solver for SDPs and maxdetproblems with matrix structure. The parser/solver parses a problem specification close to its natural mathematical description, solves the compiled problem efficiently, and returns the results in a convenient form.
Convergence Analysis of A Parametric Robust H 2 Controller Synthesis Algorithm 1
"... This paper presents an iterative algorithm for solving the parametric robust H2 controller synthesis problem and analyzes the convergence properties of the algorithm on several examples. Iterative procedures are normally applied to a large class of robust control design problems in which the formula ..."
Abstract
 Add to MetaCart
This paper presents an iterative algorithm for solving the parametric robust H2 controller synthesis problem and analyzes the convergence properties of the algorithm on several examples. Iterative procedures are normally applied to a large class of robust control design problems in which the formulation naturally leads to bilinear matrix inequalities (BMIs). It is di cult to make concrete statements about the behavior of these iterative algorithms, except that it is often conjectured that the cost in each step of the solution procedure is reduced, which implies that the algorithms should converge to a local minimum. Similar di culties exist for the new LMIbased iterative algorithm that we haverecently proposed to solve the BMIs that occur in robust H2 control design. The e ectiveness of the new algorithm has already been demonstrated on several numerical examples. This paper adds an important component tothediscussion on the convergence of the new algorithm by verifying that it e ciently converges to the optimal solution. In the process, we provide some new key insights on the proposed design technique which indicate that it exhibits properties similar to the D{K iteration of the complex =Kmsynthesis. 1
Parametric robust H 2 control design with generalized multipliers via LMI synthesis
"... A new combined analysis and synthesis procedure that provides a less conservative robust control design technique for systems with real parametric uncertainty is presented. The robust stability for these systems is analysed by the passivity theorem with generalized multipliers, and the worst case H2 ..."
Abstract
 Add to MetaCart
A new combined analysis and synthesis procedure that provides a less conservative robust control design technique for systems with real parametric uncertainty is presented. The robust stability for these systems is analysed by the passivity theorem with generalized multipliers, and the worst case H2 performance is investigated using an upper bound on the total output energy. The dynamics of the multipliers are systematically chosen using knowledge from the linear part of the uncertain systems. This approach provides additional degrees of freedom in the synthesis that lead to a reduction of the conservatism in the worstcase H2 performance and achieved robustness bounds. However, the formulation of the control design problem is very complicated and it is di � cult to solve directly. This paper presents an iterative algorithm, which in an H2 equivalent of the D ± K iteration for the /Km synthesis, to account for the complicated couplings in the synthesis problem. We use a simple beam system with an uncertain modal frequency to illustrate that this synthesis technique with generalized multipliers results in less conservative controllers than previously published Popov controller synthesis techniques. In the process, we demonstrate that this design approach is very e � ective and simple to implement numerically. 1.
LMI Synthesis of Parametric Robust H∞ Controllers
 IN PROC. AMERICAN CONTROL CONF
, 1997
"... This paper presents a new algorithm for designing full order LTI controllers for systems with real parametric uncertainty. The approach is based on the robust L2 gain analysis of the Lur'e system using Popov analysis and multipliers. The core algorithm, previously applied to the robust H2 performanc ..."
Abstract
 Add to MetaCart
This paper presents a new algorithm for designing full order LTI controllers for systems with real parametric uncertainty. The approach is based on the robust L2 gain analysis of the Lur'e system using Popov analysis and multipliers. The core algorithm, previously applied to the robust H2 performance synthesis problem, is shown to be applicable to the robust controller design with the H∞ cost. Although the performance metrics are different, we demonstrate that the same solution algorithm based on LMI synthesis leads to a very effective and efficient technique for real parametric robust H∞ control design. Furthermore, it is difficult to compare robust H2 controllers to =Km designs, but in this work we provide insights into the issue of conservatism for various robust H1 control approaches, in particular, the Popov controller synthesis, the robust H∞ design, and the =Km synthesis. The detailed analysis of these approaches is demonstrated on a exible structure benchmark problem.