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14
FIR Filter Design via Spectral Factorization and Convex Optimization
, 1997
"... We consider the design of finite impulse response (FIR) filters subject to upper and lower bounds on the frequency response magnitude. The associated optimization problems, with the filter coefficients as the variables and the frequency response bounds as constraints, are in general nonconvex. Usin ..."
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Cited by 35 (6 self)
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We consider the design of finite impulse response (FIR) filters subject to upper and lower bounds on the frequency response magnitude. The associated optimization problems, with the filter coefficients as the variables and the frequency response bounds as constraints, are in general nonconvex. Using a change of variables and spectral factorization, we can pose such problems as linear or nonlinear convex optimization problems. As a result we can solve them efficiently (and globally) by recently developed interiorpoint methods. We describe applications to filter and equalizer design, and the related problem of antenna array weight design.
Lowauthority controller design via convex optimization
 AIAA Journal of Guidance, Control, and Dynamics
, 1999
"... In this paper we address the problem of lowauthority controller (LAC) design. The premise is that the actuators have limited authority, and hence cannot significantly shift the eigenvalues of the system. As a result, the closedloop eigenvalues can be well approximated analytically using perturbati ..."
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Cited by 30 (14 self)
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In this paper we address the problem of lowauthority controller (LAC) design. The premise is that the actuators have limited authority, and hence cannot significantly shift the eigenvalues of the system. As a result, the closedloop eigenvalues can be well approximated analytically using perturbation theory. These analytical approximations may suffice to predict the behavior of the closedloop system in practical cases, and will provide at least a very strong rationale for the first step in the design iteration loop. We will show that LAC design can be cast as convex optimization problems that can be solved efficiently in practice using interiorpoint methods. Also, we will show that by optimizing the ℓ1 norm of the feedback gains, we can arrive at sparse designs, i.e., designs in which only a small number of the control gains are nonzero. Thus, in effect, we can also solve actuator/sensor placement or controller architecture design problems. Keywords: Lowauthority control, actuator/sensor placement, linear operator perturbation theory, convex optimization, secondorder cone programming, semidefinite programming, linear matrix inequality. 1
Optimal Wire and Transistor Sizing for Circuits with NonTree Topology
"... 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 ..."
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Cited by 28 (11 self)
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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 interiorpoint methods for semidefinite programming. The method is applied to two important sizing problems sizing of clock meshes, and sizing of buses in the presence of crosstalk. 1
Quadratic Stabilization and Control of PiecewiseLinear Systems
 In Proc. American Control Conf
, 1998
"... We consider analysis and controller synthesis of piecewiselinear systems. The method is based on constructing quadratic and piecewisequadratic Lyapunov functions that prove stability and performance for the system. It is shown that proving stability and performance, or designing (statefeedback) c ..."
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Cited by 22 (3 self)
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We consider analysis and controller synthesis of piecewiselinear systems. The method is based on constructing quadratic and piecewisequadratic Lyapunov functions that prove stability and performance for the system. It is shown that proving stability and performance, or designing (statefeedback) controllers, can be cast as convex optimization problems involving linear matrix inequalities that can be solved very e ciently. A couple of simple examples are included to demonstrate applications of the methods described. Key words: Piecewiselinear systems, quadratic stabilization, linear matrix inequality (LMI). 1
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 ..."
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Cited by 16 (5 self)
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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 ..."
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Cited by 6 (3 self)
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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
Parametric robust H2 control design using LMI synthesis
 AIAA Journal Guidance, Control, and Dynamics
, 2000
"... This paper presents a new, iterative algorithm for designing full order LTI controllers for systems with real parameter uncertainty. Robust stability isdetermined for these systems using the Popov analysis criterion and multiplier, and robust performance is investigated using a bound on the output e ..."
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Cited by 6 (6 self)
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This paper presents a new, iterative algorithm for designing full order LTI controllers for systems with real parameter uncertainty. Robust stability isdetermined for these systems using the Popov analysis criterion and multiplier, and robust performance is investigated using a bound on the output energy. Control design to minimize the robust performance metric naturally leads to Bilinear Matrix Inequalities, which can be decoupled to a large extent. However, coupling remains in the problem since we simultaneously optimize the parameters of both the Popov stabilitymultiplier and the compensator. We present a heuristic, iterative algorithm to solve this design problem, and demonstrate that it works effectively on two numerical examples. In the process, we illustrate that the key advantages of this control design approach are the high reliability of the numerical techniques and the relative simplicity of implementing the algorithm. 1
Output Feedback Controller Synthesis for PiecewiseAffine Systems with Multiple Equilibria
 In Proc.American Control Conference
, 2000
"... This work builds on the stability analysis of piecewisea #ne systems reported in #1# and extends it to obtain a new synthesis tool for output feedback controllers. The proposed technique relies on formulating the search for a piecewisequadratic Lyapunov function and a piecewisea#ne controller as a ..."
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Cited by 6 (4 self)
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This work builds on the stability analysis of piecewisea #ne systems reported in #1# and extends it to obtain a new synthesis tool for output feedback controllers. The proposed technique relies on formulating the search for a piecewisequadratic Lyapunov function and a piecewisea#ne controller as a Bilinear Matrix Inequality. This can be solved iteratively as a set of two convex optimization problems involving linear matrix inequalities which can be solved numerically very e#ciently. Akey point in this design technique is that it can be used to design controllers with di#erent structures depending on the number of constraints that are added. In particular, it is shown that a controller with the structure of a regulator and estimator can be designed so that switching based on state estimates rather than on the output can be performed. It is also shown that many other desired features can be included in the design, such as boundedness of the control signals. Furthermore, the applicabilit...
Connections Between SemiInfinite and Semidefinite Programming
"... We consider convex optimization problems with linear matrix inequality (LMI) constraints, i.e., constraints of the form F (x) =F0+x1F1+ +xmFm 0; (1.1) where the matrices Fi = F T ..."
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Cited by 4 (1 self)
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We consider convex optimization problems with linear matrix inequality (LMI) constraints, i.e., constraints of the form F (x) =F0+x1F1+ +xmFm 0; (1.1) where the matrices Fi = F T