Results 1  10
of
18
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 ..."
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Cited by 149 (13 self)
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. 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...
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 26 (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.
Matrixvalued NevanlinnaPick interpolation with complexity constraint: An optimization approach
 IEEE Trans. Automat. Contr
, 2003
"... Abstract—Over the last several years, a new theory of Nevanlinna–Pick interpolation with complexity constraint has been developed for scalar interpolants. In this paper we generalize this theory to the matrixvalued case, also allowing for multiple interpolation points. We parameterize a class of in ..."
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Cited by 16 (5 self)
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Abstract—Over the last several years, a new theory of Nevanlinna–Pick interpolation with complexity constraint has been developed for scalar interpolants. In this paper we generalize this theory to the matrixvalued case, also allowing for multiple interpolation points. We parameterize a class of interpolants consisting of “most interpolants ” of no higher degree than the central solution in terms of spectral zeros. This is a complete parameterization, and for each choice of interpolant we provide a convex optimization problem for determining it. This is derived in the context of duality theory of mathematical programming. To solve the convex optimization problem, we employ a homotopy continuation technique previously developed for the scalar case. These results can be applied to many classes of engineering problems, and, to illustrate this, we provide some examples. In particular, we apply our method to a benchmark problem in multivariate robust control. By constructing a controller satisfying all design specifications but having only half the McMillan degree of conventional controllers, we demonstrate the advantage of the proposed method. Index Terms—Complexity constraint, control, matrixvalued Nevanlinna–Pick interpolation, optimization, spectral
Partially augmented Lagrangian method for matrix inequalities
 SIAM J. on Optimization
"... Pierre Apkarian k Abstract We discuss a partially augmented Lagrangian method for optimization programs with matrix inequality constraints. A global convergence result is obtained. Applications to hard problems in feedback control are presented to validate the method numerically. ..."
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Cited by 15 (8 self)
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Pierre Apkarian k Abstract We discuss a partially augmented Lagrangian method for optimization programs with matrix inequality constraints. A global convergence result is obtained. Applications to hard problems in feedback control are presented to validate the method numerically.
Improved LMI Conditions For Gain Scheduling And Related Control Problems
, 1998
"... this paper concerns a linear system whose statespace equations depend rationally on real, timevarying parameters, which are measured in real time. A stabilizing, parameterdependent controller is sought, such that a given L ..."
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Cited by 6 (1 self)
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this paper concerns a linear system whose statespace equations depend rationally on real, timevarying parameters, which are measured in real time. A stabilizing, parameterdependent controller is sought, such that a given L
Input/output selection for planar tensegrity models
 In Proceedings Of The 40th IEEE Conference On Decision And Control
, 2001
"... A systematic method of selecting sensors and actuators is produced, efficiently selecting inputs and outputs that guarantee a desired level of performance in the ∞norm sense. The method employs an efficiently computable necessary and sufficient existence condition, using an effective search strateg ..."
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Cited by 6 (0 self)
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A systematic method of selecting sensors and actuators is produced, efficiently selecting inputs and outputs that guarantee a desired level of performance in the ∞norm sense. The method employs an efficiently computable necessary and sufficient existence condition, using an effective search strategy. The search strategy is based on a method to generate all socalled minimal dependent sets. This method is applied to tensegrity structures. Tensegrity structures are a prime example for application of techniques that address structural problems, because they offer a lot of flexibility in choosing actuators/sensors and in choosing their mechanical structure. The selection method is demonstrated with results for a 3 stage planar tensegrity structure where all 26 tendons can be used as control device, be it actuator, sensor, or both, making up 52 devices from which to choose. In our setup it is easy to require devices to be selected as colocated pairs, and to analyze the performance penalty associated with this restriction. Two performance criteria were explored, one is related to the dynamical stiffness of the structure, the other to vibration isolation. The optimal combinations of sensors and actuators depend on the design specifications and are really different for both performance criteria.
Stochastic H∞
, 1998
"... We consider stochastic linear plants which are controlled by dynamic output feedback and subjected to both deterministic and stochastic perturbations. Our objective is to develop an H∞ type theory for such systems. We prove a bounded real lemma for stochastic systems with deterministic and stochast ..."
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Cited by 3 (1 self)
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We consider stochastic linear plants which are controlled by dynamic output feedback and subjected to both deterministic and stochastic perturbations. Our objective is to develop an H∞ type theory for such systems. We prove a bounded real lemma for stochastic systems with deterministic and stochastic perturbations. This enables us to obtain necessary and sufficient conditions for the existence of a stabilizing compensator which keeps the effect of the perturbations on the to be controlled output below a given threshhold fl > 0. In the deterministic case the analogous conditions involve two uncoupled linear matrix inequalities but in the stochastic setting we get coupled nonlinear matrix inequalities instead. The connection between H∞ theory and stability radii is discussed and leads to a lower bound for the radii which is shown to be tight in some special cases.
H∞ Output Feedback Control for Linear, Discrete TimeVarying Systems via the Bounded Real Lemma
, 1996
"... In this paper we develop a solution to the discretetime H∞ output feedback control problem for Linear TimeVarying (LTV) systems. The solution is developed along the strategy set up in [Doyle et. al. 1989] and the main ingredient in its derivation is the extension of the wellknown bounded real l ..."
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Cited by 3 (2 self)
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In this paper we develop a solution to the discretetime H∞ output feedback control problem for Linear TimeVarying (LTV) systems. The solution is developed along the strategy set up in [Doyle et. al. 1989] and the main ingredient in its derivation is the extension of the wellknown bounded real lemma to a (discrete) timevarying context, developed in [van der Veen and Verhaegen 1995]. This approach contributes to the conceptual simplicity, and hence to the accessibility, of the solution. Apart from that, we treat the infinitehorizon case for LTV system of nonuniform state dimension, and varying input and output dimension. Both situations can easily occur in practice, e.g. in multirate sampled data control systems. The algorithm that can be derived from the solution presented is then applied to the H∞ output feedback of a dynamical system changing from one operation point in its operation envelope to another.
On the Disturbance Attenuation Problem for a Wide Class of Time Invariant Linear Stochastic Systems
, 1999
"... In this paper we extend the results of [9] on the stochastic disturbance attenuation problem to a wider class of stochastic systems. We consider timeinvariant stochastic linear plants which are controlled by dynamic output feedback and subjected to both deterministic and stochastic parameter pertur ..."
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Cited by 2 (1 self)
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In this paper we extend the results of [9] on the stochastic disturbance attenuation problem to a wider class of stochastic systems. We consider timeinvariant stochastic linear plants which are controlled by dynamic output feedback and subjected to both deterministic and stochastic parameter perturbations. The aim is to develop an H 1 type theory for such systems. The Ito equations considered in [9] contained two (not necessarily independent) scalar Wiener processes, one for the state dependent noise term and one for the input dependent noise term. In this paper the two scalar Wiener processes are replaced by (not necessarily independent) vector valued Wiener processses. For this wider class of systems a bounded real lemma is derived which provides the basis for an LMI approach towards the stochastic disturbance attenuation problem. Necessary and sufficient conditions are derived for the existence of a stabilizing controller reducing the norm of the closed loop perturbation operat...