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62
Multiobjective output feedback control via LMI
 in Proc. Amer. Contr. Conf
, 1997
"... The problem of multiobjective H2=H1 optimal controller design is reviewed. There is as yet no exact solution to this problem. We present a method based on that proposed by Scherer [14]. The problem is formulated as a convex semidefinite program (SDP) using the LMI formulation of the H2 and H1 norms. ..."
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Cited by 212 (8 self)
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The problem of multiobjective H2=H1 optimal controller design is reviewed. There is as yet no exact solution to this problem. We present a method based on that proposed by Scherer [14]. The problem is formulated as a convex semidefinite program (SDP) using the LMI formulation of the H2 and H1 norms. Suboptimal solutions are computed using finite dimensional Qparametrization. The objective value of the suboptimal Q's converges to the true optimum as the dimension of Q is increased. State space representations are presented which are the analog of those given by Khargonekar and Rotea [11] for the H2 case. A simple example computed using FIR (Finite Impulse Response) Q's is presented.
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 200 (14 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 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.
Matrixvalued NevanlinnaPick interpolation with complexity constraint: An optimization approach
 IEEE Trans. Automatic Control
, 2003
"... Abstract. Over the last several years a new theory of NevanlinnaPick 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 26 (5 self)
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Abstract. Over the last several years a new theory of NevanlinnaPick 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 H ∞ controllers, we demonstrate the efficiency of our method.
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 21 (7 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 18 (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
Consensus of multiagent systems with general linear and Lipschitz nonlinear dynamics using distributed adaptive protocols
 IEEE Transactions on Automatic Control
, 2013
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An output feedback H∞ controller design for linear systems subject to sensor nonlinearities
 IEEE Trans. on Circuits and Systems
"... Abstract—In this paper, the output feedback controller design problem is addressed for linear systems subject to sensor nonlinearity. First, the existence condition of an output feedback controller is derived for systems with sensor sector nonlinearity. A design method for the output feedback contro ..."
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Cited by 9 (0 self)
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Abstract—In this paper, the output feedback controller design problem is addressed for linear systems subject to sensor nonlinearity. First, the existence condition of an output feedback controller is derived for systems with sensor sector nonlinearity. A design method for the output feedback controller is proposed using a linearmatrix inequality (LMI) based approach. The result is then applied to the design of a regional output feedback controller for the systems subject to sensor saturation. An LMI optimization based approach is proposed to computing the feedback matrices of the regional output feedback controller. At last a numerical example is presented to show the effectiveness of the results. Index Terms—Linear systems, sector nonlinearity, sensor saturation, control, 2 gain. I.
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 9 (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.