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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)
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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...
Robust Control Tools: Graphical UserInterfaces and LMI Algorithms
, 1994
"... Robust control theory considers a fundamental and practically important issue in control engineering: plant uncertainty. It turns out that many of the simplest questions are very di cult to solve, but researchers have made considerable progress over the last twenty years. Nevertheless the theory has ..."
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Robust control theory considers a fundamental and practically important issue in control engineering: plant uncertainty. It turns out that many of the simplest questions are very di cult to solve, but researchers have made considerable progress over the last twenty years. Nevertheless the theory has so far had less impact on practice than one might imagine. (Simulation and modeling tools, for example, have probably had a wider impact on practice.) Recent techniques of robust control theory, based on convex optimization over linear matrix