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A Rank Minimization Heuristic with Application to Minimum Order System Approximation
Rank Minimization Heuristic Minimum Order System Approximation
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2015/7/10
Several problems arising in control system analysis and design, such as reduced order controller synthesis, involve minimizing the rank of a matrix variable subject to linear matrix inequality (LMI) c...
Log-Det Heuristic for Matrix Rank Minimization with Applications to Hankel and Euclidean Distance Matrices
Log-Det Heuristic Matrix Rank Minimization Applications Hankel Euclidean Distance Matrices
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2015/7/10
We present a heuristic for minimizing the rank of a positive semidefinite matrix over a convex set. We use the logarithm of the determinant as a smooth approximation for rank, and locally minimize thi...
Rank Minimization and Applications in System Theory
Rank Minimization Applications System Theory
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2015/7/10
In 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...
Generalized Low Rank Models
Generalized Low Rank Models
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2015/7/8
Principal components analysis (PCA) is a well-known technique for approximating a data set represented by a matrix by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets c...