Statistics for Sparse, High-Dimensional, and Nonparametric System Identification
Anil Aswani, Peter Bickel, Claire Tomlin

Citation
Anil Aswani, Peter Bickel, Claire Tomlin. "Statistics for Sparse, High-Dimensional, and Nonparametric System Identification". IEEE ICRA 2009, 2133–2138, 15, May, 2009.

Abstract
Local linearization techniques are an important class of nonparametric system identification. Identifying local linearizations in practice involves solving a linear regression problem that is ill-posed. The problem can be ill-posed either if the dynamics of the system lie on a manifold of lower dimension than the ambient space or if there are not enough measurements of all the modes of the dynamics of the system. We describe a set of linear regression estimators that can handle data lying on a lower-dimension manifold. These estimators differ from previous estimators, because these estimators are able to improve estimator performance by exploiting the sparsity of the system – the existence of direct interconnections between only some of the states – and can work in the “large p, small n” setting in which the number of states is comparable to the number of data points. We describe our system identification procedure, which consists of a presmoothing step and a regression step, and then we apply this procedure to data taken from a quadrotor helicopter. We use this data set to compare our procedure with existing procedures.

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• HTML

  Anil Aswani, Peter Bickel, Claire Tomlin. <a
  href="http://chess.eecs.berkeley.edu/pubs/604.html"
  >Statistics for Sparse, High-Dimensional, and
  Nonparametric System Identification</a>, IEEE ICRA
  2009, 2133�2138, 15, May, 2009.

• Plain text

  Anil Aswani, Peter Bickel, Claire Tomlin. "Statistics
  for Sparse, High-Dimensional, and Nonparametric System
  Identification". IEEE ICRA 2009, 2133�2138, 15,
  May, 2009.

• BibTeX

  @inproceedings{AswaniBickelTomlin09_StatisticsForSparseHighDimensionalNonparametricSystem,
      author = {Anil Aswani and Peter Bickel and Claire Tomlin},
      title = {Statistics for Sparse, High-Dimensional, and
                Nonparametric System Identification},
      booktitle = {IEEE ICRA 2009},
      pages = {2133�2138},
      day = {15},
      month = {May},
      year = {2009},
      abstract = {Local linearization techniques are an important
                class of nonparametric system identi�cation.
                Identifying local linearizations in practice
                involves solving a linear regression problem that
                is ill-posed. The problem can be ill-posed either
                if the dynamics of the system lie on a manifold of
                lower dimension than the ambient space or if there
                are not enough measurements of all the modes of
                the dynamics of the system. We describe a set of
                linear regression estimators that can handle data
                lying on a lower-dimension manifold. These
                estimators differ from previous estimators,
                because these estimators are able to improve
                estimator performance by exploiting the sparsity
                of the system � the existence of direct
                interconnections between only some of the states
                � and can work in the �large p, small n�
                setting in which the number of states is
                comparable to the number of data points. We
                describe our system identi�cation procedure,
                which consists of a presmoothing step and a
                regression step, and then we apply this procedure
                to data taken from a quadrotor helicopter. We use
                this data set to compare our procedure with
                existing procedures.},
      URL = {http://chess.eecs.berkeley.edu/pubs/604.html}
  }
  

Posted by Anil Aswani on 17 Jun 2009.
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