3 research outputs found
N2SID: Nuclear Norm Subspace Identification
The identification of multivariable state space models in innovation form is
solved in a subspace identification framework using convex nuclear norm
optimization. The convex optimization approach allows to include constraints on
the unknown matrices in the data-equation characterizing subspace
identification methods, such as the lower triangular block-Toeplitz of
weighting matrices constructed from the Markov parameters of the unknown
observer. The classical use of instrumental variables to remove the influence
of the innovation term on the data equation in subspace identification is
avoided. The avoidance of the instrumental variable projection step has the
potential to improve the accuracy of the estimated model predictions,
especially for short data length sequences. This is illustrated using a data
set from the DaSIy library. An efficient implementation in the framework of the
Alternating Direction Method of Multipliers (ADMM) is presented that is used in
the validation study
Maximum Entropy Vector Kernels for MIMO system identification
Recent contributions have framed linear system identification as a
nonparametric regularized inverse problem. Relying on -type
regularization which accounts for the stability and smoothness of the impulse
response to be estimated, these approaches have been shown to be competitive
w.r.t classical parametric methods. In this paper, adopting Maximum Entropy
arguments, we derive a new penalty deriving from a vector-valued
kernel; to do so we exploit the structure of the Hankel matrix, thus
controlling at the same time complexity, measured by the McMillan degree,
stability and smoothness of the identified models. As a special case we recover
the nuclear norm penalty on the squared block Hankel matrix. In contrast with
previous literature on reweighted nuclear norm penalties, our kernel is
described by a small number of hyper-parameters, which are iteratively updated
through marginal likelihood maximization; constraining the structure of the
kernel acts as a (hyper)regularizer which helps controlling the effective
degrees of freedom of our estimator. To optimize the marginal likelihood we
adapt a Scaled Gradient Projection (SGP) algorithm which is proved to be
significantly computationally cheaper than other first and second order
off-the-shelf optimization methods. The paper also contains an extensive
comparison with many state-of-the-art methods on several Monte-Carlo studies,
which confirms the effectiveness of our procedure