7,065 research outputs found
On the smoothness of nonlinear system identification
We shed new light on the \textit{smoothness} of optimization problems arising
in prediction error parameter estimation of linear and nonlinear systems. We
show that for regions of the parameter space where the model is not
contractive, the Lipschitz constant and -smoothness of the objective
function might blow up exponentially with the simulation length, making it hard
to numerically find minima within those regions or, even, to escape from them.
In addition to providing theoretical understanding of this problem, this paper
also proposes the use of multiple shooting as a viable solution. The proposed
method minimizes the error between a prediction model and the observed values.
Rather than running the prediction model over the entire dataset, multiple
shooting splits the data into smaller subsets and runs the prediction model
over each subset, making the simulation length a design parameter and making it
possible to solve problems that would be infeasible using a standard approach.
The equivalence to the original problem is obtained by including constraints in
the optimization. The new method is illustrated by estimating the parameters of
nonlinear systems with chaotic or unstable behavior, as well as neural
networks. We also present a comparative analysis of the proposed method with
multi-step-ahead prediction error minimization
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
A unified framework for solving a general class of conditional and robust set-membership estimation problems
In this paper we present a unified framework for solving a general class of
problems arising in the context of set-membership estimation/identification
theory. More precisely, the paper aims at providing an original approach for
the computation of optimal conditional and robust projection estimates in a
nonlinear estimation setting where the operator relating the data and the
parameter to be estimated is assumed to be a generic multivariate polynomial
function and the uncertainties affecting the data are assumed to belong to
semialgebraic sets. By noticing that the computation of both the conditional
and the robust projection optimal estimators requires the solution to min-max
optimization problems that share the same structure, we propose a unified
two-stage approach based on semidefinite-relaxation techniques for solving such
estimation problems. The key idea of the proposed procedure is to recognize
that the optimal functional of the inner optimization problems can be
approximated to any desired precision by a multivariate polynomial function by
suitably exploiting recently proposed results in the field of parametric
optimization. Two simulation examples are reported to show the effectiveness of
the proposed approach.Comment: Accpeted for publication in the IEEE Transactions on Automatic
Control (2014
Regularized linear system identification using atomic, nuclear and kernel-based norms: the role of the stability constraint
Inspired by ideas taken from the machine learning literature, new
regularization techniques have been recently introduced in linear system
identification. In particular, all the adopted estimators solve a regularized
least squares problem, differing in the nature of the penalty term assigned to
the impulse response. Popular choices include atomic and nuclear norms (applied
to Hankel matrices) as well as norms induced by the so called stable spline
kernels. In this paper, a comparative study of estimators based on these
different types of regularizers is reported. Our findings reveal that stable
spline kernels outperform approaches based on atomic and nuclear norms since
they suitably embed information on impulse response stability and smoothness.
This point is illustrated using the Bayesian interpretation of regularization.
We also design a new class of regularizers defined by "integral" versions of
stable spline/TC kernels. Under quite realistic experimental conditions, the
new estimators outperform classical prediction error methods also when the
latter are equipped with an oracle for model order selection
Optimal and Robust Feedback Controller Estimation for a Vibrating Plate using Subspace Model Identification
This paper presents a method to estimate the H2 optimal and a robust feedback controller by means of Subspace Model Identification using the internal model control (IMC) approach. Using IMC an equivalent feed forward control problem is obtained, which is solved by the Causal Wiener filter for the H2 optimal controller. The robust variant, called the Cautious Wiener filter, optimizes the average performance w.r.t. probabilistic model errors. The identification of the Causal and Cautious Wiener filters are control-relevant. The method is illustrated by experiments on a 4-inputs 4-outputs vibrating plate with additional mass variation
Flight test trajectory control analysis
Recent extensions to optimal control theory applied to meaningful linear models with sufficiently flexible software tools provide powerful techniques for designing flight test trajectory controllers (FTTCs). This report describes the principal steps for systematic development of flight trajectory controllers, which can be summarized as planning, modeling, designing, and validating a trajectory controller. The techniques have been kept as general as possible and should apply to a wide range of problems where quantities must be computed and displayed to a pilot to improve pilot effectiveness and to reduce workload and fatigue. To illustrate the approach, a detailed trajectory guidance law is developed and demonstrated for the F-15 aircraft flying the zoom-and-pushover maneuver
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