4,945 research outputs found
Analysis of A Nonsmooth Optimization Approach to Robust Estimation
In this paper, we consider the problem of identifying a linear map from
measurements which are subject to intermittent and arbitarily large errors.
This is a fundamental problem in many estimation-related applications such as
fault detection, state estimation in lossy networks, hybrid system
identification, robust estimation, etc. The problem is hard because it exhibits
some intrinsic combinatorial features. Therefore, obtaining an effective
solution necessitates relaxations that are both solvable at a reasonable cost
and effective in the sense that they can return the true parameter vector. The
current paper discusses a nonsmooth convex optimization approach and provides a
new analysis of its behavior. In particular, it is shown that under appropriate
conditions on the data, an exact estimate can be recovered from data corrupted
by a large (even infinite) number of gross errors.Comment: 17 pages, 9 figure
Identification of Piecewise Linear Models of Complex Dynamical Systems
The paper addresses the realization and identification problem or a subclass
of piecewise-affine hybrid systems. The paper provides necessary and sufficient
conditions for existence of a realization, a characterization of minimality,
and an identification algorithm for this subclass of hybrid systems. The
considered system class and the identification problem are motivated by
applications in systems biology
Observer design for piecewise smooth and switched systems via contraction theory
The aim of this paper is to present the application of an approach to study
contraction theory recently developed for piecewise smooth and switched
systems. The approach that can be used to analyze incremental stability
properties of so-called Filippov systems (or variable structure systems) is
based on the use of regularization, a procedure to make the vector field of
interest differentiable before analyzing its properties. We show that by using
this extension of contraction theory to nondifferentiable vector fields, it is
possible to design observers for a large class of piecewise smooth systems
using not only Euclidean norms, as also done in previous literature, but also
non-Euclidean norms. This allows greater flexibility in the design and
encompasses the case of both piecewise-linear and piecewise-smooth (nonlinear)
systems. The theoretical methodology is illustrated via a set of representative
examples.Comment: Preprint accepted to IFAC World Congress 201
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