27,200 research outputs found
Concentration inequalities for mean field particle models
This article is concerned with the fluctuations and the concentration
properties of a general class of discrete generation and mean field particle
interpretations of nonlinear measure valued processes. We combine an original
stochastic perturbation analysis with a concentration analysis for triangular
arrays of conditionally independent random sequences, which may be of
independent interest. Under some additional stability properties of the
limiting measure valued processes, uniform concentration properties, with
respect to the time parameter, are also derived. The concentration inequalities
presented here generalize the classical Hoeffding, Bernstein and Bennett
inequalities for independent random sequences to interacting particle systems,
yielding very new results for this class of models. We illustrate these results
in the context of McKean-Vlasov-type diffusion models, McKean collision-type
models of gases and of a class of Feynman-Kac distribution flows arising in
stochastic engineering sciences and in molecular chemistry.Comment: Published in at http://dx.doi.org/10.1214/10-AAP716 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems
This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version
Schwinger-Dyson equations in large-N quantum field theories and nonlinear random processes
We propose a stochastic method for solving Schwinger-Dyson equations in
large-N quantum field theories. Expectation values of single-trace operators
are sampled by stationary probability distributions of the so-called nonlinear
random processes. The set of all histories of such processes corresponds to the
set of all planar diagrams in the perturbative expansions of the expectation
values of singlet operators. We illustrate the method on the examples of the
matrix-valued scalar field theory and the Weingarten model of random planar
surfaces on the lattice. For theories with compact field variables, such as
sigma-models or non-Abelian lattice gauge theories, the method does not
converge in the physically most interesting weak-coupling limit. In this case
one can absorb the divergences into a self-consistent redefinition of expansion
parameters. Stochastic solution of the self-consistency conditions can be
implemented as a "memory" of the random process, so that some parameters of the
process are estimated from its previous history. We illustrate this idea on the
example of two-dimensional O(N) sigma-model. Extension to non-Abelian lattice
gauge theories is discussed.Comment: 16 pages RevTeX, 14 figures; v2: Algorithm for the Weingarten model
corrected; v3: published versio
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