23,094 research outputs found
On stability of randomly switched nonlinear systems
This article is concerned with stability analysis and stabilization of
randomly switched nonlinear systems. These systems may be regarded as piecewise
deterministic stochastic systems: the discrete switches are triggered by a
stochastic process which is independent of the state of the system, and between
two consecutive switching instants the dynamics are deterministic. Our results
provide sufficient conditions for almost sure global asymptotic stability using
Lyapunov-based methods when individual subsystems are stable and a certain
``slow switching'' condition holds. This slow switching condition takes the
form of an asymptotic upper bound on the probability mass function of the
number of switches that occur between the initial and current time instants.
This condition is shown to hold for switching signals coming from the states of
finite-dimensional continuous-time Markov chains; our results therefore hold
for Markov jump systems in particular. For systems with control inputs we
provide explicit control schemes for feedback stabilization using the universal
formula for stabilization of nonlinear systems.Comment: 13 pages, no figures. A slightly modified version is scheduled to
appear in IEEE Transactions on Automatic Control, Dec 200
Mathematical control of complex systems
Copyright © 2013 ZidongWang et al.This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
Stabilizing Randomly Switched Systems
This article is concerned with stability analysis and stabilization of
randomly switched systems under a class of switching signals. The switching
signal is modeled as a jump stochastic (not necessarily Markovian) process
independent of the system state; it selects, at each instant of time, the
active subsystem from a family of systems. Sufficient conditions for stochastic
stability (almost sure, in the mean, and in probability) of the switched system
are established when the subsystems do not possess control inputs, and not
every subsystem is required to be stable. These conditions are employed to
design stabilizing feedback controllers when the subsystems are affine in
control. The analysis is carried out with the aid of multiple Lyapunov-like
functions, and the analysis results together with universal formulae for
feedback stabilization of nonlinear systems constitute our primary tools for
control designComment: 22 pages. Submitte
Distributive Power Control Algorithm for Multicarrier Interference Network over Time-Varying Fading Channels - Tracking Performance Analysis and Optimization
Distributed power control over interference limited network has received an
increasing intensity of interest over the past few years. Distributed solutions
(like the iterative water-filling, gradient projection, etc.) have been
intensively investigated under \emph{quasi-static} channels. However, as such
distributed solutions involve iterative updating and explicit message passing,
it is unrealistic to assume that the wireless channel remains unchanged during
the iterations. Unfortunately, the behavior of those distributed solutions
under \emph{time-varying} channels is in general unknown. In this paper, we
shall investigate the distributed scaled gradient projection algorithm (DSGPA)
in a pairs multicarrier interference network under a finite-state Markov
channel (FSMC) model. We shall analyze the \emph{convergence property} as well
as \emph{tracking performance} of the proposed DSGPA. Our analysis shows that
the proposed DSGPA converges to a limit region rather than a single point under
the FSMC model. We also show that the order of growth of the tracking errors is
given by \mathcal{O}\(1 \big/ \bar{N}\), where is the \emph{average
sojourn time} of the FSMC. Based on the analysis, we shall derive the
\emph{tracking error optimal scaling matrices} via Markov decision process
modeling. We shall show that the tracking error optimal scaling matrices can be
implemented distributively at each transmitter. The numerical results show the
superior performance of the proposed DSGPA over three baseline schemes, such as
the gradient projection algorithm with a constant stepsize.Comment: To Appear on the IEEE Transaction on Signal Processin
New advances in H∞ control and filtering for nonlinear systems
The main objective of this special issue is to
summarise recent advances in H∞ control and filtering
for nonlinear systems, including time-delay, hybrid and
stochastic systems. The published papers provide new
ideas and approaches, clearly indicating the advances
made in problem statements, methodologies or applications
with respect to the existing results. The special
issue also includes papers focusing on advanced and
non-traditional methods and presenting considerable
novelties in theoretical background or experimental
setup. Some papers present applications to newly
emerging fields, such as network-based control and
estimation
A survey on gain-scheduled control and filtering for parameter-varying systems
Copyright © 2014 Guoliang Wei et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.This paper presents an overview of the recent developments in the gain-scheduled control and filtering problems for the parameter-varying systems. First of all, we recall several important algorithms suitable for gain-scheduling method including gain-scheduled proportional-integral derivative (PID) control, H 2, H ∞ and mixed H 2 / H ∞ gain-scheduling methods as well as fuzzy gain-scheduling techniques. Secondly, various important parameter-varying system models are reviewed, for which gain-scheduled control and filtering issues are usually dealt with. In particular, in view of the randomly occurring phenomena with time-varying probability distributions, some results of our recent work based on the probability-dependent gain-scheduling methods are reviewed. Furthermore, some latest progress in this area is discussed. Finally, conclusions are drawn and several potential future research directions are outlined.The National Natural Science Foundation of China under Grants 61074016, 61374039, 61304010, and 61329301; the Natural Science Foundation of Jiangsu Province of China under Grant BK20130766; the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning; the Program for New Century Excellent Talents in University under Grant NCET-11-1051, the Leverhulme Trust of the U.K., the Alexander von Humboldt Foundation of Germany
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