243 research outputs found
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
Output-input stability and minimum-phase nonlinear systems
This paper introduces and studies the notion of output-input stability, which
represents a variant of the minimum-phase property for general smooth nonlinear
control systems. The definition of output-input stability does not rely on a
particular choice of coordinates in which the system takes a normal form or on
the computation of zero dynamics. In the spirit of the ``input-to-state
stability'' philosophy, it requires the state and the input of the system to be
bounded by a suitable function of the output and derivatives of the output,
modulo a decaying term depending on initial conditions. The class of
output-input stable systems thus defined includes all affine systems in global
normal form whose internal dynamics are input-to-state stable and also all
left-invertible linear systems whose transmission zeros have negative real
parts. As an application, we explain how the new concept enables one to develop
a natural extension to nonlinear systems of a basic result from linear adaptive
control.Comment: Revised version, to appear in IEEE Transactions on Automatic Control.
See related work in http://www.math.rutgers.edu/~sontag and
http://black.csl.uiuc.edu/~liberzo
Towards ISS disturbance attenuation for randomly switched systems
We are concerned with input-to-state stability (ISS) of randomly switched
systems. We provide preliminary results dealing with sufficient conditions for
stochastic versions of ISS for randomly switched systems without control
inputs, and with the aid of universal formulae we design controllers for
ISS-disturbance attenuation when control inputs are present. Two types of
switching signals are considered: the first is characterized by a statistically
slow-switching condition, and the second by a class of semi-Markov processes.Comment: 6 pages, to appear in the Proceedings of the 46th IEEE Conference on
Decision & Control, 200
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
Moth-inspired navigation algorithm in a turbulent odor plume from a pulsating source
Some female moths attract male moths by emitting series of pulses of
pheromone filaments propagating downwind. The turbulent nature of the wind
creates a complex flow environment, and causes the filaments to propagate in
the form of patches with varying concentration distributions. Inspired by moth
navigation capabilities, we propose a navigation strategy that enables a flier
to locate a pulsating odor source in a windy environment using a single
threshold-based detection sensor. The strategy is constructed based on the
physical properties of the turbulent flow carrying discrete puffs of odor and
does not involve learning, memory, complex decision making or statistical
methods. We suggest that in turbulent plumes from a pulsating point source, an
instantaneously measurable quantity referred as a "puff crossing time",
improves the success rate as compared to the navigation strategy based on
"internal counter" that does not use this information. Using computer
simulations of fliers navigating in turbulent plumes of the pulsating point
source for varying flow parameters: turbulent intensities, plume meandering and
wind gusts, we obtained trajectories qualitatively resembling male moths
flights towards the pheromone sources. We quantified the probability of a
successful navigation as well as the flight parameters such as the time spent
searching and the total flight time, with respect to different turbulent
intensities, meandering or gusts. The concepts learned using this model may
help to design odor-based navigation of miniature airborne autonomous vehicles
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