12,244 research outputs found
Stabilizing switching signals: a transition from point-wise to asymptotic conditions
Characterization of classes of switching signals that ensure stability of
switched systems occupies a significant portion of the switched systems
literature. This article collects a multitude of stabilizing switching signals
under an umbrella framework. We achieve this in two steps: Firstly, given a
family of systems, possibly containing unstable dynamics, we propose a new and
general class of stabilizing switching signals. Secondly, we demonstrate that
prior results based on both point-wise and asymptotic characterizations follow
our result. This is the first attempt in the switched systems literature where
these switching signals are unified under one banner.Comment: 7 page
Adaptive Quantizers for Estimation
In this paper, adaptive estimation based on noisy quantized observations is
studied. A low complexity adaptive algorithm using a quantizer with adjustable
input gain and offset is presented. Three possible scalar models for the
parameter to be estimated are considered: constant, Wiener process and Wiener
process with deterministic drift. After showing that the algorithm is
asymptotically unbiased for estimating a constant, it is shown, in the three
cases, that the asymptotic mean squared error depends on the Fisher information
for the quantized measurements. It is also shown that the loss of performance
due to quantization depends approximately on the ratio of the Fisher
information for quantized and continuous measurements. At the end of the paper
the theoretical results are validated through simulation under two different
classes of noise, generalized Gaussian noise and Student's-t noise
Robust Adaptive Control
Several concepts and results in robust adaptive control are are discussed and is organized in three parts. The first part surveys existing algorithms. Different formulations of the problem and theoretical solutions that have been suggested are reviewed here. The second part contains new results related to the role of persistent excitation in robust adaptive systems and the use of hybrid control to improve robustness. In the third part promising new areas for future research are suggested which combine different approaches currently known
Asymptotic behavior of splitting schemes involving time-subcycling techniques
This paper deals with the numerical integration of well-posed multiscale
systems of ODEs or evolutionary PDEs. As these systems appear naturally in
engineering problems, time-subcycling techniques are widely used every day to
improve computational efficiency. These methods rely on a decomposition of the
vector field in a fast part and a slow part and take advantage of that
decomposition. This way, if an unconditionnally stable (semi-)implicit scheme
cannot be easily implemented, one can integrate the fast equations with a much
smaller time step than that of the slow equations, instead of having to
integrate the whole system with a very small time-step to ensure stability.
Then, one can build a numerical integrator using a standard composition method,
such as a Lie or a Strang formula for example. Such methods are primarily
designed to be convergent in short-time to the solution of the original
problems. However, their longtime behavior rises interesting questions, the
answers to which are not very well known. In particular, when the solutions of
the problems converge in time to an asymptotic equilibrium state, the question
of the asymptotic accuracy of the numerical longtime limit of the schemes as
well as that of the rate of convergence is certainly of interest. In this
context, the asymptotic error is defined as the difference between the exact
and numerical asymptotic states. The goal of this paper is to apply that kind
of numerical methods based on splitting schemes with subcycling to some simple
examples of evolutionary ODEs and PDEs that have attractive equilibrium states,
to address the aforementioned questions of asymptotic accuracy, to perform a
rigorous analysis, and to compare them with their counterparts without
subcycling. Our analysis is developed on simple linear ODE and PDE toy-models
and is illustrated with several numerical experiments on these toy-models as
well as on more complex systems. Lie andComment: IMA Journal of Numerical Analysis, Oxford University Press (OUP):
Policy A - Oxford Open Option A, 201
Controlling Chaos Faster
Predictive Feedback Control is an easy-to-implement method to stabilize
unknown unstable periodic orbits in chaotic dynamical systems. Predictive
Feedback Control is severely limited because asymptotic convergence speed
decreases with stronger instabilities which in turn are typical for larger
target periods, rendering it harder to effectively stabilize periodic orbits of
large period. Here, we study stalled chaos control, where the application of
control is stalled to make use of the chaotic, uncontrolled dynamics, and
introduce an adaptation paradigm to overcome this limitation and speed up
convergence. This modified control scheme is not only capable of stabilizing
more periodic orbits than the original Predictive Feedback Control but also
speeds up convergence for typical chaotic maps, as illustrated in both theory
and application. The proposed adaptation scheme provides a way to tune
parameters online, yielding a broadly applicable, fast chaos control that
converges reliably, even for periodic orbits of large period
- …