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Filtering for uncertain 2-D discrete systems with state delays
This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2007 Elsevier Ltd.This paper is concerned with the problem of robust H∞ filtering for two-dimensional (2-D) discrete systems with time-delays in states. The 2-D systems under consideration are described in terms of the well-known Fornasini–Marchesini local state-space (FMLSS) models with time-delays. Our attention is focused on the design of a full-order filter such that the filtering error system is guaranteed to be asymptotically stable with a prescribed H∞ disturbance attenuation performance. Sufficient conditions for the existence of desired filters are established by using a linear matrix inequality (LMI) approach, and the corresponding filter design problem is then cast into a convex optimization problem that can be efficiently solved by resorting to some standard numerical software. Furthermore, the obtained results are extended to more general cases where the system matrices contain either polytopic or norm-bounded parameter uncertainties. A simulation example is provided to illustrate the effectiveness of the proposed design method.This work was partially supported by the National Natural Science Foundation of China (60504008), Program for New Century Excellent Talents in University of China and the Postdoctoral Science Foundation of China (20060390231)
Online identification and nonlinear control of the electrically stimulated quadriceps muscle
A new approach for estimating nonlinear models of the electrically stimulated quadriceps muscle group under nonisometric conditions is investigated. The model can be used for designing controlled neuro-prostheses. In order to identify the muscle dynamics (stimulation pulsewidth-active knee moment relation) from discrete-time angle measurements only, a hybrid model structure is postulated for the shank-quadriceps dynamics. The model consists of a relatively well known time-invariant passive component and an uncertain time-variant active component. Rigid body dynamics, described by the Equation of Motion (EoM), and passive joint properties form the time-invariant part. The actuator, i.e. the electrically stimulated muscle group, represents the uncertain time-varying section. A recursive algorithm is outlined for identifying online the stimulated quadriceps muscle group. The algorithm requires EoM and passive joint characteristics to be known a priori. The muscle dynamics represent the product of a continuous-time nonlinear activation dynamics and a nonlinear static contraction function described by a Normalised Radial Basis Function (NRBF) network which has knee-joint angle and angular velocity as input arguments. An Extended Kalman Filter (EKF) approach is chosen to estimate muscle dynamics parameters and to obtain full state estimates of the shank-quadriceps dynamics simultaneously. The latter is important for implementing state feedback controllers. A nonlinear state feedback controller using the backstepping method is explicitly designed whereas the model was identified a priori using the developed identification procedure
Robust synchronization for 2-D discrete-time coupled dynamical networks
This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2012 IEEEIn this paper, a new synchronization problem is addressed for an array of 2-D coupled dynamical networks. The class of systems under investigation is described by the 2-D nonlinear state space model which is oriented from the well-known Fornasini–Marchesini second model. For such a new 2-D complex network model, both the network dynamics and the couplings evolve in two independent directions. A new synchronization concept is put forward to account for the phenomenon that the propagations of all 2-D dynamical networks are synchronized in two directions with influence from the coupling strength. The purpose of the problem addressed is to first derive sufficient conditions ensuring the global synchronization and then extend the obtained results to more general cases where the system matrices contain either the norm-bounded or the polytopic parameter uncertainties. An energy-like quadratic function is developed, together with the intensive use of the Kronecker product, to establish the easy-to-verify conditions under which the addressed 2-D complex network model achieves global synchronization. Finally, a numerical example is given to illustrate the theoretical results and the effectiveness of the proposed synchronization scheme.This work was supported in part by the National Natural Science Foundation of China under Grants 61028008 and 61174136, the International Science and Technology Cooperation Project of China under
Grant No. 2009DFA32050, the Natural Science Foundation of Jiangsu Province of China under Grant BK2011598, the Qing Lan Project of Jiangsu Province of China, the Project sponsored by SRF for ROCS of SEM of China, the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany
Generation of Sound Bullets with a Nonlinear Acoustic Lens
Acoustic lenses are employed in a variety of applications, from biomedical
imaging and surgery, to defense systems, but their performance is limited by
their linear operational envelope and complexity. Here we show a dramatic
focusing effect and the generation of large amplitude, compact acoustic pulses
(sound bullets) in solid and fluid media, enabled by a tunable, highly
nonlinear acoustic lens. The lens consists of ordered arrays of granular
chains. The amplitude, size and location of the sound bullets can be controlled
by varying static pre-compression on the chains. We support our findings with
theory, numerical simulations, and corroborate the results experimentally with
photoelasticity measurements. Our nonlinear lens makes possible a qualitatively
new way of generating high-energy acoustic pulses, enabling, for example,
surgical control of acoustic energy.Comment: 19 pages, 7 figures, includes supplementary informatio
Controlling cluster synchronization by adapting the topology
We suggest an adaptive control scheme for the control of zero-lag and cluster
synchronization in delay-coupled networks. Based on the speed-gradient method,
our scheme adapts the topology of a network such that the target state is
realized. It is robust towards different initial condition as well as changes
in the coupling parameters. The emerging topology is characterized by a
delicate interplay of excitatory and inhibitory links leading to the
stabilization of the desired cluster state. As a crucial parameter determining
this interplay we identify the delay time. Furthermore, we show how to
construct networks such that they exhibit not only a given cluster state but
also with a given oscillation frequency. We apply our method to coupled
Stuart-Landau oscillators, a paradigmatic normal form that naturally arises in
an expansion of systems close to a Hopf bifurcation. The successful and robust
control of this generic model opens up possible applications in a wide range of
systems in physics, chemistry, technology, and life science
Time-domain Ramsey interferometry with interacting Rydberg atoms
We theoretically investigate the dynamics of a gas of strongly interacting
Rydberg atoms subject to a time-domain Ramsey interferometry protocol. The
many-body dynamics is governed by an Ising-type Hamiltonian with long range
interactions of tunable strength. We analyze and model the contrast degradation
and phase accumulation of the Ramsey signal and identify scaling laws for
varying interrogation times, ensemble densities, and ensemble dimensionalities.Comment: 16 pages, 3 figure
Dicke Superradiance in Solids
Recent advances in optical studies of condensed matter have led to the
emergence of phenomena that have conventionally been studied in the realm of
quantum optics. These studies have not only deepened our understanding of
light-matter interactions but also introduced aspects of many-body correlations
inherent in optical processes in condensed matter systems. This article is
concerned with superradiance (SR), a profound quantum optical process predicted
by Dicke in 1954. The basic concept of SR applies to a general -body system
where constituent oscillating dipoles couple together through interaction with
a common light field and accelerate the radiative decay of the system. In the
most fascinating manifestation of SR, known as superfluorescence (SF), an
incoherently prepared system of inverted atoms spontaneously develops
macroscopic coherence from vacuum fluctuations and produces a delayed pulse of
coherent light whose peak intensity . Such SF pulses have been
observed in atomic and molecular gases, and their intriguing quantum nature has
been unambiguously demonstrated. Here, we focus on the rapidly developing field
of research on SR in solids, where not only photon-mediated coupling but also
strong Coulomb interactions and ultrafast scattering exist. We describe SR and
SF in molecular centers in solids, molecular aggregates and crystals, quantum
dots, and quantum wells. In particular, we will summarize a series of studies
we have recently performed on quantum wells in strong magnetic fields. These
studies show that cooperative effects in solid-state systems are not merely
small corrections that require exotic conditions to be observed; rather, they
can dominate the nonequilibrium dynamics and light emission processes of the
entire system of interacting electrons.Comment: 23 pages, 26 figure
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