635 research outputs found
Storing cycles in Hopfield-type networks with pseudoinverse learning rule: admissibility and network topology
Cyclic patterns of neuronal activity are ubiquitous in animal nervous
systems, and partially responsible for generating and controlling rhythmic
movements such as locomotion, respiration, swallowing and so on. Clarifying the
role of the network connectivities for generating cyclic patterns is
fundamental for understanding the generation of rhythmic movements. In this
paper, the storage of binary cycles in neural networks is investigated. We call
a cycle admissible if a connectivity matrix satisfying the cycle's
transition conditions exists, and construct it using the pseudoinverse learning
rule. Our main focus is on the structural features of admissible cycles and
corresponding network topology. We show that is admissible if and only
if its discrete Fourier transform contains exactly nonzero
columns. Based on the decomposition of the rows of into loops, where a
loop is the set of all cyclic permutations of a row, cycles are classified as
simple cycles, separable or inseparable composite cycles. Simple cycles contain
rows from one loop only, and the network topology is a feedforward chain with
feedback to one neuron if the loop-vectors in are cyclic permutations
of each other. Composite cycles contain rows from at least two disjoint loops,
and the neurons corresponding to the rows in from the same loop are
identified with a cluster. Networks constructed from separable composite cycles
decompose into completely isolated clusters. For inseparable composite cycles
at least two clusters are connected, and the cluster-connectivity is related to
the intersections of the spaces spanned by the loop-vectors of the clusters.
Simulations showing successfully retrieved cycles in continuous-time
Hopfield-type networks and in networks of spiking neurons are presented.Comment: 48 pages, 3 figure
New positive realness conditions for uncertain discrete descriptor systems: Analysis and synthesis
This paper deals with the problems of positive real (PR) analysis and PR control for uncertain discrete-time descriptor systems. The parameter uncertainties are assumed to be time-invariant norm bounded and appear in both the state and input matrices. A new necessary and sufficient condition for a discrete-time descriptor system to be regular, causal, stable and extended strictly PR (ESPR) is proposed in terms of a strict linear matrix inequality. Based on this, the concepts of strong robust admissibility with ESPR and strong robust admissibilizability with ESPR were introduced. Without any additional assumptions on the system matrices, necessary and sufficient conditions for strong robust admissibility with ESPR and strong robust admissibilizability with ESPR are obtained. Through these results, the problems of PR analysis and PR control are solved. Furthermore, an explicit expression of a desired state feedback controller is also given, which involves no decomposition of the system matrices. © 2004 IEEE.published_or_final_versio
Data-Adaptive Wavelets and Multi-Scale Singular Spectrum Analysis
Using multi-scale ideas from wavelet analysis, we extend singular-spectrum
analysis (SSA) to the study of nonstationary time series of length whose
intermittency can give rise to the divergence of their variance. SSA relies on
the construction of the lag-covariance matrix C on M lagged copies of the time
series over a fixed window width W to detect the regular part of the
variability in that window in terms of the minimal number of oscillatory
components; here W = M Dt, with Dt the time step. The proposed multi-scale SSA
is a local SSA analysis within a moving window of width M <= W <= N.
Multi-scale SSA varies W, while keeping a fixed W/M ratio, and uses the
eigenvectors of the corresponding lag-covariance matrix C_M as a data-adaptive
wavelets; successive eigenvectors of C_M correspond approximately to successive
derivatives of the first mother wavelet in standard wavelet analysis.
Multi-scale SSA thus solves objectively the delicate problem of optimizing the
analyzing wavelet in the time-frequency domain, by a suitable localization of
the signal's covariance matrix. We present several examples of application to
synthetic signals with fractal or power-law behavior which mimic selected
features of certain climatic and geophysical time series. A real application is
to the Southern Oscillation index (SOI) monthly values for 1933-1996. Our
methodology highlights an abrupt periodicity shift in the SOI near 1960. This
abrupt shift between 4 and 3 years supports the Devil's staircase scenario for
the El Nino/Southern Oscillation phenomenon.Comment: 24 pages, 19 figure
Variance-constrained dissipative observer-based control for a class of nonlinear stochastic systems with degraded measurements
The official published version of the article can be obtained from the link below.This paper is concerned with the variance-constrained dissipative control problem for a class of stochastic nonlinear systems with multiple degraded measurements, where the degraded probability for each sensor is governed by an individual random variable satisfying a certain probabilistic distribution over a given interval. The purpose of the problem is to design an observer-based controller such that, for all possible degraded measurements, the closed-loop system is exponentially mean-square stable and strictly dissipative, while the individual steady-state variance is not more than the pre-specified upper bound constraints. A general framework is established so that the required exponential mean-square stability, dissipativity as well as the variance constraints can be easily enforced. A sufficient condition is given for the solvability of the addressed multiobjective control problem, and the desired observer and controller gains are characterized in terms of the solution to a convex optimization problem that can be easily solved by using the semi-definite programming method. Finally, a numerical example is presented to show the effectiveness and applicability of the proposed algorithm.This work was supported in part by the Distinguished Visiting Fellowship of the Royal Academy of Engineering of the UK, the Royal Society of the UK, the GRF HKU 7137/09E, the National Natural Science Foundation of China under Grant 61028008, the International Science and Technology Cooperation Project of China under Grant 2009DFA32050, and the Alexander von Humboldt Foundation of Germany
Recent advances on recursive filtering and sliding mode design for networked nonlinear stochastic systems: A survey
Copyright © 2013 Jun Hu 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.Some recent advances on the recursive filtering and sliding mode design problems for nonlinear stochastic systems with network-induced phenomena are surveyed. The network-induced phenomena under consideration mainly include missing measurements, fading measurements, signal quantization, probabilistic sensor delays, sensor saturations, randomly occurring nonlinearities, and randomly occurring uncertainties. With respect to these network-induced phenomena, the developments on filtering and sliding mode design problems are systematically reviewed. In particular, concerning the network-induced phenomena, some recent results on the recursive filtering for time-varying nonlinear stochastic systems and sliding mode design for time-invariant nonlinear stochastic systems are given, respectively. Finally, conclusions are proposed and some potential future research works are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grant nos. 61134009, 61329301, 61333012, 61374127 and 11301118, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant no. GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany
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This study is concerned with the H∞ control problem for singular neutral system based on sampled-data. By input delay approach and a composite state-derivative control law, the singular system is turned into a singular neutral system with time-varying delay. Less conservative result is derived for the resultant system by incorporating the delay decomposition technique, Wirtinger-based integral inequality, and an augmented Lyapunov-Krasovskii functional. Sufficient conditions are derived to guarantee that the resulting system is regular, impulse-free, and asymptotically stable with prescribed H∞ performance. Then, the H∞ sampled-data controller is designed by means of linear matrix inequalities. Finally, two simulation results have shown that the proposed method is effective
Sampled-Data Control for Singular Neutral System
This study is concerned with the ∞ control problem for singular neutral system based on sampled-data. By input delay approach and a composite state-derivative control law, the singular system is turned into a singular neutral system with time-varying delay. Less conservative result is derived for the resultant system by incorporating the delay decomposition technique, Wirtinger-based integral inequality, and an augmented Lyapunov-Krasovskii functional. Sufficient conditions are derived to guarantee that the resulting system is regular, impulse-free, and asymptotically stable with prescribed ∞ performance. Then, the ∞ sampled-data controller is designed by means of linear matrix inequalities. Finally, two simulation results have shown that the proposed method is effective
Robust stability and stabilization of discrete singular systems: An equivalent characterization
This note deals with the problems of robust stability and stabilization for uncertain discrete-time singular systems. The parameter uncertainties are assumed to be time-invariant and norm-bounded appearing in both the state and input matrices. A new necessary and sufficient condition for a discrete-time singular system to be regular, causal and stable is proposed in terms of a strict linear matrix inequality (LMI). Based on this, the concepts of generalized quadratic stability and generalized quadratic stabilization for uncertain discrete-time singular systems are introduced. Necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are obtained in terms of a strict LMI and a set of matrix inequalities, respectively. With these conditions, the problems of robust stability and robust stabilization are solved. An explicit expression of a desired state feedback controller is also given, which involves no matrix decomposition. Finally, an illustrative example is provided to demonstrate the applicability of the proposed approach.published_or_final_versio
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