Global synchronization for discrete-time stochastic complex networks with randomly occurred nonlinearities and mixed time delays

Copyright [2010] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, the problem of stochastic synchronization analysis is investigated for a new array of coupled discrete-time stochastic complex networks with randomly occurred nonlinearities (RONs) and time delays. The discrete-time complex networks under consideration are subject to: (1) stochastic nonlinearities that occur according to the Bernoulli distributed white noise sequences; (2) stochastic disturbances that enter the coupling term, the delayed coupling term as well as the overall network; and (3) time delays that include both the discrete and distributed ones. Note that the newly introduced RONs and the multiple stochastic disturbances can better reflect the dynamical behaviors of coupled complex networks whose information transmission process is affected by a noisy environment (e.g., Internet-based control systems). By constructing a novel Lyapunov-like matrix functional, the idea of delay fractioning is applied to deal with the addressed synchronization analysis problem. By employing a combination of the linear matrix inequality (LMI) techniques, the free-weighting matrix method and stochastic analysis theories, several delay-dependent sufficient conditions are obtained which ensure the asymptotic synchronization in the mean square sense for the discrete-time stochastic complex networks with time delays. The criteria derived are characterized in terms of LMIs whose solution can be solved by utilizing the standard numerical software. A simulation example is presented to show the effectiveness and applicability of the proposed results

State estimation for coupled uncertain stochastic networks with missing measurements and time-varying delays: The discrete-time case

Copyright [2009] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This paper is concerned with the problem of state estimation for a class of discrete-time coupled uncertain stochastic complex networks with missing measurements and time-varying delay. The parameter uncertainties are assumed to be norm-bounded and enter into both the network state and the network output. The stochastic Brownian motions affect not only the coupling term of the network but also the overall network dynamics. The nonlinear terms that satisfy the usual Lipschitz conditions exist in both the state and measurement equations. Through available output measurements described by a binary switching sequence that obeys a conditional probability distribution, we aim to design a state estimator to estimate the network states such that, for all admissible parameter uncertainties and time-varying delays, the dynamics of the estimation error is guaranteed to be globally exponentially stable in the mean square. By employing the Lyapunov functional method combined with the stochastic analysis approach, several delay-dependent criteria are established that ensure the existence of the desired estimator gains, and then the explicit expression of such estimator gains is characterized in terms of the solution to certain linear matrix inequalities (LMIs). Two numerical examples are exploited to illustrate the effectiveness of the proposed estimator design schemes

Simulation of networks of spiking neurons: A review of tools and strategies

We review different aspects of the simulation of spiking neural networks. We start by reviewing the different types of simulation strategies and algorithms that are currently implemented. We next review the precision of those simulation strategies, in particular in cases where plasticity depends on the exact timing of the spikes. We overview different simulators and simulation environments presently available (restricted to those freely available, open source and documented). For each simulation tool, its advantages and pitfalls are reviewed, with an aim to allow the reader to identify which simulator is appropriate for a given task. Finally, we provide a series of benchmark simulations of different types of networks of spiking neurons, including Hodgkin-Huxley type, integrate-and-fire models, interacting with current-based or conductance-based synapses, using clock-driven or event-driven integration strategies. The same set of models are implemented on the different simulators, and the codes are made available. The ultimate goal of this review is to provide a resource to facilitate identifying the appropriate integration strategy and simulation tool to use for a given modeling problem related to spiking neural networks.Comment: 49 pages, 24 figures, 1 table; review article, Journal of Computational Neuroscience, in press (2007

Memristor models for machine learning

In the quest for alternatives to traditional CMOS, it is being suggested that digital computing efficiency and power can be improved by matching the precision to the application. Many applications do not need the high precision that is being used today. In particular, large gains in area- and power efficiency could be achieved by dedicated analog realizations of approximate computing engines. In this work, we explore the use of memristor networks for analog approximate computation, based on a machine learning framework called reservoir computing. Most experimental investigations on the dynamics of memristors focus on their nonvolatile behavior. Hence, the volatility that is present in the developed technologies is usually unwanted and it is not included in simulation models. In contrast, in reservoir computing, volatility is not only desirable but necessary. Therefore, in this work, we propose two different ways to incorporate it into memristor simulation models. The first is an extension of Strukov's model and the second is an equivalent Wiener model approximation. We analyze and compare the dynamical properties of these models and discuss their implications for the memory and the nonlinear processing capacity of memristor networks. Our results indicate that device variability, increasingly causing problems in traditional computer design, is an asset in the context of reservoir computing. We conclude that, although both models could lead to useful memristor based reservoir computing systems, their computational performance will differ. Therefore, experimental modeling research is required for the development of accurate volatile memristor models.Comment: 4 figures, no tables. Submitted to neural computatio

Spiking Neural Networks for Inference and Learning: A Memristor-based Design Perspective

On metrics of density and power efficiency, neuromorphic technologies have the potential to surpass mainstream computing technologies in tasks where real-time functionality, adaptability, and autonomy are essential. While algorithmic advances in neuromorphic computing are proceeding successfully, the potential of memristors to improve neuromorphic computing have not yet born fruit, primarily because they are often used as a drop-in replacement to conventional memory. However, interdisciplinary approaches anchored in machine learning theory suggest that multifactor plasticity rules matching neural and synaptic dynamics to the device capabilities can take better advantage of memristor dynamics and its stochasticity. Furthermore, such plasticity rules generally show much higher performance than that of classical Spike Time Dependent Plasticity (STDP) rules. This chapter reviews the recent development in learning with spiking neural network models and their possible implementation with memristor-based hardware

A review on analysis and synthesis of nonlinear stochastic systems with randomly occurring incomplete information

Copyright q 2012 Hongli Dong 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.In the context of systems and control, incomplete information refers to a dynamical system in which knowledge about the system states is limited due to the difficulties in modeling complexity in a quantitative way. The well-known types of incomplete information include parameter uncertainties and norm-bounded nonlinearities. Recently, in response to the development of network technologies, the phenomenon of randomly occurring incomplete information has become more and more prevalent. Such a phenomenon typically appears in a networked environment. Examples include, but are not limited to, randomly occurring uncertainties, randomly occurring nonlinearities, randomly occurring saturation, randomly missing measurements and randomly occurring quantization. Randomly occurring incomplete information, if not properly handled, would seriously deteriorate the performance of a control system. In this paper, we aim to survey some recent advances on the analysis and synthesis problems for nonlinear stochastic systems with randomly occurring incomplete information. The developments of the filtering, control and fault detection problems are systematically reviewed. Latest results on analysis and synthesis of nonlinear stochastic systems are discussed in great detail. In addition, various distributed filtering technologies over sensor networks are highlighted. Finally, some concluding remarks are given and some possible future research directions are pointed out. © 2012 Hongli Dong et al.This work was supported in part by the National Natural Science Foundation of China under Grants 61273156, 61134009, 61273201, 61021002, and 61004067, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK, the National Science Foundation of the USA under Grant No. HRD-1137732, and the Alexander von Humboldt Foundation of German

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 $\Sigma$ 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 $\Sigma$ is admissible if and only if its discrete Fourier transform contains exactly $r={rank}(\Sigma)$ nonzero columns. Based on the decomposition of the rows of $\Sigma$ 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 $\Sigma$ are cyclic permutations of each other. Composite cycles contain rows from at least two disjoint loops, and the neurons corresponding to the rows in $\Sigma$ 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