1,720,980 research outputs found
Convergence and Multistability of Nonsymmetric Cellular Neural Networks With Memristors
No full textRecent work has considered a class of cellular neural networks (CNNs) where each cell contains an ideal capacitor and an ideal flux-controlled memristor. One main feature is that during the analog computation the memristor is assumed to be a dynamic element, hence each cell is second-order with state variables given by the capacitor voltage and the memristor flux. Such CNNs, named dynamic memristor (DM)-CNNs, were proved to be convergent when a symmetry condition for the cell interconnections is satisfied. The goal of this paper is to investigate convergence and multistability of DM-CNNs in the general case of nonsymmetric interconnections. The main result is that convergence holds when there are (possibly) nonsymmetric, non-negative interconnections between cells and an irreducibility assumption is satisfied. This result appears to be similar to the classic convergence result for standard (S)-CNNs with positive cell-linking templates. Yet, due to the presence of DMs, a DM-CNN displays some basically different and peculiar dynamical properties with respect to S-CNNs. One key difference is that the DM-CNN processing is based on the time evolution of memristor fluxes instead of capacitor voltages as it happens for S-CNNs. Moreover, when a steady state is reached, all voltages and currents, and hence power consumption of a DM-CNN vanish. This notwithstanding the memristors are able to store in a nonvolatile way the result of the processing. Voltages, currents and power instead do not vanish when an S-CNN reaches a steady state
The dichotomy of omega-limit sets fails for cooperative standard CNNs
No full textThe paper investigates some basic aspects of the solution semiflow associated to a class of cooperative standard (S) cellular neural networks (CNNs) with a typical three-segment pwl neuron activation. It is assumed that the SCNN neuron interconnection matrix is irreducible. By means of two counterexamples the following basic facts are shown: 1) in general the semiflow associated to the SCNN is not eventually strongly monotone; 2) in the general case also the fundamental property of the omega-limit set dichotomy fails. The consequences of these results are discussed in the context of the existing methods for addressing convergence of cooperative dynamical systems
Convergent Dynamics of Nonreciprocal Differential Variational Inequalities Modeling Neural Networks
Full text linkThe paper addresses convergence of solutions for a class of differential inclusions termed differential variational inequalities (DVIs). Each DVI describes the dynamics of a neural network (NN) evolving in a closed hypercube of and defined by a continuously differentiable, {\em cooperative\/} and (possibly) nonreciprocal vector field . The main result in the paper is that under a new condition on , which is called strong Kamke-Muller condition, the solution semiflow generated by the DVI is strongly order preserving (SOP) and hence it satisfies a {\sc Limit Set Dichotomy} and enjoys generic convergence properties. A characterization of the SKM condition is given in terms of the interconnection properties of the Jacobian matrix of . In the case where is an affine, or a linear, vector field the considered DVIs include two relevant classes of NNs, namely, the linear systems operating on a closed hypercube, also known as linear systems in saturated mode (LSSMs), and the full-range (FR) model of cellular neural networks (CNNs). By applying the results to LSSMs it is obtained that any cooperative LSSM with a (possibly) nonsymmetric and fully interconnected matrix is generically convergent. Analogous results hold for FRCNNs. All the obtained convergence results hold in the general case where the DVIs, and the LSSMs and FRCNNs, possess multiple equilibrium points
Lojasiewicz inequality and exponential convergence of the full-range model of CNNs
No full textThis paper considers the Full-range (FR) model of Cellular Neural Networks (CNNs) in the case where the signal range is delimited by an ideal hard-limiter nonlinearity with two vertical segments in the i−v characteristic. A Łojasiewicz inequality around any equilibrium point, for a FRCNN with a symmetric interconnection matrix, is proved. It is also shown that the Łojasiewicz exponent is equal to 1/2. The main consequence is that any forward solution of a symmetric FRCNN has finite length and is exponentially convergent toward an equilibrium point, even in degenerate situations where the FRCNN possesses non-isolated equilibrium points. The obtained results are shown to improve the previous results in literature on convergence or almost convergence of symmetric FRCNNs
Discontinuous Neural Networks for Finite-Time Solution of Time-Dependent Linear Equations
No full textThis paper considers a class of nonsmooth neural networks with discontinuous hard-limiter (signum) neuron activations for solving time-dependent (TD) systems of algebraic linear equations (ALEs). The networks are defined by the subdifferential with respect to the state variables of an energy function given by the L1 norm of the error between the state and the TD-ALE solution. It is shown that when the penalty parameter exceeds a quantitatively estimated threshold the networks are able to reach in finite time, and exactly track thereafter, the target solution of the TD-ALE. Furthermore, this paper discusses the tightness of the estimated threshold and also points out key differences in the role played by this threshold with respect to networks for solving time-invariant ALEs. It is also shown that these convergence results are robust with respect to small perturbations of the neuron interconnection matrices. The dynamics of the proposed networks are rigorously studied by using tools from nonsmooth analysis, the concept of subdifferential of convex functions, and that of solutions in the sense of Filippov of dynamical systems with discontinuous nonlinearities
Power-Delay-Area-Noise Margin Trade-offs in Positive-Feedback Source-Coupled Logic Gates
No full textIn this paper, Positive Feedback Source-Coupled Logic (PFSCL) gates are analyzed from a design point of view. The design space is explored through analytical relationships which relate the gate delay, power consumption and noise margin, which are modeled through a simplified circuit analysis. To be more specific, a simple and accurate model of the noise margin is used to derive a systematic design strategy to size the transistors’ aspect ratios ensuring an assigned noise margin for a given bias current. From the knowledge of the transistor sizes, the gate delay is then expressed as a function of the bias current and the supply voltage, both of which define the static power consumption of PFSCL gates, as well as of the logic swing, which determines the noise margin. Therefore, this delay model simply relates the speed performance, the power consumption and the noise margin of PFSCL gates, and accounts for the dependence on the fan-in and the fan-out. Extensive SPICE simulations with a 0.18-m CMOS process confirm the adequate accuracy of the analytical models and the validity of the approximations introduced to simplify the analysis, and a practical design example of an equality comparator is also presented.
In order to derive clear guidelines to manage the delay-power-noise margin trade-off, PFSCL gates are analyzed in typical design cases (i.e. design for high speed, low power and power efficiency). For the sake of completeness, the effect of each design parameter on the silicon area occupied by a PFSCL gate is also qualitatively analyzed. The resulting criteria are thus useful to design PFSCL gates without resorting to time-consuming design iterations with a trial and error approach based on simulations
Nonsmooth Neural Network for Convex Time-Dependent Constraint Satisfaction Problems
No full textThis paper introduces a nonsmooth (NS) neural network that is able to operate in a time-dependent (TD) context and is potentially useful for solving some classes of NS-TD problems. The proposed network is named nonsmooth time-dependent network (NTN) and is an extension to a TD setting of a previous NS neural network for programming problems. Suppose C(t), t ≥ 0, is a nonempty TD convex feasibility set defined by TD inequality constraints. The constraints are in general NS (nondifferentiable) functions of the state variables and time. NTN is described by the subdifferential with respect to the state variables of an NS-TD barrier function and a vector field corresponding to the unconstrained dynamics. This paper shows that for suitable values of the penalty parameter, the NTN dynamics displays two main phases. In the first phase, any solution of NTN not starting in C(0) at t = 0 is able to reach the moving set C(·) in finite time th, whereas in the second phase, the solution tracks the moving set, i.e., it stays within C(t) for all subsequent times t ≥ th. NTN is thus able to find an exact feasible solution in finite time and also to provide an exact feasible solution for subsequent times. This new and peculiar dynamics displayed by NTN is potentially useful for addressing some significant TD signal processing tasks. As an illustration, this paper discusses a number of examples where NTN is applied to the solution of NS-TD convex feasibility problems
Limit set dichotomy and multistability for a class of cooperative neural networks with delays
No full textRecent papers have pointed out the interest to study convergence in the presence of multiple equilibrium points (EPs) (multistability) for neural networks (NNs) with nonsymmetric cooperative (nonnegative) interconnections and neuron activations modeled by piecewise linear (PL) functions. One basic difficulty is that the semiflows generated by such NNs are monotone but, due to the horizontal segments in the PL functions, are not eventually strongly monotone (ESM). This notwithstanding, it has been shown that there are subclasses of irreducible interconnection matrices for which the semiflows, although they are not ESM, enjoy convergence properties similar to those of ESM semiflows. The results obtained so far concern the case of cooperative NNs without delays. The goal of this paper is to extend some of the existing results to the relevant case of NNs with delays. More specifically, this paper considers a class of NNs with PL neuron activations, concentrated delays, and a nonsymmetric cooperative interconnection matrix A and delay interconnection matrix Aτ. The main result is that when A+Aτ satisfies a full interconnection condition, then the generated semiflows, which are monotone but not ESM, satisfy a limit set dichotomy analogous to that valid for ESM semiflows. It follows that there is an open and dense set of initial conditions, in the state space of continuous functions on a compact interval, for which the solutions converge toward an EP. The result holds in the general case where the NNs possess multiple EPs, i.e., is a result on multistability, and is valid for any constant value of the delays
Necessary and sufficient condition for multistability of neural networks evolving on a closed hypercube
No full textThe paper considers nonsmooth neural networks described by a class of differential inclusions termed differential variational inequalities (DVIs). The DVIs include the relevant class of neural networks, introduced by Li, Michel and Porod, described by linear systems evolving in a closed hypercube of Rn. The main result in the paper is a necessary and sufficient condition for multistability of DVIs with nonsymmetric and cooperative (nonnegative) interconnections between neurons. The condition is easily checkable and provides a sharp bound between DVIs that can store multiple patterns, as asymptotically stable equilibria, and those for which this is not possible. Numerical examples and simulations are presented to confirm and illustrate the theoretic findings
Memristor standard cellular neural networks computing in the flux-charge domain
No full textThe paper introduces a class of memristor neural networks (NNs) that are characterized by the following salient features. (a) The processing of signals takes place in the fluxâcharge domain and is based on the time evolution of memristor charges. The processing result is given by the constant asymptotic values of charges that are stored in the memristors acting as non-volatile memories in steady state. (b) The dynamic equations describing the memristor NNs in the fluxâcharge domain are analogous to those describing, in the traditional voltageâcurrent domain, the dynamics of a standard (S) cellular (C) NN, and are implemented by using a realistic model of memristors as that proposed by HP. This analogy makes it possible to use the bulk of results in the SCNN literature for designing memristor NNs to solve processing tasks in real time. Convergence of memristor NNs in the presence of multiple asymptotically stable equilibrium points is addressed and some applications to image processing tasks are presented to illustrate the real-time processing capabilities. Computing in the fluxâcharge domain is shown to have significant advantages with respect to computing in the voltageâcurrent domain. One advantage is that, when a steady state is reached, currents, voltages and hence power in a memristor NN vanish, whereas memristors keep in memory the processing result. This is basically different from SCNNs for which currents, voltages and power do not vanish at a steady state, and batteries are needed to keep in memory the processing result
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