Showing papers by "Anthony N. Michel published in 1995"

Qualitative analysis of Cohen-Grossberg neural networks with multiple delays

Abstract: It is well known that a class of artificial neural networks with symmetric interconnections and without transmission delays, known as Cohen-Grossberg neural networks, possesses global stability (ie, all trajectories tend to some equilibrium) We demonstrate in the present paper that many of the qualitative properties of Cohen-Grossberg networks will not be affected by the introduction of sufficiently small delays Specifically, we establish some bound conditions for the time delays under which a given Cohen-Grossberg network with multiple delays is globally stable and possesses the same asymptotically stable equilibria as the corresponding network without delays An effective method of determining the asymptotic stability of an equilibrium of a Cohen-Grossberg network with multiple delays is also presented The present results are motivated by some of the authors earlier work [Phys Rev E 50, 4206 (1994)] and by some of the work of Marcus and Westervelt [Phys Rev A 39, 347 (1989)] These works address qualitative analyses of Hopfield neural networks with one time delay The present work generalizes these results to Cohen-Grossberg neural networks with multiple time delays Hopfield neural networks constitute special cases of Cohen-Grossberg neural networks

Analysis and synthesis of a class of discrete-time neural networks with multilevel threshold neurons

Abstract: In contrast to the usual types of neural networks which utilize two states for each neuron, a class of synchronous discrete-time neural networks with multilevel threshold neurons is developed. A qualitative analysis and a synthesis procedure for the class of neural networks considered constitute the principal contributions of this paper. The applicability of the present class of neural networks is demonstrated by means of a gray level image processing example, where each neuron can assume one of sixteen values. When compared to the usual neural networks with two state neurons, networks which are endowed with multilevel neurons will, in general, for a given application, require fewer neurons and thus fewer interconnections. This is an important consideration in VLSI implementation. >

Lagrange Stability and Boundedness of Discrete Event Systems

Abstract: Recently it has been shown that the conventional notions of stability in the sense of Lyapunov and asymptotic stability can be used to characterize the stability properties of a class of “logical” discrete event systems (DES). Moreover, it has been shown that stability analysis via the choice of appropriate Lyapunov functions can be used for DES and can be applied to several DES applications including manufacturing systems and computer networks (Passino et al. 1994, Burgess and Passino 1994). In this paper we extend the conventional notions and analysis of uniform boundedness, uniform ultimate boundedness, practical stability, finite time stability, and Lagrange stability so that they apply to the class of logical DES that can be defined on a metric space. Within this stability-theoretic framework we show that the standard Petri net-theoretic notions of boundedness are special cases of Lagrange stability and uniform boundedness. In addition we show that the Petri ent-theoretic approach to boundedness analysis is actually a Lyapunov approach in that the net-theoretic analysis actually produces an appropriate Lyapunov function. Moreover, via the Lyapunov approach we provide a sufficient condition for the uniform ultimate boundedness of General Petri nets. To illustrate the Petri net results, we study the boundedness properties of a rate synchronization network for manufacturing systems. In addition, we provide a detailed analysis of the Lagrange stability of a single-machine manufacturing system that uses a priority-based part servicing policy.

Qualitative limitations incurred in implementations of recurrent neural networks

Abstract: During the implementation process of artificial neural networks, deviations from the desired ideal neural network are frequently introduced. These include parameter perturbations, transmission delays, and interconnection constraints. In the present article, we study the effects of these realities of imperfection on the qualitative behavior of artificial feedback neural networks. To accomplish this, we utilize a specific class of neural networks (Hopfield-like neural networks) with a specific application (the realization of associative memories) as a vehicle for our study. The principal issues which we address concern the effects of parameter perturbations, transmission delays, and interconnection constraints on the accuracy and on the qualitative properties of the network memories. >

A general model for the qualitative analysis of hybrid dynamical systems

Abstract: First formulates a definition of hybrid dynamical system which covers a very large number of classes of hybrid systems and which is suitable for the qualitative analysis of such systems. Next, the authors present several specific examples of hybrid dynamical systems.

Stability analysis of a class of systems with parameter uncertainties and with state saturation nonlinearities

Abstract: For linear systems with parameter uncertainties and subject to state saturation, we establish results concerning the global asymptotic stability of an equilibrium. In addition to providing a means for a qualitative analysis, these results also enable us to address the stabilizability of such systems by means of linear state feedback. Systems of the type considered herein capture two important phenomena commonly encountered in the modelling process: (i) system parameter uncertainties (which in the present case are modelled by means of interval matrices), and (ii) operation of systems over a wide range (which in the present case is accounted for by state saturation nonlinearities). We demonstrate the applicability of the present results by means of several specific examples.

Stochastic adaptive control of nonminimum phase systems in the presence of unmodelled dynamics

Abstract: We consider the problem of robust stochastic adaptive control of not necessarily minimum phase systems in the presence of unmodelled dynamics. Stochastic gradient algorithms with parameter projection and modified gain sequence are used for the estimation of the unknown controller parameters. Global stability of the adaptive system is achieved without requiring the strictly positive real condition and the persistency exciting condition to be satisfied.

Robust stability of linear time-delay systems: retarded and neutral types

Abstract: In this paper we consider retarded and neutral linear, time-delay systems with perturbations. For such systems, we present two types of sufficient conditions for asymptotic stability. One type involves norm conditions while the other type involves corner conditions. Some of our results constitute generalizations of existing results. We demonstrate the applicability of our results by means of three specific examples.

Stability of nonlinear time-delay systems with parameter uncertainties with an application to neural networks

Abstract: First considers a family of nonlinear time-delay systems with uncertainties and establishes sufficient conditions for the asymptotic stability of an equilibrium for this family. The authors then apply these results to the stability analysis of a class of artificial neural networks with transmission delays. These results require the verification of the definiteness of a certain matrix or the verification of a certain inequality. The authors' results provide also a method of estimating the domain of attraction of an asymptotically stable equilibrium of the time-delay neural networks.

Qualitative analysis of artificial neural networks with multiple delays

Abstract: It is well known that a class of artificial neural networks with symmetric interconnections and without transmission delays, known as Cohen-Grossberg neural networks, possesses global stability (i.e., all trajectories tend to some equilibrium). The authors demonstrate in the present paper that many of the qualitative properties of Cohen-Grossberg networks will not be affected by the introduction of sufficiently small delays. Specifically, the authors establish some bound conditions for the time delays under which a given Cohen-Grossberg network with multiple delays is globally stable and possesses the same asymptotically stable equilibria as the corresponding network without delays. An effective method of determining the asymptotic stability of an equilibrium of a Cohen-Grossberg network with multiple delays is also presented.

Theory and applications of sparsely interconnected feedback neural networks

Abstract: This paper presents some developments in the analysis and design of a class of feedback neural networks with sparse interconnecting structure. The analysis results presented make it possible to determine whether a given vector is a stable memory of a neural network and to what extent implementation errors are permissible. The design methods presented allow the synthesis of neural networks with predetermined sparse interconnecting structures with or without symmetry constraints on the interconnection weights. An example is included to demonstrate the applicability of the methodology advanced herein.

Qualitative analysis of Hopfield neural nets with delays: Global and local results

Abstract: It is well known that Hopfield neural networks without delays exhibit no oscillations and possess global stability (i.e., all trajectories tend to some equilibrium). In the present paper we show that if the bound /spl tau//spl beta//spl par/T/sub 2//spl par/ 0, interconnection matrix T/sub 2/ associated with delays, and gain of the neurons given by /spl beta/, will exhibit similar qualitative properties as the original Hopfield neural network without delays (/spl par/T/sub 2//spl par/ denotes the matrix norm induced by the Euclidean vector norm).