Showing papers by "Anthony N. Michel published in 1991"

Analysis and synthesis of a class of discrete-time neural networks described on hypercubes

Abstract: A qualitative analysis is presented for a class of synchronous discrete-time neural networks defined on hypercubes in the state space. Analysis results are utilized to establish a design procedure for associative memories to be implemented on the present class of neural networks. To demonstrate the storage ability and flexibility of the synthesis procedure, several specific examples are considered. The design procedure has essentially the same desirable features as the results of J. Li et al. (1988, 1989) for continuous-time neural networks. For a given system dimension, networks designed by the present method may have the ability to store more patterns (as asymptotically stable equilibria) than corresponding discrete-time networks designed by other techniques. The design method guarantees the storage of all the desired patterns as asymptotically stable equilibrium points. The present method provides guidelines for reducing the number of spurious states and for estimating the extent of the patterns' domains of attraction. The present results provide a means of implementing neural networks by serial processors and special digital hardware. >

A learning and forgetting algorithm in associative memories: results involving pseudo-inverses

Abstract: The authors develop a design technique for associative memories with learning and forgetting abilities via artificial feedback neural networks. The method utilizes the theory of large-scale interconnected dynamical systems, instead of the usual energy methods. Networks synthesized by this design method are capable of learning new patterns as well as forgetting old patterns without recomputing the entire interconnection matrix. The method, in which the properties of pseudo-inverse matrices are used to iteratively solve systems of linear equations, provides significant improvements over the outer product method and the projection learning rule. Several specific examples are given to illustrate the strengths and weaknesses of the methodology. >

Exponential stability and trajectory bounds of neural networks under structural variations

Abstract: The dynamic behavior of neural networks under arbitrary unknown structural perturbations depends essentially on the compatibility/incompatibility of input variables in these networks. Estimates of the upper bounds of the motions of neural networks of either type and exponential stability of compatible neural networks are established by using three different forms of Lyapunov functions. Conditions for the maximum possible estimate of the domain of structural exponential stability are determined. All new concepts such as compatible/incompatible neural networks and structural exponential stability are defined. All the conditions are stated in simple algebraic forms. Their applications are straightforward. >

Analysis and synthesis of discrete-time neural networks with multilevel threshold functions

Abstract: In contrast to the usual types of neural networks which utilize two states for each neuron, a class of synchronous discrete-time multilevel threshold neural networks is developed. A qualitative analysis and a synthesis procedure of the class of neural networks constitute the principal contributions of this work. The applicability of the class of neural networks is demonstrated by means of a gray-level image processing example in which each neutron of the present model assumes one of 16 values. In doing so, the number of neurons and the number of interconnections are reduced, when compared to the usual binary state networks. >

A learning and forgetting algorithm in associative memories. The eigenstructure method

Abstract: The authors develop a design technique for associative memories with learning and forgetting capabilities via artificial feedback neural networks. The proposed synthesis technique utilizes the eigenstructure method. Networks generated by this method are capable of learning new patterns as well as forgetting learned patterns without the necessity of recomputing the entire interconnection weights and external inputs. In many respects, these results constitute significant improvements over the outer product method, the projection learning rule, and the pseudo-inverse method with stability constraints. Several specific examples are given to illustrate the strengths and weaknesses of the methodology advocated. >

Interval analysis techniques in linear systems: an application in power systems

Abstract: The authors apply the technique of interval analysis to get bounds on the initial value response of a linearized single-machine-infinite-bus problem when a parameter is varied. Generally it is believed that responses for parameter variations in an interval should lie within the responses for the extrema of the parameter variations. This is not generally true and an example demonstrates this. Interval analysis techniques permit derivation of the overall bound on the response. Further experimentation also revealed that the method has some limitations particularly involving lightly damped long term dynamics. >

Verification of the Self-Stabilization Mechanism in Robust Stochastic Adaptive Control using Lyapunov Function Arguments

Abstract: The objective of this paper is to propose a new algorithm for self-tuning control in the presence of unmodeled dynamics. It is shown (with probability one) that the resulting closed-loop system is globally stable and the mean-square tracking error is proportional to the size of unmodeled dynamics. In the absence of unmodeled dynamics, the algorithm produces the minimum-variance self-timing control. It is analytically verified that the proposed algorithm has self-stabilization property, i.e., possible occurance of instability results in mean-square bounded signals.

The training and use of an artificial neural network to monitor use of medication in treatment of complex patients.

Abstract: An artificial-neural-network-based drug interaction warning system was developed for use with a computerized real-time entry medical records system. The goal of the study was to provide physicians and nurses with timely warnings of potential drug interactions as therapies were prescribed. In a dialysis unit, physicians and clinical pharmacists defined rules of proper drug therapy, then trained a neural network with those rules. When the network was used to review the therapies of this patient population, a number of inconsistencies were discovered, and medication orders were changed on several patients. Real-time implementation of this monitoring system could provide messages to assure that drug therapy is consistent and proper, according to rules created by the providers of healthcare, thus preventing occasional mistakes in drug therapy.

A learning and forgetting algorithm in associative memories: results involving pseudo inverses

Abstract: The authors develop a design technique for associative memories with learning and forgetting abilities via artificial feedback neural networks. The proposed method utilizes the theory of large-scale dynamical systems, instead of the usual energy methods. Networks synthesized by this design method are capable of learning new patterns as well as forgetting existing patterns without the necessity of recomputing the entire interconnection weights and external inputs. The method employs the properties of pseudo-inverse matrices to iteratively solve systems of linear equations, and provides significant improvements over the outer product method and the projection learning rule. Several specific examples are given to illustrate the strengths and weaknesses of the methodology. >

Qualitative theory for dynamical systems with saturation nonlinearities

Abstract: The authors consider general dynamical systems formed from linear dynamics, but with provisions for the control variables to be bounded and for the state variables and output variables to go into saturation. Such systems are, for example, common in digital filters and in hybrid digital feedback control strategies. Building upon results from the theory of neural networks, they recast the problem as a collection of linear, reduced order systems with linear constraints and make precise the meaning of solutions including the various saturation modes. In addition, the existence and qualitative properties of equilibria in the various regions of the state space are discussed. When compared with classical analyses of these issues, the results are surprisingly sharp and simple. They appear to be an example of a situation in which an algebraic approach has pointed the way into a nonlinear problem area. >