Stefano Manetti

Necessary and sufficient condition for absolute stability of neural networks

The main result in this paper is that for a neural circuit of the Hopfield type with a symmetric connection matrix T, the negative semidefiniteness of T is a necessary and sufficient condition for Absolute Stability. The most significant theoretical implication is that the class of neural circuits with a negative semidefinite T is the largest class of circuits that can be employed for embedding and solving optimization problems without the risk of spurious responses. >

On a class of nonsymmetrical neural networks with application to ADC

For nonzero initial conditions a neural network may stop in a spurious state-that is, in an equilibrium point that does not correspond to the correct digital representation of the input signal. A method based on a particular class of nonsymmetrical neural networks is proposed for eliminating the problem of stopping in spurious states. The dynamical behavior of these structures is studied to prove that they are characterized by a unique equilibrium point which is globally attractive-that is, the system will converge toward this point for every choice of initial conditions and for every choice of (continuous) nonlinearities. The explicit expression obtained for the unique equilibrium point permits one to design the connection strengths between neurons so that the equilibrium coincides with the desired output for a given input signal. The proposed design procedure is applied to the classical example of A/D conversion, showing that this A/D converter structure has no spurious states. The A/D was simulated using SPICE, and experimental results obtained with a discrete component prototype of the converter are presented. >

A condition for global convergence of a class of symmetric neural circuits

A sufficient condition is proved guaranteeing that a class of neural circuits that includes the Hopfield model as a special case is globally convergent towards a unique stable equilibrium. The condition only requires symmetry and negative semi-definiteness of the neuron connection matrix T and is extremely simple to check and apply in practice. The consequences of the above result are discussed in the context of neural circuits for optimization of quadratic cost functions. >

Determination of an optimum set of testable components in the fault diagnosis of analog linear circuits

A procedure for the determination of an optimum set of testable components in the fault diagnosis of analog linear circuits is presented. The proposed method has its theoretical foundation in the testability concept and in the canonical ambiguity group concept. New considerations relevant to the existence of unique solution in the k-fault diagnosis problem of analog linear circuits are presented, and examples of application of the developed procedure are considered by exploiting a software package based on symbolic analysis techniques.

Finding ambiguity groups in low testability analog circuits

This paper discusses a numerically efficient approach to identify complex ambiguity groups for the purpose of analog fault diagnosis in low-testability circuits. The approach presented uses a numerically efficient QR factorization technique applied to the testability matrix. Various ambiguity groups are identified. This helps to find unique solution of fault diagnosis equations or identifies which groups of components can be uniquely determined. This work extends results reported earlier in literature, where QR factorization was used in low-testability circuits, significantly increasing efficiency to determine ambiguity groups. A Matlab program that implements this method was integrated with a symbolic analysis program that generates test equations. The method is illustrated on two low-testability electronic circuits. Finally, method efficiency is tested on larger electronic circuits with several hundred tested parameters.

On the application of symbolic techniques to the multiple fault location in low testability analog circuits

A new approach for the multiple fault location in linear analog circuits is proposed. It presents the characteristic of using classical numerical procedures together with symbolic analysis techniques, which is particularly useful in the parametric fault diagnosis field. The proposed approach is based on the k-fault hypothesis and is provided with efficient algorithms for fault location also in the case of low testability circuits. The developed algorithms have been used for realizing a software package prototype which implements a fully automated system for the fault location in linear analog circuits of moderate size.

A Method for the Automatic Selection of Test Frequencies in Analog Fault Diagnosis

A new procedure for the selection of test frequencies in the parametric fault diagnosis of analog circuits is presented. It is based on the evaluation of algebraic indices, as the condition number and the norm of the inverse, of a sensitivity matrix of the circuit under test. This matrix is obtained starting from the testability analysis of the circuit. A test index (T.I.) that permits the selection of the set of frequencies that better leads to locating parametric faults in analog circuits is defined. By exploiting symbolic analysis techniques, a program that implements the proposed procedure has been developed. It yields the requested set of frequencies by means of an optimization procedure based on a genetic algorithm that minimizes the T.I. Examples of the application of the proposed procedure are also included.

SAPWIN-a symbolic simulator as a support in electrical engineering education

Gaining an insight into circuit properties in electrical engineering classes can be achieved by using computer based tools. A computer program which combines symbolic and numerical simulation capabilities is of great help, because such a program provides students with automatic analysis tools. This paper presents the program SAPWIN, which has been developed to perform an automatic symbolic and numerical analysis of linear circuits. The paper presents program features, their development lines and fundamental aspects. Also, the educational purposes which are contained in the use of the program itself are presented.

SAPEC-a personal computer program for the symbolic analysis of electric circuits

A personal computer program for the symbolic analysis of lumped, linear, time-invariant networks is presented. The program, written in Microsoft Lisp, utilizes methods of symbolic manipulation of algebraic expressions. The proposed approach is based on modified nodal analysis and an algorithm developed by the authors for the completely symbolic solution of the related linear systems. A useful property of the program is that it allows the user to select the circuit components which he wishes to consider as symbolic parameters. In order words, with SAPEC, it is possible to obtain the network functions in complete or partial symbolic form.<<ETX>>

Analog network testability measurement: a symbolic formulation approach

A symbolic formulation approach is applied to the problem of computing testability features of analog linear networks. The program, SAPTES, obtained by following this approach is presented. The program can be a very useful tool for designers and researchers in the field of linear analog circuits. SAPTES, which is written in LISP and runs on MS-DOS personal computers, is able to compute the testability of linear circuits of rather high complexity (composed of tens of components and nodes). Computational times range from a few tens of seconds to some tens of minutes on medium speed computers. The program is easily transportable to workstations or a mainframe, and, for the mainframe, program performance will considerably increase. >