Second-order bounds on the domain of attraction and the rate ofconvergence of nonlinear dynamical systems and neural networks

We present a method for analyzing the convergence properties of nonlinear dynamical systems yielding second-order bounds on the domain of attraction of an asymptotically stable equilibrium point and on the time of convergence in the estimated domain. We show that under certain conditions on the system, there exists an analytic solution to the corresponding optimization problem. The method is applied in analyzing the dynamics of a neural network model.     

Connectivity and performance tradeoffs in the cascade correlationlearning architecture

The cascade correlation is a very flexible, efficient and fast algorithm for supervised learning. It incrementally builds the network by adding hidden units one at a time, until the desired input/output mapping is achieved. It connects all the previously installed units to the new unit being added. Consequently, each new unit in effect adds a new layer and the fan-in of the hidden and output units keeps on increasing as more units get added. The resulting structure could be hard to implement in VLSI, because the connections are irregular and the fan-in is unbounded. Moreover, the depth or the propagation delay through the resulting network is directly proportional to the number of units and can be excessive. We have modified the algorithm to generate networks with restricted fan-in and small depth (propagation delay) by controlling the connectivity. Our results reveal that there is a tradeoff between connectivity and other performance attributes like depth, total number of independent parameters, and learning time.     

A delta transform approach to loop gain-phase shaping design of robust digital control systems

This paper addresses the existence of loop gain-phase shaping (LGPS) solutions for the design of robust digital control systems for SISO, minimum-phase, continuous-time processes with parametric uncertainty. We develop the frequency response properties of LGPS for discrete-time systems using the Δ-transform, a transform method that applies to both continuous-time and discrete-time systems. A theorem is presented which demonstrates that for reasonable specifications there always exists a sampling period such that the robust digital control problem has a solution. Finally, we offer a procedure for estimating the maximum feasible sampling period for LGPS solutions to robust digital control problems.     

Base-type languages: Program design by upper semantic approximation

Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 140–155, July–August 1994.     

Fault trees—Problems and the modern state of investigations

Published in Kibernetika i Sistemnyi Analiz, No. 3, pp. 128–150, May–June, 1994.     

Fuzzy sets-a convenient fiction for modeling vagueness andpossibility

This paper is a reply to Laviolette and Seaman's critical discussion of fuzzy set theory. Rather than questioning the interest of the Bayesian approach to uncertainty, some reasons why Bayesian find the idea of a fuzzy set not palatable are laid bare. Some links between fuzzy sets and probability that Laviolette and Seaman seem not to be aware of are pointed out. These links suggest that, contrary to the claim sometimes found in the literature, probability theory is not a special case of fuzzy set theory. The major objection to Laviolette and Seaman is that they found their critique on as very limited view of fuzzy sets, including debatable papers, while they fail to account for significant works pertaining to axiomatic derivation of fuzzy set connectives, possibility theory, fuzzy random variables, among others     

Statistical synchronization among participants in real-time multimedia conferencing

In this paper, an algorithm to determine the set of packets generated continuously and periodically from different participants that are arriving at a node either for mixing at the master of a conference, or for simply playing back at a regular participant of a conference, is proposed. The essence of the algorithm is to estimate the expected packet arrival time (or reference time) for each participant. With the reference time at hand, the maximum jitter and the optimum waiting time for a mixer to wait packets from all participants can be determined. An enhancement to improve synchronization which deals with the estimation of the time offsets between the individual periods of the sources and the period of the receiver is also presented. The error of the proposed algorithm is enumerated by the Chernoff bound and demonstrated by simulation and is shown to be acceptable in practical application. The algorithm can also be employed when traffic sources operate with different periods.