Fathi M. A. Salam

On the analysis of dynamic feedback neural nets

A formulation for dynamic feedback neural networks of the Hopfield type is presented. A description is given of the general design framework used, in which a neural network would only have a finite number of memories. Some basic properties of the nonzero equilibria as well as the (unstable) equilibrium point at zero in the proposed framework are also discussed. >

Arnold diffusion in the swing equations of a power system

We present an application of the theory of Arnold diffusion to interconnected power systems. Using a Hamiltonian formulation, we show that Arnold diffusion arises on certain energy levels of the swing equations model. The occurrence of Arnold diffusion entails complex nonperiodic dynamics and erratic transfer of energy between the subsystems. Conditions under which Arnold diffusion exists in the dynamics of the swing equations are found by using the vector-Melnikov method. These conditions become analytically explicit in the case when some of the subsystems undergo relatively small oscillations. Perturbation and parameter regions are found for which Arnold diffusion occurs. These regions allow for a class of interesting systems from the point of view of power systems engineering.

Parallel processing for the load flow of power systems: the approach and applications

A description is given of homotopy-based computational parallel algorithms for solving for all the roots of a system of algebraic polynomial equations. Also presented is a convenient polynomial representation of the load flow equations of power systems. The algorithm techniques are then applied to obtain all steady-state solutions of the load flow for five-bus and seven-bus power system networks. A special probability-one homotopy method is tailored for the load flow to reduce the computational complexity while still guaranteeing the finding of all solutions computationally. More importantly and practically, the numerical implementation of the solution procedures exploits inherent parallelism in the load flow equations to be efficiently executed on massively parallel distributed-memory multiprocessors.<<ETX>>

The Mel'nikov technique for highly dissipative systems

We present explicit calculations that extend the applicability of the Mel’nikov technique to include a general class of highly dissipative systems. In particular, the dissipation may be in the form of large positive or negative damping. The only required assumption is that each system of this class possesses a homoclinic or a heteroclinic orbit. We also show that sufficiently small time-sinusoidal perturbation of these systems results in (nonempty) transversal intersection of stable and unstable manifolds for all but at most discretely many frequencies. The results are then demonstrated via computer simulation of the highly damped pendulum with constant plus small time-sinusoidal forcing.

A robust algorithm for detecting speech segments using an entropic contrast

This paper addresses the issue of automatic word/sentence boundary detection in both quiet and noisy environments. We propose to use an entropy based contrast function between the speech segments and the background noise. A simplified data based scheme of computing the entropy of the speech data is presented. The entropy-based contrast exhibits better-behaved characteristics as compared to the energy-based methods. An adaptive threshold is used to determine the candidate speech segments, which are subjected to word/sentence constraints. Experimental. results show that this algorithm outperforms energy-based algorithms. The improved detection accuracy of speech segments results in at least 25% improvement of recognition performance for isolated speech and more than 16% for connected speech. For continuous speech, a preprocessing stage comprising of the proposed speech segment detection makes the overall HMM based scheme more computationally efficient by rejection of silence periods.

Complicated dynamics of prototype continuous-line adaptive control system

The authors investigate the possible dynamics that a prototype model reference adaptive control system can experience when using the so-called sigma -modification adaption law described by P.I. Ioannou and P.V. Kokotovic (1984). Limiting their attention to first-order plants with a single unknown pole and an external disturbance, they verify analytically the bifurcations that an example adaptive system has previously been shown to exhibit based on computer simulations. The parameter-space-to-bifurcation diagram is constructed summarizing all possible behaviors of the class of prototype systems under consideration. It is shown that a certain range of constant-plus-sinusoidal disturbances generate chaos. For a certain range of constant disturbances, it is shown that a sinusoidal reference input signal generates chaos as well. In both cases, chaos arises form transversal homoclinic orbits. The use of the parameter space as a design tool for the proper implementation of the scheme is demonstrated. >

Disturbance-generated bifurcations in a simple adaptive system: Simulation evidence

Abstract We present complete characterization based on computer simulation of the possible dynamics exhibited by an adaptive control system where the (first order) plant with a single unknown pole has constant disturbance at the input. The adaptive system is taken from the current adaptive control systems literature. Here we show that the system in fact undergoes bifurcations and exhibits rich dynamics. As the constant disturbance is varied, the system undergoes saddle-node bifurcation, (subcritical) Hopf bifurcation, and a saddle connection bifurcation. The last bifurcation means that the system acquires a homoclinic orbit for a specific disturbance. While the first two bifurcations are local, the presence of the homoclinic orbit has the potential, when periodically disturbed, to generate nonlocal complicated behavior. This latter behavior is often referred to as ‘horseshoe chaos’.

A data-derived quadratic independence measure for adaptive blind source recovery in practical applications

We present a novel performance index to measure the statistical independence of data sequences and apply it to the framework of blind source recovery (BSR) that includes blind source separation, deconvolution and equalization. This performance index is capable of measuring the mutual independence of data sequences directly from the data. This information theoretic; quadratic independence measure (QIM) is derived based on Renyis quadratic entropy estimated by a finite data length Parzen window using a Gaussian kernel. Simulation results are presented to validate the performance of the proposed benchmark and compare it with other established benchmarks.

Blind source recovery: algorithms for static and dynamic environments

This paper integrates our contributions in the domain of blind source separation and blind source deconvolution, both in static and dynamic environments. We focus on the use of the state space formulation and the development of a generalized optimization framework, using Kullback-Liebler divergence as the performance measure subject to the constraints of a state space representation. Various special cases are subsequently derived from this general case and are compared with material in recent literature. Some of these reported works have also been implemented in dedicated hardware/software and experimental designs have been compared with their computer simulations.

An adaptive network for blind separation of independent signals

The problem of separating two or several independent signals (or independent speakers) from an array of sensors within the framework of adaptive systems is formulated. The delayed signals are modeled as a dynamic state model. The crucial aspect of this formulation is to quantify the property of independence of signals in terms of an explicit function to be optimized. Then, the derived adaptive dynamics will work to minimize (or maximize) the explicit function. The convergence of this newly derived adaptive scheme is shown. As the dynamics converge, the network will succeed in identifying the mixing and the delays in the original signals, and will reproduce the original independent signals.<<ETX>>