Strength Of Interconnections Research Articles

Decentralized disturbance attenuation for interconnected systems

The problem of disturbance attenuation for interconnected systems by local state feedback control is investigated. By introducing a set of parameters, one characterizing the strength of interconnections and the other scaling subsystems, necessary and sufficient conditions are obtained under which the collection of such local controllers achieves the H8 requirement for the overall system. The H8 performance of the closed‐loop interconnected system is guaranteed and the required local state feedback control is simultaneously derived. The relationship between the H8 control theory and the decentralized controller design under a prespecified level of disturbance attenuation is also established. This also show that a complete solution to this problem is carried out merely by solving a set of algebraic Riccati equations.

Holographic implementation of a binary associative memory for improved recognition

Neural network associative memory has found wide applications in pattern recognition techniques. We propose an associative memory model for binary character recognition. The interconnection strengths of the memory are binary valued. The concept of sparse coding is used to enhance the storage efficiency of the model. The question of imposed preconditioning of pattern vectors, which is inherent in a sparsely coded conventional memory, is eliminated by using a multistep correlation technique and the ability of correct association is enhanced in a real-time application. A potential optoelectronic implementation of the proposed associative memory is also described. The learning and recall is possible by using digital optical matrix-vector multiplication, where full use of parallelism and connectivity of optics is made. A hologram is used in the experiment as a longterm memory (LTM) for storing all input information. The short-term memory or the interconnection weight matrix required during the recall process is configured by retrieving the necessary information from the holographic LTM.

Diagnostic system responsive to learned audio signatures

Loose parts are sensed moving in a conduit carrying a flowing material, such as the cooling circuit of a pressurized water nuclear reactor. An acoustic pickup produces an electrical signal with vibration of the conduit due to impact of the loose part, and background noise. A signal processor encodes the values of distinct parameters of the electrical signal such as amplitude, amplitude at particular frequencies, etc., in an ongoing manner, producing discrete output values. These outputs are coupled as inputs to a neural network with physical or logical neuron cells loaded with weighting factors affecting the strength and polarity of neural interconnections. The factors represent the acoustic signature of the loose part. Products of the input values and the weighting factors are summed to produce one or more neural network outputs, compared to a threshold. The sum normally varies randomly, but has a strong swing when the pattern is encountered, due to the factors emphasizing the pattern over background noise. The threshold comparison operates a display or alarm. The weighting factors are learned by repeating empirical tests and correlating the factors to the signal to minimize error.

Neural network approach to the TLS linear prediction frequency estimation problem

This paper presents a neural network approach to solving in real-time the linear prediction (LP) equation under the total least squares (TLS) criterion for the frequency estimation problem. We show both analytically and by simulations that this proposed neural network is guaranteed to be stable and to provide the results arbitrarily close to the accurate TLS solution of the LP equation within an elapsed time of only a few characteristic time constants of the circuit. The parameters such as the interconnection strengths of this proposed network can be obtained from the available data without any computation.

Dynamic behavior of a neural network model of locomotor control in the lamprey.

1. Experimental studies have shown that a central pattern generator in the spinal cord of the lamprey can produce the basic rhythm for locomotion. This pattern generator interacts with the reticular neurons forming a spinoreticulospinal loop. To better understand and investigate the mechanisms for locomotor pattern generation in the lamprey, we examine the dynamic behavior of a simplified neural network model representing a unit spinal pattern generator (uPG) and its interaction with the reticular system. We use the techniques of bifurcation analysis and specifically examine the effects on the dynamic behavior of the system of 1) changing tonic drives to the different neurons of the uPG; 2) altering inhibitory and excitatory interconnection strengths among the uPG neurons; and 3) feedforward-feedback interactions between the uPG and the reticular neurons. 2. The model analyzed is a qualitative left-right symmetric network based on proposed functional architecture with one class of phasic reticular neurons and three classes of uPG neurons: excitatory (E), lateral (L), and crossed (C) interneurons. In the model each class is represented by one left and one right neuron. Each neuron has basic passive properties akin to biophysical neurons and receives tonic synaptic drive and weighted synaptic input from other connecting neurons. The neuron's output as a function of voltage is given by a nonlinear function with a strict threshold and saturation. 3. With an appropriate set of parameter values, the voltage of each neuron can oscillate periodically with phase relationships among the different neurons that are qualitatively similar to those observed experimentally. The uPG alone can also oscillate, as observed experimentally in isolated lamprey spinal cords. Varying the parameters can, however, profoundly change the state of the system via different kinds of bifurcations. Change in a single parameter can move the system from nonoscillatory to oscillatory states via different kinds of bifurcations. For some parameter values the system can also exhibit multistable behavior (e.g., an oscillatory state and a nonoscillatory state). The analysis also shows us how the amplitudes of the oscillations vary and the periods of limit cycles change as different bifurcation points are approached. 4. Altering tonic drive to just one class of uPG neurons (without altering the interconnections) can change the state of the system by altering the stability of fixed points, converting fixed points to oscillations, single oscillations to two stable oscillations, etc. Two-parameter bifurcation diagrams show the critical regions in which a balance between the tonic drives is necessary to maintain stable oscillations. A minimum tonic drive is necessary to obtain stable oscillatory output. With appropriate changes in the tonic drives to the L and C neurons, stable oscillatory output can be obtained even after eliminating the E neurons. Indeed, the presence of active E neurons in the biological system does not prove they play a functional role in the system, because tonic drive from other sources can substitute for them. On the other hand, very high excitation of any one class of neurons can terminate oscillations. Appropriate balance of tonic drives to different neuron classes can help sustain stable oscillations for larger tonic drives. Published experimental results concerning changes in amplitude and swimming frequency with increased tonic drives are mimicked by the model's responses to increased tonic drive. 5. Interconnectivity among the neurons plays a crucial role. The analysis indicates that the C and L classes of neurons are essential components of the model network. Sufficient inhibition from the L to C neurons as well as mutual inhibition between the left and right halves is necessary to obtain stable oscillatory output. When the E neurons are present in the model network, they must receive appropriate tonic drive and provide appropriate excitation

Behavioral simulation of densely-connected analog cellular array processors for high-performance computing

The analog cellular neural network (CNN) model is a powerful parallel processing paradigm in solving many scientific and engineering problems. The network consists of densely-connected analog computing cells. Various applications can be accomplished by changing the local interconnection strengths, which are also called coefficient templates. The behavioral simulator could help designers not only gain insight on the system operations, but also optimize the hardware-software co-design characteristics. An unique feature of this simulator is the hardware annealing capability which provides an efficient method of finding globally optimal solutions. This paper first gives an overview of the cellular network paradigm, and then discusses the nonlinear integration techniques and related partition issues, previous work on the simulator and our own simulation environment. Selective simulation results are also presented at the end.

The use of random weights for the training of multilayer networks of neurons with Heaviside characteristics

Artificial neural networks have, in recent years, been very successfully applied in a wide range of areas. A major reason for this success has been the existence of a training algorithm called backpropagation. This algorithm relies upon the neural units in a network having input/output characteristics that are continuously differentiable. Such units are significantly less easy to implement in silicon than are neural units with Heaviside (step-function) characteristics. In this paper, we show how a training algorithm similar to backpropagation can be developed for 2-layer networks of Heaviside units by treating the network weights (i.e., interconnection strengths) as random variables. This is then used as a basis for the development of a training algorithm for networks with any number of layers by drawing upon the idea of internal representations. Some examples are given to illustrate the performance of these learning algorithms.

Real-time neural computation of the eigenvector corresponding to the largest eigenvalue of positive matrix

This paper proposes a neural network approach to compute in real time the eigenvector corresponding to the largest eigenvalue of a positive matrix. We show analytically and by simulations that the proposed neural network is guaranteed to be stable and provides results arbitrarily close to the accurate eigenvector within an elapsed time of only a few characteristic time constants of the network. The parameters of the network such as interconnection strengths can be obtained from the given matrix without any computations. As a result, this proposed neural network is satisfactory for the real time application of signal processing in which it is desired to provide as fast as possible the eigenvector corresponding to the largest eigenvalue of a positive matrix.

An improved scheme for direct adaptive control of dynamical systems using backpropagation neural networks

This paper presents an improved direct control architecture for the on-line learning control of dynamical systems using backpropagation neural networks. The proposed architecture is compared with the other direct control schemes. In this scheme the neural network interconnection strengths are updated based on the output error of the dynamical system directly, rather than using a transformed version of the error employed in other schemes. The ill effects of the controlled dynamics on the on-line updating of the network weights are moderated by including a compensating gain layer. An error feedback is introduced to improve the dynamic response of the control system. Simulation studies are performed using the nonlinear dynamics of an underwater vehicle and the promising results support the effectiveness of the proposed scheme.

Neural network for restoration of signals blurred by a random, shift-variant impulse response function

A novel regularization technique is proposed for the restoration of signals distorted by a stochastic, shift-variant impulse response (blur) function and additive noise. The generic ill-posed inverse problem is formulated as a constrained optimization problem wherein a new cost function, termed <i>stochastic constrained restoration error energy</i>, is minimized. For signals that are quantized in amplitude and sampled in time or space, an artificial neural network is developed and implemented for computational efficiency. By matching the cost function with the energy function of the neural network, the interconnection strengths and bias inputs of the neural network are related to the degraded signal, blur statistics, and constraint parameters. The solution that minimizes the energy function of the neural network is then obtained by the simulated annealing algorithm. Simulation results are also provided to demonstrate the effectiveness of the proposed approach.

A recurrent neural network controller and learning algorithm for the on-line learning control of autonomous underwater vehicles

A new on-line direct control scheme for the Autonomous Underwater Vehicles ( AUV), using recurrent neural networks, is investigated. In the proposed scheme, the controller consists of a three-layer network architecture having feedforward input and output layers, and a totally recurrent hidden layer. All the interconnection strengths are synchronously updated using a computationally inexpensive learning algorithm called Alopex. The updating is based on the output error of the system directly, rather than using a transformed version of the error employed in the other neural network based direct control schemes. In the present implementation, the network starts from random initial conditions without needing any prior training, and learns the dynamics of the AUV to provide the correct control signal. Based on the simulation experiments using the nonlinear dynamics of an AUV, we demonstrate that the proposed learning algorithm and the network architecture provide stable and accurate tracking performance. We have also addressed the issue of robustness of the controller to system parameter variations as well as to measurement disturbances.

A 2d neural network with application to solving a class of matrix equations

AbstractThis paper presents a 2D neural network with application to solving a class of matrix equations. We show both analytically and by simulations that this neural network is guaranteed to be stable and to provide results arbitrarily close to the accurate solutions of the matrix equations within an elapsed time of only a few characteristic time constants of the network. Parameters such as the interconnection strengths and bias currents of this proposed network can be obtained from the known matrices of the matrix equations without any computations.

Decentralized Quadratic Stabilization of Interconnected Systems

In this paper, the problem of quadratically stabilizing a linear interconnected system with parameter uncertainties by decentralized control is considered. The obtained stabilizability condition is given in terms of quadratic stabilizability with disturbance attenuation for each subsystem and the attenuation values are determined using only upper bounds of the strength of interconnections among subsystems. A decentralized control for quadratically stabilization is also given to demonstrate the feasibility of the design

Real-time neural computation of the maximum likelihood criterion for bearing estimation problems

This paper presents a neural network to compute the projection operator which lies the major computational burden of the real-time computation of the maximum likelihood criterion for bearing estimation. We show both analytically and by simulations that this neural network is guaranteed to be stable and to provide the results arbitrarily close to the accurate projection operator within an elapsed time of only a few characteristic time constants of the network. The parameters such as the interconnection strengths and bias currents of this proposed network can be obtained from the given matrix without any computations.

Neural network approach to computing matrix inversion

A neural network for matrix inversion is proposed. We show both analytically and by simulations that this network is guaranteed to be stable and to provide results arbitrarily close to the accurate inversion of a matrix within an elapsed time of only a few characteristic time constants of the network. The parameters such as the interconnection strengths of this network can be obtained from the known matrix without any computations.

Real-time implementation of 'propagator' bearing estimation algorithm by use of neural network

A neural network for implementing the Marcos 'propagator' bearing estimation algorithm is presented. It is shown both analytically and by simulations that this neural network is guaranteed to be stable and to provide the results arbitrarily close to the accurate propagator operator and the orthogonal projection operator on the noise subspace within an elapsed time of only a few characteristic time constants of the network. The parameters such as the interconnection strengths and bias currents of this proposed network can be obtained from the cross-spectral matrix without any computations. >

Simulating modular neural networks on message-passing multiprocessors

While simulation programs for single neural networks, running on parallel machines, always use a fixed problem decomposition and mapping strategy, we show that this is not possible for modular neural networks. We demonstrate this by analysing decomposition and mapping issues for a particular modular neural network model: the entropy-driven artificial neural network. The classic approach to simulations consists of two steps: first a data structure is built, describing the problem to be simulated. For a neural network this data structure contains the network topology, the interconnection strengths, etc. In a second step, this data structure is read into the simulation program, which performs a fixed decomposition and mapping before simulation can take place. Since this approach cannot be used any more for simulations of modular networks, we propose a new, three-step approach, in which decomposition and mapping are taken out of the simulation program. A compiler is used to prepare the problem data structure, a splitter program takes care of problem decomposition, and the simulator program takes the decomposed problem as its input. Since all decisions with respect to decomposition and mapping are taken by the splitter, the simulator program is independent of decomposition and mapping, and hence it can handle any decomposition and mapping. Following this approach, a machine-independent simulation environment was designed, and this design was implemented on a transputer system. To show that our approach is generic (i.e. not limited to simulations of modular networks) an implementation of a Hopfield network for image restoration is described. In spite of the classic preconceptions about generic software, performance analysis and benchmark results show that our novel, generic approach can be implemented efficiently on transputer arrays.

Neural networks in radiology: An introduction and evaluation in a signal detection task

Neural networks are a computer architecture, implementable in software or hardware, that allow an entirely new approach to the computerized perception of data. These so-called connectionist models are inspired by what is known about the architecture of biological neurons, in which the "intelligence" or processing capability of the network is a result of the interconnection strengths between large arrays of nonlinear processing nodes. Neural networks are described and then are used to analyze the common radiological problem of pattern recognition on a noisy background. Classical signal detection theory is used to compare network performance against that of human observers, using computer-generated sets of very simple "nodules." The neural network performed with better accuracy, relative to human observer performance, in the detection of this elementary test object. Although these results may not scale up with more complex images, the favorable performance of neural networks at this level suggests that further investigation is warranted.

Decentralized adaptive control: structural conditions for stability

Decentralized adaptive control schemes are presented for a class of large-scale interconnected systems. These schemes have the advantage that in addition to the standard assumption about the uncertainty of the subsystems, the strength of interconnection is assumed unknown. Provided certain structural constraints are satisfied, the adaptation gains automatically adjust to levels that assure stability of the overall system. Simulations of a spring-coupled dual pendulum showed that for high interconnection strengths, the proposed algorithm exhibits better tracking performance than existing algorithms.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Neural networks: introduction to the 1 December 1987 issue of Applied Optics

In recent decades, research on the structure and function of mind and brain has led to the development of a powerful new paradigm which is now being applied and adapted to a variety of problems in many disciplines. This paradigm is based on the mathematical theory of neural networks. Neural network theory includes formal architectures comprised of a large number of highly interconnected neuronlike processing elements having adjustable or adaptive interconnection strengths. Some twenty-one papers in the 1 December 1987 issue of Applied Optics bring together the work of scientists who are developing the basic theory as well as its technological uses.