Daniela Danciu

A CNN based approach for solving a hyperbolic PDE arising from a system of conservation laws: the case of the overhead crane

The paper proposes a neurocomputing approach for numerical solving of a hyperbolic partial differential equation (PDE) arising from a system of conservation laws. The main idea is to combine the method of lines (transforming the mixed initial boundary value problem for PDE into a high dimensional system of ordinary differential equations (ODEs)) with a cellular neural network (CNN) optimal structure which exploits the inherent parallelism of the new problem in order to reduce the computational effort and storage. The method ensure from the beginning the convergence of the approximation and preserve the stability of the initial problem.

Numerics for hyperbolic partial differential equations (PDE) via Cellular Neural Networks (CNN)

The paper proposes an Artificial Intelligence approach for computing an approximate solution for a hyperbolic partial differential equation (PDE) modeling the vibration of a drilling plant. The basic idea relies on using the repetitive structure induced by the Method of Lines for assigning a Cellular Neural Network (CNN) to perform the numerics. The method ensures from the beginning the convergence of the approximation and preserves the stability of the initial problem.

Gradient Like Behavior and High Gain Design of KWTA Neural Networks

It is considered the static and dynamic analysis of an analog electrical circuit having the structure of the Hopfield neural network, the KWTA (K-Winners-Take-All) network. The mathematics of circuit design and operation is discussed via two basic tools: the Liapunov function ensuring the gradient like behavior and the rational choice of the weights that stands for network training to ensure order-preserving trajectories. Dynamics and behavior at equilibria are considered in their natural interaction, and some connections to the ideas in general dynamical systems of convolution type are suggested.

Delays and Propagation: Control Liapunov Functionals and Computational Issues

There are considered some controlled objects with distributed parameters described by partial differential equations of hyperbolic type inducing wave propagation, connected at its turn with propagation delays. The boundary conditions are non-standard being described by ordinary differential or integro-differential equations. Basic theory—existence, uniqueness, well posedness-, stability and stabilization and numerical computations are considered for the benchmark problem of the marine vessel crane: its model is very much alike not only to other cranes but also to the flexible manipulator or the oilwell drillstring. In the lossless case basic theory is associated to the basic theory for some functional differential equations of neutral type. Stabilization is achieved by synthesizing low order controllers via c.l.f. (Control Liapunov Functional) induced by the energy identity for the partial differential equations. The numerics are considered within the framework of the method of lines implemented by applying the paradigm of the Cellular Neural Networks, an applied issue of Neuromathematics. After an illustrating simulation for the closed loop model some general conclusions and open problems are enumerated.

Nonlinear feedback control and artificial intelligence computational methods applied to a dissipative dynamic contact problem

In this paper we consider a vibrational percussion system described by a one-dimensional hyperbolic partial differential equation with boundary dissipation at one extremity and a normal compliance contact condition at the other extremity. Firstly, we obtain the mathematical model using the Calculus of variations and we prove the existence of weak solutions. Secondly, we focus on the numerical approximation of solutions by using a neuromathematics approach - a well-structured numerical technique which combines a specific approach of Method of Lines with the paradigm of Cellular Neural Networks. Our technique ensures from the beginning the requirements for convergence and stability preservation of the initial problem and, exploiting the local connectivity of the approximating system, leads to a low computational effort. A comprehensive set of numerical simulations, considering both contact and non-contact cases, ends the contribution.

Systems with slope restricted nonlinearities and neural networks dynamics

The quite large standard class of additive neural networks is considered from the point of view of the qualitative theory of differential equations. Connections with the theory of absolute stability are pointed out and a new class of Liapunov functions is introduced, starting from the positiveness theory (Yakubovich-Kalman-Popov lemma). The results are valid for a quite large class of dynamical systems and they are tested on some neural network structures. In the concluding part some perspective research is mentioned, including synchronization and time-delay effects.

Preliminary results on using an extension of gradient method for detection of red lesions on eye fundus photographs

The paper presents an extension of the gradient method for detection of red lesions on images of eye fundus, like a step in an automated system for recognition of diabetic retinopathy. Images of high resolution were corrected for shading and noise and the method was applied by calculating on every pixel the ldquoexpanding gradientrdquo of that pixel. This way, a map of the image was obtained and by thresholding conveniently, the interest objects of the image were detected with a certain level of certainty. After removing vessels, optic disc and other objects, each of the remaining objects are studied and the decision of being or not red lesion is taken. From 687 true red lesions included by 47 images of eye fundus, 584 red lesions were found using this method and a number of 106 false red spots were additionally found.

Distributed parameter system from Contact mechanics: Modelling and computational issues based on cellular neural networks paradigm

The paper deals with modelling and computational issues for a unified model from the Contact Mechanics belonging to the class of longitudinal vibrations of rods. The mathematical model is deduced by using the Calculus of Variation methods. The distributed parameter system is modelled by a mixed initial boundary value problem for hyperbolic partial differential equations with derivative boundaries. The computational issues can be viewed within the framework of the Neural mathematics. The approach is based on a procedure which combines a convergent Method of Lines with the Cellular Neural Networks paradigm in order to obtain a good approximation, preservation of the stability of the initial problem and a reduced computational effort even for approximating systems of huge dimension.

Bio-inspired systems. several equilibria. qualitative behavior

This paper is a survey on the approaches and results concerning the encountered behaviors and the qualitative properties of a class of bio-inspired dynamical learning machines. An overview and some results of several qualitative behaviors encountered both in natural and artificial dynamical systems - including synchronization and the dynamics affected by time-delays are presented in the main part of the paper. Some conclusions and open problems will end the survey.

Frequency domain stability inequalities for nonlinear time delay systems

Motivated by various applications, among which one can mention the problem of PIO - P(ilot)-I(n-the-loop)-O(scillations), it is considered the problem of the absolute (global asymptotic) stability of the zero equilibrium for systems with slope restricted nonlinearities. Since the linear part incorporates also time delay, it is taken the approach of integral equations subject to the so-called IQC - Integral Quadratic Constraints. It is thus obtained an early stability inequality due to V.A. Yakubovich, but valid for time delay systems in the basic (stable) case - when the linear part is exponentially stable.