Search

Abstract In this paper, we investigate the supervised backpropagation training of multilayer neural networks from a dynamical systems point of view. We discuss some links with the qualitative theory of differential equations and introduce the overfly algorithm to tackle the local minima problem. Our approach is based on the existence of first integrals of the generalised gradient system with build-in dissipation. [ABSTRACT FROM AUTHOR]

In this paper, neural algorithms, including the multi-layered perceptron (MLP) differential approximator, generalized hybrid power series, discrete Hopfield neural network, and the hybrid numerical, are used for constructing models that incorporate a priori knowledge in the form of differential equations for dynamic engineering processes. The properties of these approaches are discussed and compared to each other in terms of efficiency and accuracy. The presented algorithms have a number of advantages over other traditional mesh-based methods such as reduction of the computational cost, speed up of the execution time, and data integration with the a priori knowledge. Furthermore, the presented techniques are applicable when the differential equations governing a system or dynamic engineering process are not fully understood. The proposed algorithms learn to compute the unknown or free parameters of the equation from observations of the process behavior, hence a more precise theoretical description of the process is obtained. Additionally, there will be no need to solve the differential equation each time the free parameters change. The parallel nature of the approaches outlined in this paper make them attractive for parallel implementation in dynamic engineering processes. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents an approach to the well-known traveling salesman problem (TSP) using Kohonen self-organizing maps (SOM). We investigate these questions, ‘Does it converge to a feasible solution?’ ‘Is there a best adaptation law of parameters for the algorithm?’ ‘What is the effect of different sequencing of the nodes along the initial path?’ ‘How do we organize the index of winner neurons and the initial order of the cities?’ Despite many different types of SOM algorithm having already been approached to solve the TSP in the literature, the purpose of this paper is to look for the incorporation of an efficient initialization method and the definition of a parameter adaptation law to achieve better quality results and a faster convergence. Complexity of the modified SOM algorithm is analyzed. The results show an average deviation of 2.4372% from the optimal tour length for a set of 12 TSP instances. This result is better than an average deviation of 3.69% by using the same 12 TSP instances in the literature [C.V. Frederico, D.D.N. Adiao, A.F. Jose, An efficient approach to the traveling salesman problem using self-organizing maps, International Journal of Neural Systems 13(2) (2003) 59–66]. [Copyright &y& Elsevier]

Abstract: In this paper, the problem of exponential passivity analysis for uncertain neural networks with time-varying delays is considered. By constructing new augmented Lyapunov–Krasovskii’s functionals and some novel analysis techniques, improved delay-dependent criteria for checking the exponential passivity of the neural networks are established. The proposed criteria are represented in terms of linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms. A numerical example is included to show the superiority of our results. [Copyright &y& Elsevier]

Abstract: In this paper, the design problem of state estimator for a class of neural networks of neutral-type is studied. A delay-dependent linear matrix inequality (LMI) criterion for existence of the estimator is proposed by using the Lyapunov method. The criterion can be easily solved by various convex optimization algorithms. A numerical example with simulation results is given to show the effectiveness of proposed method. [Copyright &y& Elsevier]