José A. R. Vargas

An adaptive scheme for chaotic synchronization in the presence of uncertain parameter and disturbances

Recently, several schemes have been proposed in the literature to synchronize chaotic systems. However, in most of these approaches, the presence of uncertain parameters and external disturbances were not considered. Motivated by the above consideration, this paper proposes an adaptive methodology to synchronize any chaotic system with unified chaotic systems, even if bounded disturbances are present. The proposed controller is composed of both variable proportional and adaptive control actions for guaranteeing the convergence of the residual synchronization error to zero in the presence of disturbances. Two possible modifications are considered: 1) only adaptive control action is implemented to overcome the well-known assumption of prior knowledge of upper bounds to compensate for the disturbances, and 2) the control gain of the proportional part is saturated, when the residual synchronization error has, practically, been removed. Lyapunov theory, in combination with Barbalats Lemma, is used to design the proposed controller. Experimental simulations are provided to show the effectiveness of the proposed controller and its advantages, when compared with a recent work in the literature.

Adaptive observer design based on scaling and neural networks

Some works based on neural networks have been proposed to estimate adaptively the states of uncertain systems. However, they are subject to several conditions such as previous knowledge of upper bounds for the weight and approximation errors, ideal switching, and previous sample data for an off-line learning phase, which difficult their application. In this paper, an adaptive observer for uncertain nonlinear systems in the presence of disturbances is proposed in order to avoid the above mentioned limitations. Based on a neural Luenberger-like observer, scaling and Lyapunov theory, an adaptive scheme is proposed to make ultimately bounded the on-line observer error. Besides, it is shown that the scaling of unknown nonlinearities, previous to the neural approximation, has a positive impact on performance and application of our algorithm, since it allows the residual state error manipulation without any additional linear matrix inequality solution. To validate the theoretical results, the state estimation of the Rössler oscilator system is performed.

Sensor Fusion to Estimate the Depth and Width of the Weld Bead in Real Time in GMAW Processes

The arc welding process is widely used in industry but its automatic control is limited by the difficulty in measuring the weld bead geometry and closing the control loop on the arc, which has adverse environmental conditions. To address this problem, this work proposes a system to capture the welding variables and send stimuli to the Gas Metal Arc Welding (GMAW) conventional process with a constant voltage power source, which allows weld bead geometry estimation with an open-loop control. Dynamic models of depth and width estimators of the weld bead are implemented based on the fusion of thermographic data, welding current and welding voltage in a multilayer perceptron neural network. The estimators were trained and validated off-line with data from a novel algorithm developed to extract the features of the infrared image, a laser profilometer was implemented to measure the bead dimensions and an image processing algorithm that measures depth by making a longitudinal cut in the weld bead. These estimators are optimized for embedded devices and real-time processing and were implemented on a Field-Programmable Gate Array (FPGA) device. Experiments to collect data, train and validate the estimators are presented and discussed. The results show that the proposed method is useful in industrial and research environments.

Online neuro-identification of nonlinear systems using Extreme Learning Machine

In this paper, an identification scheme via extreme learning machine neural network is proposed. The proposed identification scheme ensures the convergence of the residual state error to zero and boundedness of all associated approximation errors, even in the presence of approximation error and disturbances. Lyapunov-like analysis using Barbalats Lemma and a dynamic single-hidden layer neural network (DSHLNN) model with hidden nodes randomly generated to establish the aforementioned properties are employed. Hence, faster convergence and better computational efficiency than DSHLNNs is assured. Simulations to validate the theoretical results and show the effectiveness of the proposed method are provided.

An improved on-line neuro-identification scheme

In this paper, an on-line identification scheme is proposed to enhance the residual state error performance in face of disturbances. The proposed scheme is based on an e1-modification adaptive law for the weights to approximate the unknown nonlinearities with bounded error. Besides, an identification model with feedback is introduced to improve the state error performance. The feedback is based on a bounding function to estimate an upper bound for the disturbances. Via an adaptive bounding technique and Lyapunov methods, it is proved that the residual state error performance is practically immune to disturbances. To validate the theoretical results, the identification of a four-order generalized Lü hyperchaotic system is performed.

Convergência Do Erro De Predição Em Identificação Neural Sujeita A Distúrbios E Parâmetros Variantes No Tempo

Resumo – Neste artigo é proposto um algoritmo para identificação neural de sistemas contínuos não-lineares incertos com parâmetros variantes no tempo e sujeitos a distúrbios. Prova-se, via argumentos usuais de Lyapunov e uma técnica de limitação adaptativa (adaptive bounding technique), que o erro de predição converge para zero, inclusive na presença de erros de aproximação e distúrbios, enquanto os outros erros associados permanecem limitados. Simulações são apresentadas para ilustrar a aplicação e desempenho do algoritmo proposto.

Improved Learning Algorithm for Two-Layer Neural Networks for Identification of Nonlinear Systems

Abstract This study is concerned with the asymptotic identification of nonlinear systems based on Lyapunov theory and two-layer neural networks. An improved identification model enhanced with a feedback term and a novel adaptation law for the threshold offset, associated with the output weight matrix, is introduced to assure the convergence of the online prediction error, even in the presence of approximation error and bounded disturbances and when upper bounds for these perturbations are not known in advance. The effectiveness of the proposed method and its application to the identification of a hyperchaotic system and control of a welding system is investigated.

Identification of unknown nonlinear systems based on multilayer neural networks and Lyapunov theory

This paper considers the identification problem of nonlinear systems based on single-hidden-layer neural networks (SHLNNs) and Lyapunov theory. A nonlinearly parameterized neural model, whose weights are adjusted by robust adaptive laws, which are designed via Lyapunov theory, is proposed for ensuring the convergence of the residual state error to an arbitrary neighborhood of zero. In addition, a scaling matrix is used to resize the unknown nonlinearities to be approximated by an SHLNN, which, in turn, provides a simple way to shape the residual state error. It is shown that all estimation errors are uniformly bounded and, in addition, that the residual state error is uniformly ultimately bounded with an ultimate bound that depends directly on some independent design parameters. To validate the theoretical results, the identification of a chaotic system and a comparison study with other work in the literature are performed.