Search

Unsupervised learning is a target free methodology to classify unorganized information. This study proposes a new unsupervised learning method for classifying unlabeled targets based on convex ellipsoidal sets. The method described here uses ellipsoidal calculus tools to realize pattern classification via a clustering scheme. The algorithm consisted in adjusting the number of clusters defined by an ellipsoidal set as well as their centers, shape forms and orientation. All these processes were realized without preliminary information on the data distribution. The application of an inner gradient descent algorithm permitted the adjustment of these parameters, using the standard deviation of data in the cluster with respect to the semi-axis of ellipsoid that contains the corresponding data. A specific evaluation of the proposed algorithm used two-dimensional attributes databases. The outcomes of the classification results were compared with those produced by the K-means and DBSCAN algorithm. Comparable classification results were achieved overcoming some drawbacks of the methods.

This manuscript presents an algorithm to classify continuously electroencephalographic (EEG) signals based on deep differential neural networks (DDNNs). The learning laws are obtained by the second stability method of Lyapunov that requires the solution of a set of matrix differential equations. The robustness of this technique allows the analysis and classification of bio-signals like EEG signals. The EEG signals have complex dynamics and they are strongly affected by noises in the measurements and a high degree of variability between different studies in patients. The main strength of DDNNs is their feedback property, which allows them to work with the time-dependent variation of the EEG signals. The DDNNs are tested in a database constituted of EEG signals acquired from a study made in ten volunteers. The study consisted of the acquisition of EEG measurements of the volunteers recognizing geometrical figures appearing in a graphic user interface. The DDNN obtained better performance than a single layer differential neural network and a convolutional neural network.

This manuscript deals with the problem of controlling a virtualized humanoid robot with 16 degrees of freedom (DOF), each corresponding to the articulation in a real human being. That is, three DOF for each leg in the sagittal plane and one for the abduction movement; three DOF for each arm in the sagittal plane and one for the waist. The tracking trajectory problem of any humanoid robot like the classical biped robots requires a control algorithm with robustness against parametric uncertainties, fast response and even with finite-time convergence. These main characteristics are easily covered by sliding mode controllers. This manuscript implements a terminal second order sliding mode (TSOSM) controller to ensure the finite-time tracking trajectory of each articulation of the humanoid robot to the ones that define a classical walking pattern obtained by bio-mechanical studies. The TSOSM is implemented in a virtual platform developed in a computer-aided design software.

The aim of this study was to develop a dynamic neural field (DNF) model to capture the essential non-linear characteristics of neural activity along several millimeters of visual cortex in response to local flashed stimuli. A two-layer DNF model was assessed to describe the response of both excitation and inhibitory layers of neurons. This particular structure of neurons interconnection was analyzed as a coupled system of non-linear integro-differential equations. This representation transformed the regular distributed form of DNF into an interconnected nonlinear model. A non-parametric modeling strategy yields to design the adjustment laws for the DNF weights. The algorithm used to adjust the weights considered self interconnections for each layer as well as external stimulus. The concept of controlled Lyapunov function served as the main tool to design a stable learning method for DNF. This algorithm was implemented in a class of hybrid computational model that served to execute the modeling of physiological response associated to visual external stimuli. The DNF model designed in this study can consider just the excitation response of specific neuron circuits without considering the presence of inhibitory response. This condition extends the number of electrophysiological trials where the adjusted DNF model can be evaluated. The learning method was evaluated with the information from a database that contains information coming from a selective visual attention experiment where the external stimuli appeared briefly in any of five squares arrayed horizontally above a central fixation cross. The degree of correlation (above 0.95) between signals measured at the brain cortex and the response of the DNF justified the application of the method proposed in this study.

This study addresses the problem of designing an output model reference control for non-linear systems in the presence of parametric disturbances/uncertainties in the state model and output noise measurements. A state observer based on a differential neural network (DNN) estimates the unknown states and the unknown disturbance simultaneously. The control design includes the estimated disturbance to provide a better tracking performance. The second result optimizes the gains of the controller and observer in order to obtain a reduced convergence zone for the tracking error based on the attractive ellipsoid method approach (AEM). Numerical results point out the advantages obtained by the nonlinear control based on the DNN observer when it is compared with a classical Luenberger structure.

A ray tracing model of a solar tower heliostat field was developed using SolTrace software. The optical performance of the Heliostat field was evaluated as function of the total number of heliostats, the time and date, and the aiming errors. The calibration of the simulated data was made by taking into account the results of measured experimental tests. The simulated solar radiation flux and temperature distributions in the receiver are also presented.

The control problem of nonlinear systems affected by external perturbations and parametric uncertainties has attracted the attention for many researches. Artificial Neural Networks (ANN) constitutes an option for systems whose mathematical description is uncertain or partially unknown. In this paper, a Recurrent Neural Network (RNN) is designed to address the problems of identification and control of discrete-time nonlinear systems given by a gray box. The learning laws for the RNN are designed in terms of discrete-time Lyapunov stability. The control input is developed fulfilling the existence condition to establish a Quasi Sliding Regime. In means of Lyapunov stability, the identification and tracking errors are ultimately bounded in a neighborhood around zero. Numerical examples are presented to show the behavior of the RNN in the identification and control processes of a highly nonlinear discrete-time system, a Lorentz chaotic oscillator.

The Proportional Derivative controller (PD) has been successfully implemented in many real-time applications. It is well-known, that the PD is composed by a proportional and a derivative terms of the signal error. However, the main problem in the implementation of this controller is related with the error signal derivative. Most of the existing results obtain the derivative based on first order filters. This approach is not useful if the signal is noisy and uncertain. In the present paper, the so-called Super-Twisting Algorithm (STA), that is a second order sliding mode approach, is implemented as a robust exact differentiator because it can reach the derivative of a signal in finite time. The closed loop stability of the proposed controller is analyzed in terms of a non-smooth Lyapunov function. Finite time convergence of the tracking error into a boundary layer is obtained. With a slightly modification in the control law with the addition of a discontinuous term, finite time convergence of the error to zero is obtained. Numerical results are given to show the difference between the classical PD and the proposed PD with the STA differentiator.

Sliding Mode theory has attracted the attention of many researchers due to its remarkable characteristics. A substantial amount of research is carried out in continuous time for the conventional sliding mode theory and subsequently for second order sliding modes. However, for the discrete time, case, this theory has not been exploited in comparison with the continuous case, especially for the high order sliding mode theory, There are some results about the problem of observation for discrete systems using techniques such as finite differences. In most cases, the results may only prove exponential convergence to a region delimited by the sampled period. This article proposes an observer based on the super twisting algorithm for discrete-time systems 2n dimensional. The stability proofs are given in the discrete Lyapunov sense. In terms of the linear matrix inequalities theory, the error trajectories are ultimately bounded in finite time. We present numerical results of the observer in a nonlinear biped model obtained from a discretization using the Euler approximation.

Most of state estimators implemented in real systems are not able to measure the information continuously. The sliding observers are not an exception. Nevertheless, when state observers are used in real applications or even in real systems, one must implement a sampled based observer. This means that output is obtained with an Analogical/Digital Converter and using the sampling-holding device. Using a zero order hold, one can reconstruct the sampled signal until the next measure. In this way, the output information is continuous within the next sampling period. In this paper, a sampled output based second order sliding mode and Luenberger-like observer (SOSML) is developed. A new class of Lyapunov functions is used to prove stability. This so-called strong Lyapunov function was used to demonstrate practical stability leading to define a convergence zone depending on the sampling period. So, this paper introduces the observer design and analyzes the sampling effect on the estimation quality. The result was tested for a simple pendulum system. The efficiency of the suggested SOSML is compared with the a similar sampled version of the so called super-twisting algorithm. The observer performance was evaluated for several sampled times.

Most of state observers implemented in real systems are not able to measure the information continuously. The sliding observers are not an exception. Nevertheless, when state observers are used in numerical applications or even in real systems, one must implement a sampled based observer. This means that the output was obtained by means of a Analogical/Digital Converter. Using a zero order hold we can maintain the data until the next measure. In this form the output implemented in the algorithm is continuous. In this paper, a noel variable-gain super-twisting observer is proposed based on Lyapunov theory. That is, the correction terms varies during the time. This variable gain depends on the error trajectories and known functions that are upper bounds for the disturbances that affect the system. The observer ensures finite time convergence into a boundary layer depending of the sampled period. This structure is applied in a simple pendulum model using several sample periods of time.

State estimation for uncertain systems affected by external noises is an important problem in control theory. This paper deals with the state observation problem when the dynamic model of a discrete plant contains uncertainties or is partially unknown. The suggested observer is oriented to solve the state observation problem of discrete time nonlinear systems. Most of the existing results using the neural networks approach have been developed for continuous time systems using. The recurrent neural network (RNN) have shown several advantages to treat many different control and state estimation problems. In this paper, it is presented a new discrete-time observer using the structure of a classical RNN. This observer includes a correction term using the output information and the first order sliding modes. The second method Lyapunov is applied to generate a new learning law, that contains an adaptive adjustment rate. This study proofs the stability condition for the free parameters included in the neural-observer. A numerical example is given using the RNN in the estimation of a mathematical model describing the HIV infection, that includes non-infected cells, infected cells and free virions. This model was used to generated the data using to test the observer.

Most of state observers implemented in real systems are not able to measure the information continuously. The sliding observers are not an exception. Nevertheless, when state observers are used in numerical applications or even in real systems, one must implement a sampled based observer. In this paper, a second order sliding mode observer based on the supertwisting algorithm is studied, tacking into account that the output only can be measure in specific periods of the time, to do this, a zero order hold is proposed to sampling the output. The continuous observer is analized in terms of Lyapunov stability. It have been proposed a strong Lyapunov function to show finite-time convergence into a boundary layer that depends on the sampled period. The result is applied into a two-link robot manipulator and it is compared the observer efficiency between different sampled periods to show how the result is affected by the sampling interval.

State estimation for uncertain systems affected by external noises is an important problem in control theory. This paper deals with the state observation problem when the dynamic model of a plant contains uncertainties or is completely unknown and it is oriented to discrete time nonlinear systems because most of the existent results have been developed for continous time systems. The recurrent neural network (RNN) have shown his advantages to deal with this class problem. The Lyapunov second method is applied to generate a new learning law, containing an adaptive adjustment rate, implying the stability condition for the free parameters of the neural-observer. A numerical example is given using the RNN in the estimation of a mathematical model of HIV infection with three states.