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This paper presents a non-parametric identification scheme for a class of uncertain switched nonlinear systems based on continuous-time neural networks. This scheme is based on a continuous neural network identifier. This adaptive identifier guaranteed the convergence of the identification errors to a small vicinity of the origin. The convergence of the identification error was determined by the Lyapunov theory supported by a practical stability variation for switched systems. The same stability analysis generated the learning laws that adjust the identifier structure. The upper bound of the convergence region was characterized in terms of uncertainties and noises affecting the switched system. A second finite-time convergence learning law was also developed to describe an alternative way of forcing the identification error's stability. The study presented in this paper described a formal technique for analysing the application of adaptive identifiers based on continuous neural networks for uncertain switched systems. The identifier was tested for two basic problems: a simple mechanical system and a switched representation of the human gait model. In both cases, accurate results for the identification problem were achieved.

In this paper, a non-parametric model of the neuromusculoskeletal system for the biceps brachii is presented. The model serves to generate angular paths for the control of a virtual active orthosis. The path generator uses a differential neural network (DNN) identifier that obtains the reference angular position and velocities using the raw electromyographic (EMG) signals as input. The model is validated using experimental data. The training and closed-loop implementation of the proposed model are described. The control strategy ensures that the user reaches a set-point with a predefined position constraint and that the device follows the natural reference path that corresponds to the raw EMG signal.

The aim of this article is to investigate the trajectory tracking problem of systems with uncertain models and state restrictions using differential neural networks (DNNs). The adaptive control design considers the design of a nonparametric identifier based on a class of continuous artificial neural networks (ANNs). The design of adaptive controllers used the estimated weights on the identifier structure yielding a compensating structure and a linear correction element on the tracking error. The stability of both the identification and tracking errors, considering the DNN, uses a barrier Lyapunov function (BLF) that grow to infinity whenever its arguments approach some finite limits for the state satisfying some predefined ellipsoid bounds. The analysis guarantees the semi-globally uniformly ultimately bounded (SGUUB) solution for the tracking error, which implies the achievement of an invariant set. The suggested controller produces closed-loop bounded signals. This article also presents the comparison between the tracking states forced by the adaptive controller estimated with the DNN based on BLF and quadratic Lyapunov functions as well. The effectiveness of the proposal is demonstrated with a numerical example and an implementation in a real plant (mass-spring system). This comparison confirmed the superiority of the suggested controller based on the BLF using the estimates of the upper bounds for the system states.

The main goal of this study is developing an adaptive controller which can solve the trajectory tracking for a class of quadcopter unmanned aerial system (UAS), namely a quadrotor. The control design introduces a new paradigm for adaptive controllers based on the implementation of a set of differential neural networks (DNNs) in the consequence section of a Takagi-Sugeno (T-S) fuzzy inference system. This dynamic fuzzy inference structure was used to approximate the UAS description. The particular form of interaction between neural networks and fuzzy inference systems proposed in the present work received the name of dynamic neural fuzzy system (DNFS). An adaptive controller based on this DNFS form was the main solution attained in this study. This DNFS controller was focused on the estimation and compensation of the uncertain section of the Quadrotor dynamics and then, forced the UAS to perform a hover flight while the tracking of desired angular positions succeeded, which results in tracking a desired trajectory in the X-Y plane. The control design methodology supported on the Lyapunov stability theory guaranteed ultimate boundedness of the estimation and tracking errors simultaneously. Several experimental tests in an outdoor environment by using a real Quadrotor platform was performed by using an RTK-GPS (Real Time Kinematic) system to determine the position of the vehicle in the X-Y plane. The experimental results confirmed the superior performance of the proposed algorithm based on the combination of DNNs and T-S techniques with respect to classical robust controllers., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2020 ISA. Published by Elsevier Ltd. All rights reserved.)

The design of an artificial neural network (ANN) based sub-optimal controller to solve the finite-horizon optimization problem for a class of systems with uncertainties is the main outcome of this study. The optimization problem considers a convex performance index in the Bolza form. The dynamic uncertain restriction is considered as a linear system affected by modeling uncertainties, as well as by external bounded perturbations. The proposed controller implements a min-max approach based on the dynamic neural programming approximate solution. An ANN approximates the Value function to get the estimate of the Hamilton-Jacobi-Bellman (HJB) equation solution. The explicit adaptive law for the weights in the ANN is obtained from the approximation of the HJB solution. The stability analysis based on the Lyapunov theory yields to confirm that the approximate Value function serves as a Lyapunov function candidate and to conclude the practical stability of the equilibrium point. A simulation example illustrates the characteristics of the sub-optimal controller. The comparison of the performance indexes obtained with the application of different controllers evaluates the effect of perturbations and the sub-optimal solution., (Copyright © 2020 Elsevier Ltd. All rights reserved.)

This study reports the design and implementation of a pattern recognition algorithm to classify electroencephalographic (EEG) signals based on artificial neural networks (NN) described by ordinary differential equations (ODEs). The training method for this kind of continuous NN (CNN) was developed according to the Lyapunov theory stability analysis. A parallel structure with fixed weights was proposed to perform the classification stage. The pattern recognition efficiency was validated by two methods, a generalization-regularization and a k-fold cross validation (k=5). The classifier was applied on two different databases. The first one was made up by signals collected from patients suffering of epilepsy and it is divided in five different classes. The second database was made up by 90 single EEG trials, divided in three classes. Each class corresponds to a different visual evoked potential. The pattern recognition algorithm achieved a maximum correct classification percentage of 97.2% using the information of the entire database. This value was similar to some results previously reported when this database was used for testing pattern classification. However, these results were obtained when only two classes were considered for the testing. The result reported in this study used the whole set of signals (five different classes). In comparison with similar pattern recognition methods that even considered less number of classes, the proposed CNN proved to achieve the same or even better correct classification results., (Copyright © 2016 Elsevier Ltd. All rights reserved.)

Time-delay systems have been successfully used to represent the complexity of some dynamic systems. Time-delay is often used for modeling many real systems. Among others, biological and chemical plants have been described using time-delay terms with better results than those models that have not consider them. However, getting those models represented a challenge and sometimes the results were not so satisfactory. Non-parametric modeling offered an alternative to obtain suitable and usable models. Continuous neural networks (CNN) have been considered as a real alternative to provide models over uncertain non-parametric systems. This article introduces the design of a specific class of non-parametric model for uncertain time-delay system based on CNN considering the so-called delayed learning laws analysis. The convergence analysis as well as the learning laws were produced by means of a Lyapunov-Krasovskii functional. Three examples were developed to demonstrate the effectiveness of the modeling process forced by the identifier proposed in this study. The first example was a simple nonlinear model used as benchmark example. The second example regarded the human immunodeficiency virus dynamic behavior is used to show the performance of the suggested non-parametric identifier based on CNN for no fictitious neither academic models. Finally, a third example describing the evolution of hepatitis B virus served to test the identifier presented in this study and was also useful to provide evidence of its superior performance against a non-delayed identifier based on CNN., (Copyright © 2014 Elsevier Ltd. All rights reserved.)

This paper presents the design of a complex-valued differential neural network identifier for uncertain nonlinear systems defined in the complex domain. This design includes the construction of an adaptive algorithm to adjust the parameters included in the identifier. The algorithm is obtained based on a special class of controlled Lyapunov functions. The quality of the identification process is characterized using the practical stability framework. Indeed, the region where the identification error converges is derived by the same Lyapunov method. This zone is defined by the power of uncertainties and perturbations affecting the complex-valued uncertain dynamics. Moreover, this convergence zone is reduced to its lowest possible value using ideas related to the so-called ellipsoid methodology. Two simple but informative numerical examples are developed to show how the identifier proposed in this paper can be used to approximate uncertain nonlinear systems valued in the complex domain.

This paper addresses the design of a discontinuous finite time convergent learning law for neural networks with continuous dynamics. The neural network was used here to obtain a non-parametric model for uncertain systems described by a set of ordinary differential equations. The source of uncertainties was the presence of some external perturbations and poor knowledge of the nonlinear function describing the system dynamics. A new adaptive algorithm based on discontinuous algorithms was used to adjust the weights of the neural network. The adaptive algorithm was derived by means of a non-standard Lyapunov function that is lower semi-continuous and differentiable in almost the whole space. A compensator term was included in the identifier to reject some specific perturbations using a nonlinear robust algorithm. Two numerical examples demonstrated the improvements achieved by the learning algorithm introduced in this paper compared to classical schemes with continuous learning methods. The first one dealt with a benchmark problem used in the paper to explain how the discontinuous learning law works. The second one used the methane production model to show the benefits in engineering applications of the learning law proposed in this paper., (Copyright © 2013 Elsevier Ltd. All rights reserved.)

State estimation for uncertain systems affected by external noises is an important problem in control theory. This paper deals with a state observation problem when the dynamic model of a plant contains uncertainties or it is completely unknown. Differential neural network (NN) approach is applied in this uninformative situation but with activation functions described by wavelets. A new learning law, containing an adaptive adjustment rate, is suggested to imply the stability condition for the free parameters of the observer. Nominal weights are adjusted during the preliminary training process using the least mean square (LMS) method. Lyapunov theory is used to obtain the upper bounds for the weights dynamics as well as for the mean squared estimation error. Two numeric examples illustrate this approach: first, a nonlinear electric system, governed by the Chua's equation and second the Lorentz oscillator. Both systems are assumed to be affected by external perturbations and their parameters are unknown.