The problem of asymptotic tracking control for a class of uncertain switched nonlinear systems under fuzzy approximation framework is solved in this paper. Superior to most existing results based on fuzzy adaptive control strategy that can only achieve bounded error tracking performance, our proposed control scheme can guarantee the local asymptotic tracking performance for the uncertain switched nonlinear systems under consideration. This is accomplished by constructing a nonsmooth Lyapunov function and introducing a novel discontinuous controller with dynamic feedback compensator in the design procedure. Meanwhile, some concepts, such as differential inclusion and set-valued map, are introduced to theoretically verify the local asymptotic tracking performance of the systems with our proposed controller. With the help of set-valued Lie derivative, the common virtual control functions, the desired controller, and the adaptive laws can be precisely constructed. Finally, simulation results are given to show the effectiveness of the proposed method.

Fuzzy Approximation Based Asymptotic Tracking Control for a Class of Uncertain Switched Nonlinear Systems

The Levenberg–Marquardt and Newton are two algorithms that use the Hessian for the artificial neural network learning. In this article, we propose a modified Levenberg–Marquardt algorithm for the artificial neural network learning containing the training and testing stages. The modified Levenberg–Marquardt algorithm is based on the Levenberg–Marquardt and Newton algorithms but with the following two differences to assure the error stability and weights boundedness: 1) there is a singularity point in the learning rates of the Levenberg–Marquardt and Newton algorithms, while there is not a singularity point in the learning rate of the modified Levenberg–Marquardt algorithm and 2) the Levenberg–Marquardt and Newton algorithms have three different learning rates, while the modified Levenberg–Marquardt algorithm only has one learning rate. The error stability and weights boundedness of the modified Levenberg–Marquardt algorithm are assured based on the Lyapunov technique. We compare the artificial neural network learning with the modified Levenberg–Marquardt, Levenberg–Marquardt, Newton, and stable gradient algorithms for the learning of the electric and brain signals data set.

Stability Analysis of the Modified Levenberg–Marquardt Algorithm for the Artificial Neural Network Training

The inherent volatility and unpredictable nature of renewable generations and load demand pose considerable challenges for energy exchange optimization of microgrids (MG). To address these challenges, this paper proposes a new risk-based multi-objective energy exchange optimization for networked MGs from economic and reliability standpoints under load consumption and renewable power generation uncertainties. In so doing, three various risk-based strategies are distinguished by using conditional value at risk (CVaR) approach. The proposed model is specified as a two-distinct objective function. The first function minimizes the operation and maintenance costs, cost of power transaction between upstream network and MGs as well as power loss cost, whereas the second function minimizes the energy not supplied (ENS) value. Furthermore, the stochastic scenario-based approach is incorporated into the approach in order to handle the uncertainty. Also, Kantorovich distance scenario reduction method has been implemented to reduce the computational burden. Finally, non-dominated sorting genetic algorithm (NSGAII) is applied to minimize the objective functions simultaneously and the best solution is extracted by fuzzy satisfying method with respect to risk-based strategies. To indicate the performance of the proposed model, it is performed on the modified IEEE 33-bus distribution system and the obtained results show that the presented approach can be considered as an efficient tool for optimal energy exchange optimization of MGs.

Stochastic multi-objective model for optimal energy exchange optimization of networked microgrids with presence of renewable generation under risk-based strategies

Neural network based boundary control of a vibrating string system with input deadzone

This article proposes two novel modified techniques, namely Pythagorean fuzzy hybrid Order of Preference by Similarity to an Ideal Solution (PFH-TOPSIS) method and Pythagorean fuzzy hybrid ELimination and Choice Translating REality I (PFH-ELECTRE I) method, in order to measure risk rankings in failure modes and effects analysis (FMEA). These methods are designed to overcome the flaws and shortcomings of traditional crisp risk priority numbers and fuzzy FMEA techniques in risk rankings. The proposed methods consider subjective as well as objective weight values of all factors in risk rankings of identified failures. The FMEA experts team are allowed to submit their information by linguistic terms using Pythagorean fuzzy numbers. Both techniques use a Pythagorean fuzzy weighted averaging operator to aggregate their independent evaluations into group assessments. Subsequent steps are different. The PFH-TOPSIS approach computes the distances of failure modes from the Pythagorean fuzzy positive ideal solution and Pythagorean fuzzy negative ideal solution. To evaluate failure modes, the PFH-ELECTRE I approach produces Pythagorean fuzzy concordance and Pythagorean fuzzy discordance matrices. We illustrate the structure of both techniques with the help of flowcharts. The effectiveness of the methods that we develop is described by a numerical example, namely a case study of 1.8-in. color super-twisted nematic (CSTN). To validate their effectiveness and accuracy, we provide a comprehensive comparative analysis with existing techniques of risk evaluation, including intuitionistic fuzzy hybrid TOPSIS, intuitionistic fuzzy TOPSIS, IWF-TOPSIS, and fuzzy TOPSIS methods.

Risk evaluation in failure modes and effects analysis: hybrid TOPSIS and ELECTRE I solutions with Pythagorean fuzzy information

In this work, we study the structure regulator for the perturbations attenuation which is based on the infinite structure regulator. The structure regulator is able to attenuate the perturbations if the transfer function of the departures and perturbations has a numerical value almost equal to zero, and it does not require the perturbations to attenuate them. We apply the structure regulator and the infinite structure regulator to a quadrotor which maintains the horizontal position with respect to the earth for the step and sine perturbations.

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Structure Regulator for the Perturbations Attenuation in a Quadrotor

In previous investigations, the nonlinear hypothesis use the linear bounded maps. Nonlinear hypothesis are described as the combination of the first order terms, and after of the mentioned combination, one bounded map is applied to alter the result. This document proposes two nonlinear hypothesis which use different structures instead of using the linear bounded maps. They are termed as novel nonlinear hypothesis and second order nonlinear hypothesis and their goal is to improve the second order processes modeling. The proposed nonlinear hypothesis are described as the combination of the first order and second order terms. Since the delta parallel robot is a second order process, it is an excellent platform to prove the effectiveness of the two proposed hypothesis.

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Novel Nonlinear Hypothesis for the Delta Parallel Robot Modeling

Actuators nonlinearities are unknown external perturbations in robots, which are unwanted because they can severely limit their performance. This research is focused on the stabilization of robots subject to actuators nonlinearities with a regulator containing the sigmoid mapping. Our regulator has the following three main characteristics: a) a sigmoid mapping is used to ensure boundedness of the regulator law terms, b) the chattering is reduced by the usage of the saturation mapping instead of the signum mapping, and c) the stabilization is ensured by the Lyapunov analysis. Finally, we evaluate our regulator for the stabilization of two robots.

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David Ricardo Cruz

Papers

Structure Regulator for the Perturbations Attenuation in a Quadrotor

Novel Nonlinear Hypothesis for the Delta Parallel Robot Modeling

Stabilization of Robots With a Regulator Containing the Sigmoid Mapping

ANFIS system for classification of brain signals

Convergent newton method and neural network for the electric energy usage prediction