Nonlinear Function Research Articles

Distributed finite-time adaptive consensus output-feedback control of multi-agent systems under switching topologies

The paper investigates the finite-time adaptive consensus control of nonlinear multi-agent systems (MASs) by output-feedback. During the process of control design, the fuzzy logic system (FLS) is employed to approximate nonlinear function, as well as constructing a fuzzy state observer to estimate unmeasured states. Combining the dynamic surface control (DSC) with adaptive backstepping method conquers the complexity explosion issue. Then, semi-global practical finite-time stability (SGPFS) for closed-loop system is obtained under arbitrary switching communication topologies. All the signals of the overall system are uniformly ultimately bounded (UUB). Finally, the availability of developed control approach will be demonstrated through a simulation.

Generalized nonlinear hybrid-norm parallel sparse filtering for bearing fault diagnosis under complex interference

Abstract Considerable attention has been garnered by the bearing fault diagnostic method, founded on sparse feature learning, for its exceptional robustness and adaptability to noise. Being an effective sparse learning method, parallel sparse filtering (PSF) has found successful applications in intelligent fault diagnosis. However, influenced by mechanical structural collisions and complex transmission paths, the obtained bearing signals come with abnormal impacts and noise, resulting in a reduced reliability of the PSF. Additionally, PSF constrains features and samples with l_(1⁄2) norm, which is significantly disturbed by noise. To address these issues, generalized nonlinear hybrid-norm parallel sparse filtering (GNHNPSF) is proposed. Firstly, the Sigmoid nonlinear function is examined to suppress the amplitude of the anomalous shock. Subsequently, the hybrid-norm constraints, which involve the application of a l_(1⁄2) norm to the column features of the input signal and a l_(1⁄3) norm to the row features, can be employed to effectively extract distinctive information from the original data. The GNHNPSF is demonstrated to improve the accuracy of bearing fault diagnosis under complex interference, as evidenced by the results of simulation and experiments.

Neural network-based prescribed performance tracking control for a class of nonlinear systems with mismatched disturbances

This paper addresses the prescribed performance tracking control problem for a class of nonlinear systems subject to mismatched uncertainties. A novel disturbance observer-based control (DOBC) scheme is proposed through combining radial basis function neural network (RBFNN) and prescribed performance function (PPF). In contrast to traditional DOBC, the proposed approach employs RBFNN technology to approximate unknown nonlinear functions in the system, instead of treating them as part of lumped disturbances. A novel disturbance observer is developed to estimate disturbances characterised by a nonlinear exogenous system. To enhance control performance, a PPF that characterises both transient and steady-state behaviour is used for the transformation of tracking errors. It can be proved that all the states of the closed-loop system can be guaranteed to be uniformly ultimately bounded (UUB), and that the tracking error evolves within the prespecified boundaries. Theoretical results are validated and supported by two simulation examples.

Neural networks for geospatial data

–Analysis of geospatial data has traditionally been model-based, with a mean model, customarily specified as a linear regression on the covariates, and a Gaussian process covariance model, encoding the spatial dependence. While non-linear machine learning algorithms like neural networks are increasingly being used for spatial analysis, current approaches depart from the model-based setup and cannot explicitly incorporate spatial covariance. We propose NN-GLS, embedding neural networks directly within the traditional Gaussian process (GP) geostatistical model to accommodate non-linear mean functions while retaining all other advantages of GP, like explicit modeling of the spatial covariance and predicting at new locations via kriging. In NN-GLS, estimation of the neural network parameters for the non-linear mean of the Gaussian Process explicitly accounts for the spatial covariance through use of the generalized least squares (GLS) loss, thus extending the linear case. We show that NN-GLS admits a representation as a special type of graph neural network (GNN). This connection facilitates the use of standard neural network computational techniques for irregular geospatial data, enabling novel and scalable mini-batching, backpropagation, and kriging schemes. We provide methodology to obtain uncertainty bounds for estimation and predictions from NN-GLS. Theoretically, we show that NN-GLS will be consistent for irregularly observed spatially correlated data processes. We also provide a finite sample concentration rate, which quantifies the need to accurately model the spatial covariance in neural networks for dependent data. To our knowledge, these are the first large-sample results for any neural network algorithm for irregular spatial data. We demonstrate the methodology through numerous simulations and an application to air pollution modeling. We develop a software implementation of NN-GLS in the Python package geospaNN.

Global analysis for a modified SEIR model with general non-linear incidence function

Global analysis for a modified SEIR model with general non-linear incidence function

Deep bed filtration and formation damage by particles with distributed properties

Current models for deep bed filtration describe particles with uniform properties. Yet, the sizes, densities, and mineral composition of particles vary significantly in the same injection well. The aim of this work is to provide an effective mathematical model for water injection of particles with distributed properties and formation damage prediction. We average the set of traditional population balance equations for single-property particles and obtain one upscaled equation. The upscaled equation for particle retention rate contains a non-linear function of suspended concentration, which we call the 'suspension function'. We derive analytical solutions for the upscaled equation for linear (coreflood) and radial (well injectivity) flows. Then we treat lab coreflood data to determine the model suspension function and provide a model for well injectivity prediction. The retention profile for the flow of uniform particles has an exponential form. Frequently reported in the literature, hyper-exponential forms have been hypothetically explained by multiple particle properties. The inverse solution allows revealing the individual filtration coefficients for binary mixtures from total breakthrough concentrations during coreflood. Treatment of the data from lab experiments reveals individual filtration coefficients that belong to common intervals. For the first time, deep bed filtration of particles with distributed properties is upscaled and presented using a single equation that reflects the particle property distribution. This equation provides an effective mathematical model for tuning lab coreflood data, determines the model function, and uses it for injectivity decline prediction.

Mapping for stable bilateral teleoperation of manipulators considering time delays

Teleoperation of manipulators has allowed extending the human skills to several areas, where the commands generated by a human operator on the leader robot are followed by a remote robot. For this purpose, position-position tracking requires a mapping given the mismatch between robot workspaces. This paper compares a pair of functions for mapping the haptic device commands to handle a remote robot, considering non-identical workspaces and a classic P+d control scheme. As part of the theoretical analysis, a Lyapunov-Krasovskii-based stability analysis is developed in steps, allowing us for determining the boundedness of velocities and coordination errors. Subsequently, the performance of the teleoperation system is compared using two mapping functions. To achieve a fair comparison of results, a test protocol is developed, where different levels of haptic device damping, time delays, and workspace scales are used to evaluate the time to complete the task and the average coordination errors. Based on the results, the mapping function influences the calculation of force feedback, stability of the system, and performance metrics. During a pick-and-place task, a reduction in coordination error is observed when the linear function is chosen, while the time to complete the task is lower when a non-linear function is considered.

Enhanced Wild Horse Optimizer with Cauchy Mutation and Dynamic Random Search for Hyperspectral Image Band Selection

The high dimensionality of hyperspectral images (HSIs) brings significant redundancy to data processing. Band selection (BS) is one of the most commonly used dimensionality reduction (DR) techniques, which eliminates redundant information between bands while retaining a subset of bands with a high information content and low noise. The wild horse optimizer (WHO) is a novel metaheuristic algorithm widely used for its efficient search performance, yet it tends to become trapped in local optima during later iterations. To address these issues, an enhanced wild horse optimizer (IBSWHO) is proposed for HSI band selection in this paper. IBSWHO utilizes Sobol sequences to initialize the population, thereby increasing population diversity. It incorporates Cauchy mutation to perturb the population with a certain probability, enhancing the global search capability and avoiding local optima. Additionally, dynamic random search techniques are introduced to improve the algorithm search efficiency and expand the search space. The convergence of IBSWHO is verified on commonly used nonlinear test functions and compared with state-of-the-art optimization algorithms. Finally, experiments on three classic HSI datasets are conducted for HSI classification. The experimental results demonstrate that the band subset selected by IBSWHO achieves the best classification accuracy compared to conventional and state-of-the-art band selection methods, confirming the superiority of the proposed BS method.

Decentralized Output-Feedback Adaptive Event-Triggered Control for Interconnected Nonlinear Delay Systems with Actuator Failures

This paper investigates decentralized adaptive event-triggered fault-tolerant control for interconnected nonlinear delay systems with actuator failures. The actuator failures suffered include loss of effectiveness and bias faults. A control scheme based on the K-filter is proposed, which effectively compensates for the effects of unknown actuator failures. A hyperbolic tangent function and neural network are introduced to approximate the unknown interconnection function and nonlinear delay function. By introducing the dynamic surface control method, the “explosion of complexity” issue is addressed. Furthermore, our proposed controller can ensure that all states of the corresponding closed-loop system are semi-globally uniformly ultimately bounded and that the tracking error can converge to a small neighborhood of zero. Meanwhile, Zeno behavior can be effectively avoided. Finally, the validity of the proposed control scheme is verified using a simulation example.

Adaptive neural tracking control for flexible joint robot including hydraulic actuator dynamics with disturbance observer

AbstractIn this paper, a disturbance observer‐based adaptive neural backstepping integral sliding mode control (BISMC) is developed for a flexible joint robot (FJR) with the integration of an adjustable stiffness rotary actuator (ASRA). This system suffers from unknown system dynamics, external disturbance, and the influence of variable stiffness, which is a challenge for achieving precision tracking performance. Considering the lumped disturbances in FJR generated by the hydraulic system and the stiffness modulation of the ASRA, we investigate the structural dynamics nonlinear model of the FJR system, including hydraulic actuator dynamics. While other linear control strategies are applied for the FJR, the proposed controller uses BISMC, neural networks (NN), and nonlinear disturbance observers to deal with the disadvantages mentioned above. Radial basis function neural networks (RBFNN) are designed to tackle unknown nonlinear functions, and the disturbance observers are introduced to compensate for the influence of the variable stiffness, disturbance, and the approximation error caused by NN. Simulations and experiments are independently implemented to demonstrate the effectiveness and feasibility of the proposed controller. Results exhibit that the integral absolute error‐index is reduced by 20.4% when the proposed method is deployed for the experiment with a multistep trajectory.

Sizing Energy Storage Systems to Dispatch Wind Power Plants

Integrating wind power plants into the electricity grid poses challenges due to the intermittent nature of wind energy generation. Energy storage systems (ESSs) have shown promise in mitigating the intermittent variability associated with wind power. This paper presents a distributionally robust optimization (DRO) model for sizing energy storage systems to dispatch wind power plants. The variable wind power is formulated as a moment-based ambiguity set. Dispatchability is described by the expected value of the insufficient power of wind power relative to the dispatch command, which is a sum of nonlinear functions and is taken as the optimal index. A deterministic semi-definite positive model is derived to solve the problem effectively. Numerical studies are conducted to demonstrate the effectiveness and advantages of the proposed method.

From simple to complex: a sequential method for enhancing time series forecasting with deep learning

Abstract Time series forecasting is a well-known deep learning application field in which previous data are used to predict the future behavior of the series. Recently, several deep learning approaches have been proposed in which several nonlinear functions are applied to the input to obtain the output. In this paper, we introduce a novel method to improve the performance of deep learning models in time series forecasting. This method divides the model into hierarchies or levels from simpler to more complex ones. Simpler levels handle smoothed versions of the input, whereas the most complex level processes the original time series. This method follows the human learning process where general/simpler tasks are performed first, and afterward, more precise/harder ones are accomplished. Our proposed methodology has been applied to the LSTM architecture, showing remarkable performance in various time series. In addition, a comparison is reported including a standard LSTM and novel methods such as DeepAR, Temporal Fusion Transformer, NBEATS and Echo State Network.

An Innovative Study on Stock Price Prediction for Investment Decision Through ARIMA and LSTM with Recurrent Neural Network

The securities market is extremely volatile and difficult to prognosticate. Stock prices are depending upon numerous factors. To reduce the risk of volatility, it is very important to apply an accurate mechanism to forecast stock prices. The importance of share price prediction forecasting in finance and economics has sparked researchers’ interest in creating more reliable forecasting models over time. In this research paper, the researchers try to explore two different applications based on linear and nonlinear (RNN) functions. The criteria for the stock price predictions are evolved using Auto Regressive Integrated Moving Average (ARIMA) which takes the linearity function from the past share prices. The ARIMA model assumes the future prices usually be similar to past. Sudden changes may not reflect in this model. The nonlinearity Recurrent Neural Network (RNN) is going to be applied for share price prediction so that it can be taken into account the quick changes that are occurring in the market environment. To test the RNN, the study used the Long Short Term Memory (LSTM) model which takes the support of Artificial Intelligence. Taking the sample of share prices of banks listed in the NIFTY index, the ARIMA and LSTM have been performed and analyzed. Stock price predictions for banks listed in the NIFTY bank index are found better with the ARIMA model than with the LSTM model.

Existence of Solutions for p(x)-Laplacian Elliptic BVPs on a Variable Sobolev Space Via Fixed Point Theorems

In this paper, we prove some existence theorems for elliptic boundary value problems within the p(x)-Laplacian on a variable Sobolev space. For this purpose, the main problem is transformed into a fixed point problem and then fixed point arguments such as Schaefer’s and Schauder’s theorems are used. Our approach involves fewer stringent assumptions on the nonlinearity function than the prior findings. An interesting example is presented to examine the validity of the theoretical findings.

A trajectory planning method for robotic arms based on improved dynamic motion primitives

Purpose Traditional robot arm trajectory planning methods have problems such as insufficient generalization performance and low adaptability. This paper aims to propose a method to plan the robot arm’s trajectory using the trajectory learning and generalization characteristics of dynamic motion primitives (DMPs). Design/methodology/approach This study aligns multiple demonstration motion primitives using dynamic time warping; use the Gaussian mixture model and Gaussian mixture regression methods to obtain the ideal primitive trajectory actions. By establishing a system model that improves DMPs, the parameters of the nonlinear function are learned based on the ideal primitive trajectory actions of the robotic arm, and the robotic arm motion trajectory is reproduced and generalized. Findings Experiments have proven that the robot arm motion trajectory learned by the method proposed in this article can not only learn to generalize and demonstrate the movement trend of the primitive trajectory, but also can better generate ideal motion trajectories and avoid obstacles when there are obstacles. The maximum Euclidean distance between the generated trajectory and the demonstration primitive trajectory is reduced by 29.9%, and the average Euclidean distance is reduced by 54.2%. This illustrates the feasibility of this method for robot arm trajectory planning. Originality/value It provides a new method for the trajectory planning of robotic arms in unstructured environments while improving the adaptability and generalization performance of robotic arms in trajectory planning.

Entropy pelican optimization algorithm (epoa) based feature selection and deep autoencoder (dae) of heart failure status prediction

Introduction: Heart Failure (HF) is a complicated condition as well as a significant public health issue. Data processing is now required for machine and statistical learning techniques while it helps to identify key features and eliminates unimportant, redundant, or noisy characteristics, hence minimizing the feature space's dimensions. A common cause of mortality in cases of heart disease is Dilated Cardiomyopathy (DCM). Methods: The feature selection in this work depends on the Entropy Pelican Optimization Algorithm (EPOA). It is a recreation of pelicans' typical hunting behaviour. This is comparable to certain characteristics that lead to better approaches for solving high-dimensional datasets. Then Deep Autoencoder (DAE) classifier has been introduced for the prediction of patients. DAE classifier is employed to compute the system's nonlinear function through data from the normal and failure state. Results: DAE was discovered to not only considerably increase accuracy but also to be beneficial when there is a limited amount of labelled data.Performance metrics like recall, precision, accuracy, f-measure, and error rate has been used for results analysis. Conclusion: Publicly available benchmark dataset has been collected from Gene Expression Omnibus (GEO) repository to evaluate and contrast the suitability of the suggested classifier with other existing methods.

Investigation of Macroscopic Mechanical Behavior of Magnetorheological Elastomers under Shear Deformation Using Microscale Representative Volume Element Approach

Magnetorheological elastomers (MREs) are a class of smart materials with rubber-like qualities, demonstrating revertible magnetic field-dependent viscoelastic properties, which makes them an ideal candidate for development of the next generation of adaptive vibration absorbers. This research study aims at the development of a finite element model using microscale representative volume element (RVE) approach to predict the field-dependent shear behavior of MREs. MREs with different elastomeric matrices, including silicone rubber Ecoflex 30 and Ecoflex 50, and carbonyl iron particles (CIPs) have been considered as magnetic particles. The stress–strain characteristic of the pure silicon rubbers was evaluated experimentally to formulate the nonlinear Ogden strain energy function to describe hyper-elastic behavior of the rubbery matrix. The obtained mechanical and magnetic properties of the matrix and inclusions were integrated into COMSOL Multiphysics to develop the RVE for the MREs, in 2D and 3D configurations, with CIP volume fraction varying from 5% to 40%. Periodic boundary condition (PBC) was imposed on the RVE boundaries, while undergoing shear deformation subjected to magnetic flux densities of 0–0.4 T. Comparing the results from 2D and 3D modeling of isotropic MRE-RVE with the experimental results from the literature suggests that the 3D MRE-RVE can be effectively used to accurately predict the influence of varying factors including matrix type, volume fraction of magnetic particles, and applied magnetic field on the mechanical behavior of MREs.

Octave-spanning supercontinuum generation in a CMOS-compatible thin Si3N4 waveguide coated with highly nonlinear TeO2.

Supercontinuum generation (SCG) is an important nonlinear optical process enabling broadband light sources for many applications, for which silicon nitride (Si3N4) has emerged as a leading on-chip platform. To achieve suitable group velocity dispersion and high confinement for broadband SCG the Si3N4 waveguide layer used is typically thick (>∼700 nm), which can lead to high stress and cracks unless specialized processing steps are used. Here, we report on efficient octave-spanning SCG in a thinner moderate-confinement 400-nm Si3N4 platform using a highly nonlinear tellurium oxide (TeO2) coating. An octave supercontinuum spanning from 0.89 to 2.11 µm is achieved at a low peak power of 258 W using a 100-fs laser centered at 1565 nm. Our numerical simulations agree well with the experimental results giving a nonlinear parameter of 2.5 ± 0.5 W-1m-1, an increase by a factor of 2.5, when coating the Si3N4 waveguide with a TeO2 film. This work demonstrates highly efficient SCG via effective dispersion engineering and an enhanced nonlinearity in CMOS-compatible hybrid TeO2-Si3N4 waveguides and a promising route to monolithically integrated nonlinear, linear, and active functionalities on a single silicon photonic chip.

A micromechanical scheme with nonlinear concentration functions by physics-guided neural network

The mechanical behavior of heterogeneous materials has been reported to be significantly influenced by the nonlinear properties of both the matrix and interface. However, the micromechanical homogenization methods for predicting the effective properties are challenged in nonlinear problems due to the difficulties in solving the analytical form of the concentration tensors. In this study, we develop a nonlinear micromechanical scheme for heterogeneous materials with complex interfacial behaviors, where the key component, namely nonlinear concentration functions, is determined by the devised physics-guided neural network. In particular, the nonlinear Mori–Tanaka method (NMT) implemented within this new micromechanical scheme yields accurate solutions to axisymmetric nonlinear homogenization problems considering the effects of finite deformation, loading conditions, volume fraction, etc. Furthermore, the NMT is equivalent to the linear Mori–Tanaka method in the condition of the small deformation. Notably, this neural-network-based micromechanical scheme shows good generalization for different types of nonlinear interfaces, while the corresponding approach for generating training data via the finite element method (FEM) is cost-effective. This theoretical framework introduces a novel approach to nonlinear physical modeling, namely, not by the direct regression from the dataset but by deeply embedding neural networks in physical laws.

Trajectory Planning through Model Inversion of an Underactuated Spatial Gantry Crane Moving in Structured Cluttered Environments

Handling suspended loads in cluttered environments is critical due to the oscillations arising while the load is traveling. Exploiting active control algorithms is often unviable in industrial applications, due to the necessity of installing sensors on the load side, which is expensive and often impractical due to technological limitations. In this light, this paper proposes a trajectory planning method for underactuated, non-flat, non-minimum phase spatial gantry crane moving in structured cluttered environments. The method relies on model inversion. First, the system dynamics is partitioned into actuated and unactuated coordinates and then the load displacements are described as a non-linear separable function of these. The unactuated dynamic is unstable; hence, the displacement, velocity, and acceleration references are modified through the output redefinition technique. Finally, platform trajectory is computed, and the desired displacements of the load are obtained. The effectiveness of the proposed method is assessed through numerical and experimental tests performed on a laboratory testbed composed by an Adept Quattro robot moving a pendulum. The load is moved in a cluttered environment, and collisions are avoided while simultaneously tracking the prescribed trajectory effectively.