Nonlinear Generator Research Articles

High-Q integrated lithium tantalate microring resonators for on-chip comb generation.

Lithium tantalate on insulator (LTOI), taking advantage of high cost-effectiveness, ultra-low optical loss, and prominent electro-optic (EO) coefficient, shows great potential as an integrated waveguide-based optical platform for commercialization. Further research on monolithic nonlinear source generators with tunable features is crucial in its early stages. Here, we fabricate low-loss microring resonators (intrinsic Q value above 4 × 106) via universal subtractive manufacturing. Both Kerr and EO combs are realized based on X-cut LTOI high-Q resonators. Specifically, we elucidate the complicated synergy caused by a photorefractive (PR) effect and thermo-optic modulation, observing the soliton step using the facile laser scanning technique. Furthermore, the preliminary experimental result of the static EO comb is also exploited in a 20 GHz free spectral range (FSR) LTOI microring resonator, verifying the versatility of this unique photonic platform for on-chip microcomb generation.

Observer-based control for consensus tracking of non-linear synchronous generators system using sliding mode method and a radial basis function neural network

Observer-based control for consensus tracking of non-linear synchronous generators system using sliding mode method and a radial basis function neural network

Switched sampled-data-based membership function-dependent [formula omitted] control for PMSG-based WTS with actuator failures

This paper deals with the problem of sampled-data-based H∞ control design for nonlinear permanent magnet synchronous generator (PMSG)-based wind turbine system (WTS) subject to actuator failures. First, the Takagi-Sugeno (T-S) fuzzy system is employed to handle the nonlinearities of presented model. Next, by employing a Bernoulli stochastic variable, the general scenario of switched coupling memory sampled-data control (CMSDC) is designed which contains the sampled-data control (SDC) and memory SDC scheme as special cases. By combining the membership function-dependent (MFD) asymmetric looped-type Lyapunov-Krasovskii functional (LKF) and employing the available information of membership functions in H∞ performance, the delay-dependent stabilization conditions of considered PMSG-based WTS are derived through the switched CMSDC technique. Meanwhile, the disturbances of considered systems are attenuated by taking the advantage of the newly proposed MFD H∞ performance. Eventually, the simulation results are given to demonstrate the efficacy and applicability of the proposed CMSDC technique.

Takagi-Sugeno fuzzy sampled-data observer design for nonlinear permanent magnet synchronous generator-based wind turbine systems using auxiliary function-based integral inequality technique

This study focuses on designing the fuzzy sampled-data observer (FSDO) scheme for nonlinear permanent magnet synchronous generator (PMSG)-based wind turbine systems (WTS). The primary objective of this problem is to solve an unmeasurable state problem under the mismatched premise variables conditions among system, observer, and controller, respectively. To do this, firstly, the proposed wind turbine model is described in a Takagi-Sugeno fuzzy model due to the complex nonlinearities in PMSG-based WTS. Next, based on the measured output signals and sampled estimated states, the FSDO is designed to understand some unmeasurable state variables of the studied system. Then, a novel auxiliary function-based integral inequality (AFBII) is presented to approximate the integral quadratic terms related to sampling information. Thanks to the proposed AFBII technique and the introduction of slack variables, several new and less conservative stability requirements are derived in the formulations of linear matrix inequalities (LMIs) using the looped Lyapunov function. Finally, the simulation studies for the considered wind turbine model are validated numerically, and then some comparative results are provided to show the superiority and applicability of the theoretical observations.

A Simple, Robust, and Versatile MATLAB Formulation of the Dynamic Memdiode Model for Bipolar-Type Resistive Random Access Memory Devices

Modeling in an emerging technology like RRAM devices is one of the pivotal concerns for its development. In the current bibliography, most of the models face difficulties in implementing or simulating unconventional scenarios, particularly when dealing with complex input signals. In addition, circuit simulators like Spice require long running times for high-resolution results because of their internal mathematical implementation. In this work, a fast, simple, robust, and versatile model for RRAM devices built in MATLAB is presented. The proposed model is a recursive and discretized version of the dynamic memdiode model (DMM) for bipolar-type resistive switching devices originally implemented in LTspice. The DMM model basically consists of two coupled equations: one for the current (non-linear current generator) and a second one for the memory state of the device (time-dependent differential equation). This work presents an easy-to-use tool for researchers to reproduce the experimental behavior of their devices and predict the outcome from non-trivial experiments. Three study cases are reported, aimed at capturing different phenomenologies: a frequency effect study, a cycle-to-cycle variability fit, and a stochastic resonance impact analysis.

EO nonlinear function generator.

An electro-optical programmable nonlinear function generator (PNFG) is developed on a multimode waveguide with four parallel thermal electrodes. The current on one electrode is chosen as the input, while the rest serve as function-defining units to modulate the multimode interference. The electro-thermo-optical effects are analyzed step by step and the impact on the eigenmode properties is derived. It shows that the optical output power variation by altered interference, in response to the input current, manifests as a complex ensemble of functions in general. The PNFG aims to find the special setting under which such relation can be simplified into some basic functions. Through an optimization program, a variety of such functions are found, including Sigmoid, SiLU, and Gaussian. Furthermore, the shape of these functions can be adjusted by finetuning the defining units. This device may be integrated in a large-scale photonic computing network that can tackle complex problems with nonlinear function adaptability.

Fuzzy membership-function-dependent design of aperiodic sample-data control scheme for nonlinear PMSG-based WECS with quantization measurements via refined looped Lyapunov functional

This manuscript investigates the fuzzy memory sampled-data control (MSDC) scheme for the nonlinear permanent magnet synchronous generator (PMSG)-based wind energy conversion system (WECS) with quantization measurements. First, due to the complex nonlinearity, a Takagi-Sugeno (T-S) fuzzy modeling approach is successfully applied to the dynamics of nonlinear PMSG-based WECS. Second, by using the information of both quantized aperiodic sampling pattern and signal transmission delay, an H∞-based fuzzy quantized controller is put forward to ensure the stable performance as well as disturbance suppression index of the considered PMSG model by utilizing the refined looped Lyapunov functional (RLLF) approach. This RLLF perfectly utilizes more realistic information about the time derivative of the fuzzy membership function and actual sampling pattern. Then, two new integral inequalities are introduced to approximate the quadratic integral terms arising from the derivative of RLLF. Next, we establish some less conservative stabilization results in terms of linear matrix inequalities (LMIs) using the constructed RLLF, along with the proposed integral inequalities and fuzzy membership function-dependent (MFD) switching ideas. Finally, the simulation studies of PMGS-based WECS are validated numerically, and then a comparative example is provided to emphasize the superiority and relevance of the suggested approach.

All-optical multilevel physical unclonable functions.

Disordered photonic structures are promising for the realization of physical unclonable functions-physical objects that can overcome the limitations of conventional digital security and can enable cryptographic protocols immune against attacks by future quantum computers. The physical configuration of traditional physical unclonable functions is either fixed or can only be permanently modified, allowing one token per device and limiting their practicality. Here we overcome this limitation by creating reconfigurable structures made by light-transformable polymers in which the physical structure of the unclonable function can be reconfigured reversibly. Our approach allows the simultaneous coexistence of multiple physical unclonable functions within one device. The physical transformation is done all-optically in a reversible and spatially controlled fashion, allowing the generation of more complex keys. At the same time, as a set of switchable individual physical unclonable functions, it enables the authentication of multiple clients and allows for the practical implementations of quantum secure authentication and nonlinear generators of cryptographic keys.

An algebraic attack on stream ciphers with application to nonlinear filter generators and WG-PRNG

An algebraic attack on stream ciphers with application to nonlinear filter generators and WG-PRNG

Master generators: A novel approach to construct and solve ordinary differential equations

Ordinary differential equations (ODEs) play a crucial role in applied mathematics, engineering, and various other fields. With a rich history of study and countless applications, they have attracted the attention of researchers who have developed numerous methods for solving linear and non-linear ODEs. However, despite considerable progress, there remain many unsolved equations and challenges in finding appropriate solutions. This research introduces a groundbreaking method for generating an infinite number of generators for both linear and non-linear ODEs, based on the use of master improper integrals and a set of novel theorems. The proposed method enables the creation of infinite ODEs using a single generator, providing a versatile and powerful approach to tackling various types of differential equations. This research not only presents several specific generators derived from the theorems, but also establishes general forms for linear and non-linear generators, highlighting their adaptability to a wide range of scenarios. In addition, we demonstrate the practical utility of the generators through real-world examples and applications across diverse fields such as quantum field theory, astrophysics, and fluid dynamics. These examples showcase the potential of the proposed method in solving complex problems and its far-reaching impact on multiple disciplines. Through a comprehensive presentation of the theoretical underpinnings, derivation of generators, and application examples, this research aims to provide a thorough understanding of the infinite generators for linear and non-linear ODEs, as well as to inspire further research and development in this fascinating and vital area of applied mathematics. The introduction of infinite generators not only addresses the existing challenges in solving ODEs but also opens up new avenues for exploring novel solutions and approaches, ultimately contributing to the advancement of various fields that rely on differential equations.

Period and Some Distribution Properties of a Nonlinear Filter Generator with Dynamic Mapping

Period and Some Distribution Properties of a Nonlinear Filter Generator with Dynamic Mapping

Development and analysis of magnet-engaged piezoelectric energy generator under friction-induced vibration

Piezoelectric energy transducers, which can be an efficient solution for the power supply of wireless devices, have been widely researched. This study investigated the characteristics of a magnet-engaged nonlinear piezoelectric energy generator stimulated by friction-induced vibration (FIV), in two distinct design configurations (in-parallel and in-series). A mathematical model was developed, and the dynamic response of the mechanical system and voltage output from the piezoelectric shear deformation were solved using an iterative method. A friction model considering the Stribeck effect was introduced to describe the friction motion. The emergence of a stick-slip motion induced limit cycle and its vanishing delineates the unstable and stable regions of the system, respectively. A critical sliding velocity vc splits the regions. When the sliding velocity exceeds vc, the system remains in stable region with exclusive slip friction behavior. Parameter studies were conducted to explore the effect of decay factor β, dynamic friction coefficient μk, static friction coefficient μstatic, and normal force FN on vc. The results indicate that increasing β and μk can reduce the unstable region and generation of FIV, whereas, increasing FN and μstatic can promote the occurrence of FIV. The energy generation was evaluated by a transient charging simulation that has been experimentally validated in a previous study. The influence of β, μk, μstatic, and FN on the energy generation was also investigated relative to the operating velocity range (OVR) and sum of root mean square charging power (SRCP). The in-parallel systems exhibit a higher SRCP within the same OVR, whereas the in-series systems are more likely to excite FIV with a wider OVR. Additionally, the simulation results of fluctuating working conditions show that both fluctuating FN and v0 have negative effects on the energy generation. The nonlinear in-series system exhibits better robustness with the least affected SRCP and almost unchanged OVR under fluctuating FN and v0.

Nonlinear optical feature generator for machine learning

Modern machine learning models use an ever-increasing number of parameters to train (175 × 109 parameters for GPT-3) with large datasets to achieve better performance. Optical computing has been rediscovered as a potential solution for large-scale data processing, taking advantage of linear optical accelerators that perform operations at lower power consumption. However, to achieve efficient computing with light, it remains a challenge to create and control nonlinearity optically rather than electronically. In this study, a reservoir computing approach (RC) is investigated using a 14-mm waveguide in LiNbO3 on an insulator as an optical processor to validate the benefit of optical nonlinearity. Data are encoded on the spectrum of a femtosecond pulse, which is launched into the waveguide. The output of the waveguide is a nonlinear transform of the input, enabled by optical nonlinearities. We show experimentally that a simple digital linear classifier using the output spectrum of the waveguide increases the classification accuracy of several databases by ∼10% compared to untransformed data. In comparison, a digital neural network (NN) with tens of thousands of parameters was required to achieve similar accuracy. With the ability to reduce the number of parameters by a factor of at least 20, an integrated optical RC approach can attain a performance on a par with a digital NN.

Distributed state estimation for uncertain nonlinear time-delay AC islanded micro grids

This article deals with the problem of distributed observer design containing time delays for uncertain nonlinear distributed generators systems in alternating current–islanded micro grids. In contrast with the centralized observer with the ability to accumulate full output of the plant, we design a set of distributed observers, each having access to partial output of the plant through a distributed observer network. Each observer obtains partial plant output and communicates with its neighboring observers through consensus network. The design method is based on the Lipschitz condition of uncertain nonlinear terms while having time-delay system in view. Suitable selection of Lyapunov functions is made, and the Jensen inequality is considered in delayed uncertain nonlinear micro grids in an undirected network. Furthermore, via design algorithm, the necessary and sufficient conditions for the design of parameters are determined so as to stabilize the error dynamics. Finally, numerical simulations are provided to consider the effectiveness of the proposed method.

$$2$$-Adic 1-Lipschitz Maps-Based Nonlinear Pseudorandom Generators of Arbitrary Rank Having the Longest Period

$$2$$-Adic 1-Lipschitz Maps-Based Nonlinear Pseudorandom Generators of Arbitrary Rank Having the Longest Period

Observer-Based Control for a New Stochastic Maximum Power Point Tracking for Photovoltaic Systems With Networked Control System

This study discusses the new stochastic maximum power point tracking (MPPT) control approach towards the photovoltaic cells (PCs). PC generator is isolated from the grid, resulting in a direct current (DC) microgrid that can provide changing loads. In the course of the nonlinear systems through the time-varying delays, we proposed a Networked Control Systems (NCSs) beneath an event-triggered approach basically in the fuzzy system. In this scenario, we look at how random, variable loads impact the PC generator's stability and efficiency. The basic premise of this article is to load changes and the value matching to a Markov chain. PC generators are complicated nonlinear systems that pose a modeling problem. Transforming this nonlinear PC generator model into the Takagi–Sugeno (T– S) fuzzy model is another option. Takagi–Sugeno (T–S) fuzzy model is presented in a unified framework, for which 1) the fuzzy observer–based on this premise variables can be used for approximately in the infinite states to the present system, 2) the fuzzy observer–based controller can be created using this same premises be the observer, and 3) to reduce the impact of transmission burden, an event-triggered method can be investigated. Simulating in the PC generator model for the realtime climate data obtained in China demonstrates the importance of our method. In addition, by using a new Lyapunov–Krasovskii functional (LKF) for combining to the allowed weighting matrices incorporating mode-dependent integral terms, the developed model can be stochastically stable and achieves the required performances. Based on the T-P transformation, a new depiction of the nonlinear system is derived in two separate steps in which an adequate controller input is guaranteed in the first step and an adequate vertex polytope is ensured in the second step. To present the potential of our proposed method, we simulate it for PC generators.

A New Cross Ring Neural Network: Dynamic Investigations and Application to WBAN

Wireless body area network (WBAN) is a crucial tool in modern medical areas. This refers to the intelligent interconnection of wireless sensor nodes installed outside or inside the human body to recover some human vital signs. The security and bandwidth saturation remain crucial problems of this technology. In this work, a cross-ring-based neural network model (CRNN) is obtained from the Hopfield neural network definition and its complex dynamics are deeply analyzed. The steady-state study shows that the model has a unique equilibrium point and its analysis shows that the model’s dynamics is self-excited. Based on the two-parameter Lyapunov spectrum, the set of synaptic weights has been quickly identified to illustrate hyperchaotic behavior of the CRNN. With the help of bifurcation plots, graphs of the Lyapunov spectrum, and phase portraits, we have characterized periodic, chaotic, and hyperchaotic patterns in the model. Furthermore, an experimental setup has been built using microcontroller technology to further support the results of the numerical simulations. A parallel compressive sensing algorithm combined with a nonlinear congruent generator has been used to show the application of the newly designed CRNN to medical image compression and security. Security and compression performances indicate an efficient scheme with the capability to resist various attacks and the capability to produce low-size data image from large-size data image. For instant from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$256\times 256 $ </tex-math></inline-formula> image size, an encrypted and compressed output image is obtained at the compression rate of 0.5, processing time of 0.147 ms, encryption throughput of 1783.3 MBits/s, for a 2.9-GHz processor, the number of cycles to process the algorithm is 1.62. Consequently, the proposal can be applied to WBANs.

Backward Deep BSDE Methods and Applications to Nonlinear Problems

We present a pathwise deep Backward Stochastic Differential Equation (BSDE) method for Forward Backward Stochastic Differential Equations with terminal conditions that time-steps the BSDE backwards and apply it to the differential rates problem as a prototypical nonlinear problem of independent financial interest. The nonlinear equation for the backward time-step is solved exactly or by a Taylor-based approximation. This is the first application of such a pathwise backward time-stepping deep BSDE approach for problems with nonlinear generators. We extend the method to the case when the initial value of the forward components X can be a parameter rather than fixed and similarly to also learn values at intermediate times. We present numerical results for a call combination and for a straddle, the latter comparing well to those obtained by Forsyth and Labahn with a specialized PDE solver.

Stabilization of PMSG-based wind turbine systems with sampling information: Dynamic delay partition method

This paper addresses the novel stabilization criteria for a nonlinear permanent magnet synchronous generator (PMSG)-based wind turbine systems (WTS) with sampled-data information, subject to the uncertainty and controller gain variations. In this regard, the nonlinearity in PMSG-based WTS is conferred by the Takagi–Sugeno (T–S) fuzzy systems. Next, by employing the full advantages of the variable characteristic related to the sampling pattern, a novel looped-type asymmetric augmented Lyapunov-Krasovskii functional (LKF) is developed. Then, the dynamic delay partition method is the first time to be applied for the non-fragile sampled-data control design of proposed T–S fuzzy systems. Also, the less conservativeness stabilization criteria for T–S fuzzy systems are obtained in the form of linear matrix inequality. In the end, the numerical examples confirm the applicability and efficiency of the presented results.

A review of disentangled representation learning for visual data processing and analysis

表示学习是机器学习研究的核心问题之一。机器学习算法的输入表征从过去主流的手工特征过渡到现在面向多媒体数据的潜在表示，使算法性能获得了巨大提升。然而，视觉数据的表示通常是高度耦合的，即输入数据的所有信息成分被编码进同一个特征空间，从而互相影响且难以区分，使得表示的可解释性不高。解耦表示学习旨在学习一种低维的可解释性抽象表示，可以识别并分离出隐藏在高维观测数据中的不同潜在变化因素。通过解耦表示学习，可以捕获到单个变化因素信息并通过相对应的潜在子空间进行控制，因此解耦表示更具有可解释性。解耦表征可用于提高样本效率和对无关干扰因素的容忍度，为数据中的复杂变化提供一种鲁棒性表示，提取的语义信息对识别分类、域适应等人工智能下游任务具有重要意义。本文首先介绍并分析解耦表示的研究现状及其因果机制，总结解耦表示的3个重要性质。然后，将解耦表示学习算法分为4类，并从数学描述、类型特点及适用范围3个方面进行归纳及对比。随后，分类总结了现有解耦表示工作中常用的损失函数、数据集及客观评估指标。最后，总结了解耦表示学习在实际问题中的各类应用，并对其未来发展进行了探讨。;Representation learning is essential for machine learning technique nowadays. The transition of input representations have been developing intensively in algorithm performance benefited from the growth of hand-crafted features to the representation for multi-media data. However，the representations of visual data are often highly entangled. The interpretation challenges are to be faced because all information components are encoded into the same feature space. Disentangled representation learning（DRL）aims to learn a low-dimensional interpretable abstract representation that can sort the multiple factors of variation out in high-dimensional observations. In the disentangled representation，we can capture and manipulate the information of a single factor of variation through the corresponding latent subspace，which makes it more interpretable. DRL can improve sample efficiency and tolerance to the nuisance variables and offer robust representation of complex variations. Their semantic information is extracted and beneficial for artificial intelligence（AI）downstream tasks like recognition，classification and domain adaptation. Our summary is focused on brief introduction to the definition， research development and applications of DRL. Some of independent component analysis（ICA）-nonlinear DRL researches are covered as well since the DRL is similar to the identifiability issue of nonlinear independent component analysis（nonlinear ICA）. The cause and effects mechanism of DRL as high-dimensional ground truth data is generated by a set of unobserved changing factors（generating factors）. The DRL can be used to model the factors of variation in terms of latent representation，and the observed data generation process is restored. We summarize the key elements that a well-defined disentangled representation should be qualified into three aspects，which are 1）modularity，2）compactness，and 3）explicitness. First，explicitness consists of the two sub-requirements of completeness and informativeness. Then，current DRL types are categorized into 1）dimension-wise disentanglement，2）semantic-based disentanglement，3）hierarchical disentanglement，and 4） nonlinear ICA four types in terms of its formulation，characteristics，and scope of application. Dimension-wise disentanglement is assumed that the generative factors are solely and each dimension of latent vector can be separated and mapped，which is suitable for learning the disentangled representation of simple synthetic visual data. Semantic-based disentanglement is hypnotized that some semantic information is solely as well. The generative factors are group-disentangled in terms of specific semantics and they are mapped to different latent spaces，which is suitable for complicated ground truth data. Hierarchical disentanglement is based on the assumption that there is a correlation between generative factors at different levels of abstraction. The generative factors are disentangled by group from the bottom up and they can be mapped to latent space of different semantic abstraction levels to form a hierarchical disentangled representation. Nonlinear ICA provides an identifiable method for observed data-mixed disentangling unknown generative factors through a nonlinear reversible generator. For the motivation of loss functions，the loss functions can be commonly used in disentangled representation learning，which are grouped into three categories：1）modularity constraint：a single latent variable-constrained in the disentangled representation to capture only a single or a single group of factors of variation，and it promotes the separation of factors of variation mutually；2）explicitness constraint：current latent variable of the latent representation is activated to encode the ground truth of the corresponding generating factor effectively，and the entire latent representation contains complete information about all generative factors；and 3）multi-purpose constraint：lossrelated can optimize multiple disentangled representation，including modularity，compactness，and explicitness of the disentangled representation at the same time. The model-relevant can combine multiple loss constraint terms to form the final hybrid objective function. We compare the scope of application and limitations of each type of loss functions and summarize the classical disentangled representation works using the hybrid objective function further.