Unknown Functions Research Articles

Pseudo-model-based iterative learning control for nonlinear multi-phase batch processes

In this article, a pseudo-model-based iterative learning control (ILC) is exploited for multi-phase batch processes which can be described as a nonlinear switched system with unknown functions and identical states in different phases. The nonlinear switched system is converted into a linear model whose system parameter matrix is approximated by minimizing the discrepancy from the real system output increment to the approximated system output increment. A data-driven ILC is constructed in an interactive form with system parameter matrix approximate algorithm. Meanwhile, the signs of the diagonal elements of system lower triangular parameter matrix are introduced into the construction of control input law. Theoretical analysis shows that the pseudo-model-based ILC (PM-ILC) concept can be extended to multi-phase batch processes with non-identical states in different phases. Furthermore, the approximation error of the system parameters matrix is bounded and the proposed PM-ILC is robust if the parameter is appropriately chosen. Simulation results illustrate the effectiveness and practicability of the proposed PM-ILC.

Finite‐time stabilization control of nonlinear systems with full‐state constraints

AbstractThis paper studies the finite time stabilization control (FTSC) problem of nonlinear systems with unknown functions and full‐state constraints (FSCs). A lemma dealing with unknown functions is put forward so that the assumptions and the “explosion of terms” (EOT) of backstepping are avoided. Compared with approximation algorithms, this algorithm can make the system states converge to the origin in a finite time. On the other hand, a new logarithmic constraint function is utilized to solve the drawback of barrier Lyapunov functions (BLFs). Then, combined with finite time control (FTC), an FTSC algorithm with FSCs is proposed. Finally, simulations of Chua's circuit system are given to verify the effectiveness and superiority of this algorithm. Compared with the approximation algorithm, this algorithm can theoretically make the states of Chua's circuit system to the origin in a finite time.

Propagation dynamics of diffusive disease models with infectious stages

This paper studies the spatial propagation dynamics in diffusive disease transmission models with infectious stages, which may be nonmonotonic and partially degenerate. Using the solutions of linear heat equations, we transform the system into a new system that contains nonlocal delays and two unknown functions. From this new system, it is easy to obtain an important threshold and the numerical estimation for this threshold is easy. When the initial infection satisfies proper decaying behavior, we find that this threshold is the spreading speed for all infectious subgroups. Then the minimal wave speed of traveling wave solutions is proved to be the threshold, which connects the disease-free state to the endemic case. Moreover, some numerical examples are presented to explore the possible extension.

The human infertility single-cell testis atlas (HISTA): an interactive molecular scRNA-Seq reference of the human testis.

Single-cell RNA-seq (scRNA-Seq) has been widely adopted to study gene expression of the human testis. Several datasets of scRNA-Seq from human testis have been generated from different groups processed with different informatics pipelines. An integrated atlas of scRNA-Seq expression constructed from multiple donors, developmental ages, and fertility states would be widely useful for the testis research community. To describe the generation and use of the human infertility single-cell testis atlas (HISTA), an interactive web tool for understanding human spermatogenesis through scRNA-Seq analysis. We obtained scRNA-Seq datasets derived from 12 donors, including healthy adult controls, juveniles, and several infertility cases, and reprocessed these data using methods to remove batch effects. Using Shiny, an open-source environment for data visualization, we created numerous interactive tools for exploring the data, some of which support simple statistical hypothesis testing. We used the resulting HISTA browser and its underlying data to demonstrate HISTA's value for testis researchers. A primary application of HISTA is to search by a single gene or a set of genes; thus, we present various analyses that quantify and visualize gene expression across the testis cells and pathology. HISTA also contains machine-learning-derived gene modules ("components") that capture the entire transcriptional landscape of the testis tissue. We show how the use of these components can simplify the highly complex data in HISTA and assist with the interpretation of genes with unknown functions. Finally, we demonstrate the diverse ways HISTA can be used for new data analysis, including hypothesis testing. HISTA is a research environment that can help scientists organize and understand the high-dimensional transcriptional landscape of the human testis. HISTA has already contributed to published testis research and can be updated as needed with input from the research community or downloaded and modified for individual needs.

Predefined Time and Accuracy Adaptive Fault-Tolerant Control for Nonlinear Systems with Multiple Faults

This work mainly studies the issue of predefined time and accuracy adaptive fault-tolerant control for strict-feedback nonlinear systems with multiple faults. The faults in the controlled system include actuator faults and external system faults. The unknown functions for nonlinear systems are approximated by fuzzy logic systems (FLSs). And then, according to the backstepping technique and the predefined time stability theory, an adaptive fuzzy control algorithm is presented, which can make sure that all closed-loop system signals remain predefined time bound and the tracking error converges to a predefined accuracy within the predefined time. Ultimately, the effectiveness of the presented control algorithm is proved through two simulation examples.

Event‐triggered adaptive fuzzy bipartite containment control for switched nonlinear multi‐agent systems with actuator attacks

AbstractThis paper considers the event‐triggered adaptive fuzzy bipartite containment control problem for switched nonlinear multi‐agent systems (MASs) with actuator attacks. To handle the completely unknown nonlinear functions in the considered system, fuzzy logic systems (FLSs) are applied to approximate the unknown nonlinear functions. In addition, an adaptive bipartite containment control approach is designed to deal with the actuator attacks, which can reduce the burden of communication. According to the designed adaptive bipartite containment control scheme, it is shown that all the signals are semi‐globally uniformly ultimately bounded (SGUUB), and all the outputs of the followers achieve the bipartite consensus and finally enter the convex set spanned by leaders' in the presence of actuator attacks. Eventually, a simulation example is presented to illustrate the availability of the developed strategy.

Numerical Analysis of Unsteady Vibrations of a Plate Resting on an Elastic Isotropic Half-Space

The paper is devoted to the numerical solution of the problem of vibrations of an infinite elastic plate resting on an elastic isotropic half-space using the analytical method based on the ray method with its numerical realization via the Maplesoft package. Unsteady oscillations are caused by the action of instantaneous loads on the plate, resulting in the appearance of two plane wave surfaces of strong discontinuity in the elastic half-space, behind the fronts of which, up to the contact boundary, the solution is constructed using ray series. The unknown functions entering the coefficients of the ray series and the equation of plate motion are determined from the boundary conditions of the contact interaction between the plate and the half-space. Previously, the approximate solution of this problem was obtained analytically without using mathematical packages, and the dynamic deflection of the plate involving only the first three terms of the ray series was written down. In this work, a two-layer medium with different properties was investigated using an algorithm developed to solve contact dynamic problems related to the occurrence and propagation of strong and weak discontinuity surfaces.

Finite-Time Adaptive Fuzzy Backstepping Control for Quadrotor UAV With Stochastic Disturbance

This paper proposes an adaptive fuzzy output feedback control approach for quadrotor unmanned aerial vehicles (QUAV) with stochastic disturbances, besides which we consider the unmeasurable states and unknown nonlinear functions. The QUAV system contains stochastic terms which are not bounded and not differentiable. By combining the It <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\hat{\rm \textbf{o}}$</tex-math> </inline-formula> differential equation with finite-time theory, a novel stochastic finite-time stability controller for QUAV is raised for the first time. The fuzzy logic system (FLS) is utilized to approximate the unknown nonlinear functions in the model. Dynamic surface control technology is introduced to reduce the complexity of differential. Furthermore, an observer with FLS is designed through the adaptive backstepping technique to estimate the immeasurable states. It is proved that this control approach can ensure that all states of the closed-loop QUAV system are semi-global and finite-time stable in probability. Meanwhile, the errors of system outputs and observer converge to a small neighborhood of origin. The simulation results show the effectiveness of the proposed method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —In practical applications, many systems are often affected by internal and external disturbances, and not all of them can be described by mathematical models, so they are called stochastic disturbances. Taking the QUAV as an example, when the system is disturbed by internal parameters, external environment, system input, sensor error, and other stochastic factors, the deterministic system can no longer accurately describe the controlled object. In this paper, the QUAV is regarded as a stochastic system for the first time, and a novel controller is designed to solve the above problems. In addition, the QUAV needs fast action in some applications, such as emergency collision avoidance, which has high requirements for the convergence performance of the controller. Therefore, studying the finite-time control for QUAV systems with stochastic disturbances is necessary. At the same time, this paper also considers the problem that the state is not measurable and the system contains unknown nonlinear equations.

Venom diversity in Naja mossambica: Insights from proteomic and immunochemical analyses reveal intraspecific differences.

Intraspecific variations in snake venom composition have been extensively documented, contributing to the diverse clinical effects observed in envenomed patients. Understanding these variations is essential for developing effective snakebite management strategies and targeted antivenom therapies. We aimed to comprehensively investigate venoms from three distinct populations of N. mossambica from Eswatini, Limpopo, and KwaZulu-Natal regions in Africa in terms of their protein composition and reactivity with three commercial antivenoms (SAIMR polyvalent, EchiTAb+ICP, and Antivipmyn Africa). Naja mossambica venoms from Eswatini region exhibited the highest content of neurotoxic proteins, constituting 20.70% of all venom proteins, compared to Limpopo (13.91%) and KwaZulu-Natal (12.80%), and was characterized by the highest diversity of neurotoxic proteins, including neurotoxic 3FTxs, Kunitz-type inhibitors, vespryns, and mamba intestinal toxin 1. KwaZulu-Natal population exhibited considerably lower cytotoxic 3FTx, higher PLA2 content, and significant diversity in low-abundant proteins. Conversely, Limpopo venoms demonstrated the least diversity as demonstrated by electrophoretic and mass spectrometry analyses. Immunochemical assessments unveiled differences in venom-antivenom reactivity, particularly concerning low-abundance proteins. EchiTAb+ICP antivenom demonstrated superior reactivity in serial dilution ELISA assays compared to SAIMR polyvalent. Our findings reveal a substantial presence of neurotoxic proteins in N. mossambica venoms, challenging previous understandings of their composition. Additionally, the detection of numerous peptides aligning to uncharacterized proteins or proteins with unknown functions underscores a critical issue with existing venom protein databases, emphasizing the substantial gaps in our knowledge of snake venom protein components. This underscores the need for enhanced research in this domain. Moreover, our in vitro immunological assays suggest EchiTAb+ICP's potential as an alternative to SAIMR antivenom, requiring confirmation through prospective in vivo neutralization studies.

The Roles of the Golgi in Various Diseases

The primary function of the Golgi is to perform post-translational modifications on proteins, allow them to be transported within the cell. The Golgi has more functions in the cell, according to research into its unknown structure and functions. It has been discovered that, in addition to substance process and transport, it plays a role in autophagy, lipid formation, calcium homeostasis, and apoptosis regulation.&#x0D; The fact that the Golgi has so many tasks has caused question marks about what kind of illnesses or diseases it can cause in case of a problem with Golgi. A mutation at Golgi can disrupt its function by cause of the Golgi fragmentation. It can be seized by living organisms or molecules, called infectious agents, outside the mutation. Disintegration and disorders in the Golgi structure and function are examples of neurodegenerative diseases and cancer. In addition, studies prove that the SARS-CoV-2 virus, which causes pandemic in the world, is also linked to the Golgi. The diseases that can be caused by the Golgi are highlighted in this review, as are treatment studies. Treatment strategies for the Golgi that causes many diseases are still developing and studies are ongoing.The primary function of the Golgi apparatus is to perform post-translational modifications on proteins, allowing them to be transported within the cell. The Golgi has more functions in the cell, according to research into its unknown structure and functions. It has been discovered that, in addition to substance processing and transport, it plays a role in autophagy, lipid formation, calcium homeostasis, and apoptosis regulation. The fact that Golgi has so many tasks has caused question marks about what kind of illnesses or diseases it can cause in case of a problem with Golgi. A mutation at Golgi can disrupt its function by causing Golgi fragmentation. It can be seized by living organisms or molecules, called infectious agents, outside the mutation. Disintegration and disorders in Golgi structure and function are examples of neurodegenerative diseases and cancer. In addition, studies prove that the SARS-CoV-2 virus, which causes pandemics in the world, is also linked to Golgi. The diseases that can be caused by Golgi are highlighted in this review, as are treatment studies. Treatment strategies for Golgi device that causes many diseases are still developing and studies are ongoing.

Exploring salt tolerance mechanisms using machine learning for transcriptomic insights: case study in Spartina alterniflora

Abstract Salt stress poses a significant threat to global cereal crop production, emphasizing the need for a comprehensive understanding of salt tolerance mechanisms. Accurate functional annotations of differentially expressed genes are crucial for gaining insights into the salt tolerance mechanism. The challenge of predicting gene functions in under-studied species, especially when excluding infrequent GO terms, persists. Therefore, we proposed the use of NetGO 3.0, a machine learning-based annotation method that does not rely on homology information between species, to predict the functions of differentially expressed genes under salt stress. Spartina alterniflora, a halophyte with salt glands, exhibits remarkable salt tolerance, making it an excellent candidate for in-depth transcriptomic analysis. However, current research on the S. alterniflora transcriptome under salt stress is limited. In this study, we used S. alterniflora as an example to investigate its transcriptional responses to various salt concentrations, with a focus on understanding its salt tolerance mechanisms. Transcriptomic analysis revealed substantial changes impacting key pathways such as gene transcription, ion transport, and ROS metabolism. Notably, we identified a member of the SWEET gene family in S. alterniflora, SA_12G129900.m1, showing convergent selection with the rice ortholog SWEET15. Additionally, our genome-wide analyses explored alternative splicing responses to salt stress, providing insights into the parallel functions of alternative splicing and transcriptional regulation in enhancing salt tolerance in S. alterniflora. Surprisingly, there was minimal overlap between differentially expressed and differentially spliced genes following salt exposure. This innovative approach, combining transcriptomic analysis with machine learning-based annotation, avoids the reliance on homology information and facilitates the discovery of unknown gene functions, and is applicable across all sequenced species.

Integrating the analysis of human biopsies using post-translational modifications proteomics.

Proteome diversities and their biological functions are significantly amplified by post-translational modifications (PTMs) of proteins. Shotgun proteomics, which does not typically survey PTMs, provides an incomplete picture of the complexity of human biopsies in health and disease. Recent advances in mass spectrometry-based proteomic techniques that enrich and study PTMs are helping to uncover molecular detail from the cellular level to system-wide functions, including how the microbiome impacts human diseases. Protein heterogeneity and disease complexity are challenging factors that make it difficult to characterize and treat disease. The search for clinical biomarkers to characterize disease mechanisms and complexity related to patient diagnoses and treatment has proven challenging. Knowledge of PTMs is fundamentally lacking. Characterization of complex human samples that clarify the role of PTMs and the microbiome in human diseases will result in new discoveries. This review highlights the key role of proteomic techniques used to characterize unknown biological functions of PTMs derived from complex human biopsies. Through the integration of diverse methods used to profile PTMs, this review explores the genetic regulation of proteoforms, cells of origin expressing specific proteins, and several bioactive PTMs and their subsequent analyses by liquid chromatography and tandem mass spectrometry.

Satellite glial GPR37L1 and its ligand maresin 1 regulate potassium channel signaling and pain homeostasis.

G protein-coupled receptor 37-like 1 (GPR37L1) is an orphan GPCR with largely unknown functions. Here we report that Gpr37l1/GRP37L1 ranks among the most highly expressed GPCR transcripts in mouse and human dorsal root ganglia (DRGs), selectively expressed in satellite glial cells (SGCs). Peripheral neuropathy induced by streptozotoxin (STZ) and paclitaxel (PTX) led to reduced GPR37L1 expression on the plasma membrane expression in mouse and human DRGs. Transgenic mice with Gpr37l1 deficiency exhibited impaired resolution of neuropathic pain symptoms following PTX and STZ-induced pain, whereas overexpression of Gpr37l1 in mouse DRGs reversed pain. GPR37L1 is co-expressed with potassium channels, including KCNJ10 (Kir4.1) in mouse SGCs and both KCNJ3 (Kir3.1) and KCNJ10 in human SGCs. GPR37L1 regulates the surface expression and function of the potassium channels. Notably, the pro-resolving lipid mediator maresin 1 (MaR1) serves as a ligand of GPR37L1 and enhances KCNJ10 or KCNJ3-mediated potassium influx in SGCs through GPR37L1. Chemotherapy suppressed KCNJ10 expression and function in SGCs, which MaR1 rescued through GPR37L1. Finally, genetic analysis revealed that the GPR37L1-E296K variant increased chronic pain risk by destabilizing the protein and impairing the protein's function. Thus, GPR37L1 in SGCs offers a new therapeutic target for the protection of neuropathy and chronic pain.

Predefined-time distributed optimization and anti-disturbance control for nonlinear multi-agent system with neural network estimator: A hierarchical framework

This paper addresses the predefined-time distributed optimization of nonlinear multi-agent system using a hierarchical control approach. Considering unknown nonlinear functions and external disturbances, we propose a two-layer hierarchical control framework. At the first layer, a predefined-time distributed estimator is employed to produce optimal consensus trajectories. At the second layer, a neural-network-based predefined-time disturbance observer is introduced to estimate the disturbance, with neural networks used to approximate the unknown nonlinear functions. A neural-network-based anti-disturbance sliding mode control mechanism is presented to ensure that the system trajectories can track the optimal trajectories within a predefined time. The feasibility of this hierarchical control framework is verified by utilizing the Lyapunov method. Numerical simulations are conducted separately using models of robotic arms and mobile robots to validate the effectiveness of the proposed method.

Hypothetical protein MAA_07646 is required for stress resistance and pathogenicity in Metarhizium robertsii.

Metarhizium robertsii, a vital entomopathogenic fungus for pest management, relies on various virulence-related proteins for infection. Identifying these proteins, especially those with unknown functions, can illuminate the fungus's virulence mechanisms. Through RNA-seq, we discovered that the hypothetical protein MAA_07646 was significantly upregulated during appressorium formation in M. robertsii. In this study, we characterized MAA_07646, finding its presence in both the nucleus and cytoplasm. Surprisingly, it did not affect vegetative growth, conidiation, or chemical tolerance. However, it played a role in heat and UV radiation sensitivity. Notably, ΔMAA_07646 exhibited reduced virulence in Galleria mellonella larvae due to impaired appressorium formation and decreased expression of virulence-related genes. In conclusion, MAA_07646 contributes to thermotolerance, UV resistance, and virulence in M. robertsii. Understanding its function sheds light on the insecticidal potential of M. robertsii's hypothetical proteins.

Funnel-Based Adaptive Neural Fault-Tolerant Control for Nonlinear Systems with Dead-Zone and Actuator Faults: Application to Rigid Robot Manipulator and Inverted Pendulum Systems

This study addresses an adaptive neural funnel fault-tolerant control problem for a class of strict-feedback nonlinear systems with actuator faults and input dead zone. To guarantee the boundedness of the tracking error, a modified transformation for funnel error is devised and incorporated into the control design process. To manage unknown nonlinear functions, radial basis function neural networks (RBFNN) are employed in designing an adaptive neural funnel fault-tolerant controller through the backstepping technique. The proposed controller guarantees the output tracking error stays within a predefined funnel, and all signals in the closed-loop system are semiglobally uniformly ultimately bounded (SGUUB). Finally, simulations of a rigid robot manipulator system and an inverted pendulum system are conducted to validate the practicality and effectiveness of the proposed control method.

Finite-time state-constrained adaptive fault-tolerant control for heavy launch vehicles with input quantization

This paper proposes the finite-time state-constrained adaptive fault-tolerant control method for a class of heavy launch vehicles subject to quantized input signals and actuator faults. Firstly, the attitude dynamic model of the heavy launch vehicles suffering from the actuator faults and disturbances is formulated. Secondly, to deal with the completely unknown nonlinear functions, radial basis function neural networks (RBFNNs) are introduced for approximation and compensation. Meanwhile, the barrier Lyapunov function (BLF) is introduced to ensure that all the states in the closed-loop system are bounded and the constraints of the system states are satisfied. As a result, the finite-time state-constrained adaptive fault-tolerant control structure is constructed for the heavy launch vehicles and the semi-globally practical finite-time stability (SGPFS) of the closed-loop control system is proved. Finally, numerical simulation results show the effectiveness and the satisfactory performance of the proposed control algorithm.

Multilayered neural network for power series‐based approximation of fractional delay differential equations

This paper trains a multilayered neural network (MLNN) for solving fractional delay differential equations (FDDEs), including nonlinear and singular types. The proposed methodology involves replacing the unknown functions in the equations with a truncated power series expansion. Subsequently, a collection of algebraic equations is solved utilizing an iterative minimization technique that leverages the capabilities of the MLNN architecture. The outcomes demonstrate that the MLNN architecture provides the required accuracy and strong stability compared to several numerical methods.

Discover an accurate approximation of dynamical system without prior information and customized design

Modeling dynamical systems is fraught with challenges when data can be collected but thorough analysis of the mechanism is absent. We design a method to discover unknown dynamical systems from data. The method discovers an accurate approximation of the model without the prior information and the customized design for each problem. The identification steps are straightforward as bringing in the data and then obtaining the model. The method begins with the simple idea that the equations of motion of many practical problems are Riemann integrable functions. For this reason, the Fourier series can decompose the equations of motion. In order to improve the accuracy, we design an extension that helps us to approximate unknown functions by the Fourier series with a high rate of convergence. The idea converts the difficulty of modeling the dynamical system into finding its Fourier series approximation. Convenient procedures enable the modeling of different problems. Numerical examples show that the new method discovers linear and nonlinear dynamical systems in the same steps and without the prior information.

Estimator-based neural adaptive event-triggered control for strict-feedback nonlinear systems with incomplete measurements

This article addresses a neural adaptive event-triggered tracking control for a class of strict-feedback nonlinear dynamics with incomplete measurements, which is novel on the research of Cyber-physical Systems. The incomplete measurement problem caused by packet loss, saturation, and other issues during data transmission can lead to the unavailability of system state variables, which can degrade system performance and even lead to instability. To solve these problems, a state estimator for data-losing case and two controllers for normal and data-losing cases are designed utilising event-triggered strategies which can reduce the burden of calculation and data transmission. Radial basis function neural networks are adopted to approximate the unknown nonlinear system functions. A strict stability analysis in probability shows that the control laws for the considered strict-feedback nonlinear system can guarantee all the closed-loop to be uniformly ultimately bounded in mean square. Two examples are performed to demonstrate the effectiveness of the provided control method.