Boundary Function Research Articles

Disturbance Observer‐Based Neural Adaptive Command Filtered BacksStepping Funnel‐Like Control for the Chaotic PMSM With Asymmetric Prescribed Performance Constraints

ABSTRACTThis paper suggests a neural adaptive command filtered backstepping tracking control strategy for the chaotic permanent magnet synchronous motors with asymmetric prescribed performance constraints. Therefore, enable chaotic permanent magnet synchronous motors (PMSM) to obtain good robustness and better universality in practical industrial environments, and realizes more accurate control effect. The main challenge lies in devising a valid funnel‐like solution within the backstepping frame to handle the asymmetric performance constraints that traditional solutions cannot solve. To achieve this, a novel funnel‐like function is introduced, integrating a performance boundary function independent of initial output error, thereby transforming the system into an unbounded one. Additionally, the “explosion of complexity” with conventional backstepping is mitigated by introducing command filtering and constructing an error compensating system to reduce errors. By combining the theory of Lyapunov function and backstepping technique, the virtual controller and the real controller with adaptive law ensure the stability of the system. The disturbance observer and neural network solve the external disturbance and the uncertain nonlinear problem, respectively. Simulation comparisons confirm the robustness of the proposed control scheme and demonstrate its superiority over existing solutions.

Assessing management factors limiting yield and starch content of cassava in the western Brazilian Cerrado

AbstractCassava (Manihot esculenta Crantz) was declared the “crop of the 21st century” by the Food and Agriculture Organization of the United Nations due to its high starch content and low input requirements. The management factors that govern yields and starch content in cassava in Brazil are still unclear. The aim of this study was to identify the main factors that limit the yield and starch content of cassava fields in Brazilian Cerrado. The data were collected as part of a survey covering 300 cassava fields in two growing seasons (2020–2021 and 2021–2022). Throughout the development cycle, management practices, yield, and percentage starch content in the roots were described. The database was divided into high and low yield tertiles. Mean comparison tests, regression tree analyses, and boundary functions were applied. The importance of genetics, environment, and associated crop constraints on cassava production (yields and starch content) was assessed. The yield gap in cassava was 44.6 Mg ha−1. The most important factors leading to yield and starch losses were variety, planting date, and potassium fertilization. By adapting optimal practices, it is possible to produce an additional 1.5 million tons of cassava on the current cultivation area in the western Brazilian Cerrado, which corresponds to 8.3% of total production in Brazil and could increase the production of cassava starch by more than 400,000 Mg.

Analytical model and stress behavior of consolidated load bearing geotextile tubes

Accurately predicting stress-strain characteristics is crucial to ensuring the regulated capacity and controlled deformation of the tubes during and after construction. However, research on the shear strength of geotextile tubes under surcharge loading, especially after dewatering, is insufficient. This study proposes an analytical model with a Stress-State Boundary (SSB) and Yield Function to comprehensively describe the stress-strain behavior of Load-Bearing Geotextile Tubes (LGTs). The SSB is designed to predict the initial state of stress in the infill soil prior to load application, while the Yield Function is formulated to express the shear stress path experienced by the LGT before fabric failure. The model considers various factors that affect LGT behavior, including diverse soil mechanical parameters, nonlinear fabric stiffness, initial tension due to self-weight and principal stress axes rotation. Results show that a decrease in Poisson's ratio corresponds to an increase in failure stress. Moreover, it was demonstrated that the axial failure strain can be influenced by the geotextile linear or nonlinear behavior. Notably, the study highlights that tube height and inclination angle significantly affect the geotextile's confining effect. Beyond theoretical contributions, the analytical model serves as a valuable tool for optimizing geotextile tube design and execution, contributing to project success and longevity through enhanced structural stability.

Logic-Based Fixed-Time Control for Uncertain Nonlinear Systems With Unknown Control Directions.

The fixed-time control problem is investigated for a class of uncertain nonlinear systems subjected to multiple unknown control directions. The control coefficients of nonlinear systems under consideration are time varying and their signs are not required to be identical. To tackle this challenge, a switching mechanism along with a novel dynamic boundary function is proposed. Utilizing the devised dynamic boundary function, adaptive parameters are introduced into the controller to effectively handle system uncertainties. It is proved that the system output converges to a small neighborhood of the origin in fixed time and the boundedness of all system signals is maintained. Finally, two simulation examples are used to show the validity of the presented switching control strategy.

Practically fast finite-time stability of stochastic constrained nonlinear systems with actuator dead zone

This article addresses the challenge of achieving practically fast finite-time stabilization for stochastic constrained nonlinear systems, which are subject to both quantization effects and actuator dead zones. To tackle these issues, adaptive parameterization and partial control strategies are introduced with the aim of efficiently approximating and counteracting nonlinear disturbances. This approach ensures the robust stabilization of the controlled system within a finite time frame, despite the presence of uncertainties. Additionally, a novel barrier function is propose that mitigates the constraints usually imposed by boundary functions, while also leveraging a fuzzy logic system to manage nonlinear terms adeptly. Building on these innovations, we formulate a new theorem dedicated to practically fast finite-time control mechanisms for stochastic nonlinear systems. The efficacy of our theoretical developments is substantiated through an illustrative example involving a current-controlled DC motor system, demonstrating the practical applicability and robustness of the proposed control scheme.

Stem-loop and circle-loop TADs generated by directional pairing of boundary elements have distinct physical and regulatory properties.

The chromosomes in multicellular eukaryotes are organized into a series of topologically independent loops called TADs. In flies, TADs are formed by physical interactions between neighboring boundaries. Fly boundaries exhibit distinct partner preferences, and pairing interactions between boundaries are typically orientation-dependent. Pairing can be head-to-tail or head-to-head. The former generates a stem-loop TAD, while the latter gives a circle-loop TAD. The TAD that encompasses the Drosophila even skipped (eve) gene is formed by the head-to-tail pairing of the nhomie and homie boundaries. To explore the relationship between loop topology and the physical and regulatory landscape, we flanked the nhomie boundary region with two attP sites. The attP sites were then used to generate four boundary replacements: λ DNA, nhomie forward (WT orientation), nhomie reverse (opposite of WT orientation), and homie forward (same orientation as WT homie). The nhomie forward replacement restores the WT physical and regulatory landscape: in MicroC experiments, the eve TAD is a 'volcano' triangle topped by a plume, and the eve gene and its regulatory elements are sequestered from interactions with neighbors. The λ DNA replacement lacks boundary function: the endpoint of the 'new' eve TAD on the nhomie side is ill-defined, and eve stripe enhancers activate a nearby gene, eIF3j. While nhomie reverse and homie forward restore the eve TAD, the topology is a circle-loop, and this changes the local physical and regulatory landscape. In MicroC experiments, the eve TAD interacts with its neighbors, and the plume at the top of the eve triangle peak is converted to a pair of 'clouds' of contacts with the next-door TADs. Consistent with the loss of isolation afforded by the stem-loop topology, the eve enhancers weakly activate genes in the neighboring TADs. Conversely, eve function is partially disrupted.

Stem-loop and circle-loop TADs generated by directional pairing of boundary elements have distinct physical and regulatory properties

The chromosomes in multicellular eukaryotes are organized into a series of topologically independent loops called TADs. In flies, TADs are formed by physical interactions between neighboring boundaries. Fly boundaries exhibit distinct partner preferences, and pairing interactions between boundaries are typically orientation-dependent. Pairing can be head-to-tail or head-to-head. The former generates a stem-loop TAD, while the latter gives a circle-loop TAD. The TAD that encompasses the Drosophila even skipped (eve) gene is formed by the head-to-tail pairing of the nhomie and homie boundaries. To explore the relationship between loop topology and the physical and regulatory landscape, we flanked the nhomie boundary region with two attP sites. The attP sites were then used to generate four boundary replacements: λ DNA, nhomie forward (WT orientation), nhomie reverse (opposite of WT orientation), and homie forward (same orientation as WT homie). The nhomie forward replacement restores the WT physical and regulatory landscape: in MicroC experiments, the eve TAD is a ‘volcano’ triangle topped by a plume, and the eve gene and its regulatory elements are sequestered from interactions with neighbors. The λ DNA replacement lacks boundary function: the endpoint of the ‘new’ eve TAD on the nhomie side is ill-defined, and eve stripe enhancers activate a nearby gene, eIF3j. While nhomie reverse and homie forward restore the eve TAD, the topology is a circle-loop, and this changes the local physical and regulatory landscape. In MicroC experiments, the eve TAD interacts with its neighbors, and the plume at the top of the eve triangle peak is converted to a pair of ‘clouds’ of contacts with the next-door TADs. Consistent with the loss of isolation afforded by the stem-loop topology, the eve enhancers weakly activate genes in the neighboring TADs. Conversely, eve function is partially disrupted.

Impaired instructive and protective barrier functions of the endothelial cell glycocalyx pericellular matrix is impacted in COVID-19 disease.

The aim of this study was to review the roles of endothelial cells in normal tissue function and to show how COVID-19 disease impacts on endothelial cell properties that lead to much of its associated symptomatology. This places the endothelial cell as a prominent cell type to target therapeutically in the treatment of this disorder. Advances in glycosaminoglycan analytical techniques and functional glycomics have improved glycosaminoglycan mimetics development, providing agents that can more appropriately target various aspects of the behaviour of the endothelial cell in-situ and have also provided polymers with potential to prevent viral infection. Thus, promising approaches are being developed to combat COVID-19 disease and the plethora of symptoms this disease produces. Glycosaminoglycan mimetics that improve endothelial glycocalyx boundary functions have promising properties in the prevention of viral infection, improve endothelial cell function and have disease-modifying potential. Endothelial cell integrity, forming tight junctions in cerebral cell populations in the blood-brain barrier, prevents the exposure of the central nervous system to circulating toxins and harmful chemicals, which may contribute to the troublesome brain fogging phenomena reported in cognitive processing in long COVID disease.

Asymptotics for viscous Burgers equation under impulsive forcing

An initial value problem to the viscous Burgers equation under the influence of an external forcing of distribution type is considered. The existence and uniqueness of weak solutions for it are investigated. To do this, we linearize the viscous Burgers equation and show the existence and uniqueness of common boundary function for the associated initial-boundary problems. Jump discontinuity of the spatial derivative of the solution makes a key role in determining large time asymptotics to the solutions. The explicit representation of the common boundary function and its asymptotic behavior are discussed for a specific case of the jump discontinuity. Here, the common boundary is obtained in terms of Associated Legendre functions of the first and second kind. For the general case, asymptotic behavior of the common boundary of the associated initial-boundary problems is used to determine the large time asymptotics for the Cauchy problem to the viscous Burgers equation.

Shuffling-type gradient method with bandwidth-based step sizes for finite-sum optimization

Shuffling-type gradient method is a popular machine learning algorithm that solves finite-sum optimization problems by randomly shuffling samples during iterations. In this paper, we explore the convergence properties of shuffling-type gradient method under mild assumptions. Specifically, we employ the bandwidth-based step size strategy that covers both monotonic and non-monotonic step sizes, thereby providing a unified convergence guarantee in terms of step size. Additionally, we replace the lower bound assumption of the objective function with that of the loss function, thereby eliminating the restrictions on the variance and the second-order moment of stochastic gradient that are difficult to verify in practice. For non-convex objectives, we recover the last iteration convergence of shuffling-type gradient algorithm with a less cumbersome proof. Meanwhile, we also establish the convergence rate for the minimum iteration of gradient norms. Under the Polyak-Łojasiewicz (PL) condition, we prove that the function value of last iteration converges to the lower bound of the objective function. By selecting appropriate boundary functions, we further improve the previous sublinear convergence rate results. Overall, this paper contributes to the understanding of shuffling-type gradient method and its convergence properties, providing insights for optimizing finite-sum problems in machine learning. Finally, numerical experiments demonstrate the efficiency of shuffling-type gradient method with bandwidth-based step size and validate our theoretical results.

Asymptotical convergence of solutions of boundary value problems for singularly perturbed higher-order integro-differential equations

The article considers a two-point boundary value problem for a linear integro-differential equation of the n + m order with small parameters for m higher derivatives, provided that the roots of the additional characteristic equation are negative. The aim of the study is to obtain asymptotic estimates of the solution, to find out the asymptotic behavior of solutions in the vicinity of points where additional conditions are set, as well as to construct a degenerate problem, the solution of which tend to the solution of the initial perturbed boundary value problem. The Cauchy function and boundary functions of a boundary value problem for a singularly perturbed homogeneous differential equation are constructed, and their asymptotic estimates are obtained. Using the Cauchy functions and boundary functions, an analytical formula for solutions to the boundary value problem is obtained. A theorem on an asymptotic estimate for the solution of the considered boundary value problem is proved. The asymptotic behavior of the solution with respect to a small parameter and the order of growth of its derivatives are established. It is shown that the solution of the boundary value problem under consideration at the left end of this segment has the phenomenon of an initial jump and the order of this jump is determined. A modified degenerate boundary value problem containing initial jumps of the solution and the integral term is constructed.

Establishing a water-use boundary function for potato through crop modeling

The yield to water-use boundary function is a valuable method for estimating attainable yield and yield gap (the difference between attainable yield and actual yield) in water-limited regions. However, the water-use boundary function for potato has not been clearly defined yet. In current research, we established a water-use boundary function for fresh potato tubers in a climatic transition zone (Longzhong Plateau, China) using a simple crop growth model. We validated this function using extensive long-term experimental data collected from field experiments and the literature. The results showed that the crop model accurately simulated the weight of fresh potato tubers with a relative root mean square error (RRMSE) of less than 30 %, a coefficient of determination (d) greater than 0.7, and a root mean square error (RMSE) of 5426 kg ha−1. The established water-use boundary function for fresh potato tubers is defined as: yield (kg ha−1) = 167 × (water use [mm] - 121), with a plateau yield of 48,082 kg ha−1 when water use exceeds 410 mm. Furthermore, the water-use boundary function was found to be highly applicable to water use-yield data collected from the literature and precipitation-yield data for the potato growing season from long-term observations. Utilizing precipitation data for the potato growing season from 1988 to 2018, the water-use boundary function was employed to calculate the average attainable yield for fresh potato tubers, ranging from 10,000 to 48,082 kg ha−1 in the Longzhong Plateau. The water-use boundary function for potato could aid farmers in water-limited regions in identifying the most profitable crop management systems.

The Public Sphere Is “Too Darn Hot”: Social Identity Complexity as a Basis for Authentic Communication

A growing body of research suggests that the contemporary media environment enables motivated reasoning, which intensifies affective polarization. This is especially the case in the U.S., where elections are capital-intensive and media are largely commercially owned. From a normative perspective, these commercial forces may interfere with authentic communication by hijacking the “lifeworld” and thus undermining the sincerity of our speech. From a psychological and empirical perspective, this means we are an affective public steeping in “hot cognitions” that unconsciously motivate us toward processing (mis)information in biased and distorted ways. This kind of cognitive limitation intensifies as current affairs heat up, but starts well before, as a function of media market boundaries aligning with human psychology. Through a synthetic literature review of theory and empirical research, this essay argues that “social identity complexity” may help to overcome some of the worst outcomes of motivated reasoning, pointing toward a developmental basis for more authentic communication in the public sphere.

Operator-valued multiplier theorems for causal translation-invariant operators with applications to control theoretic input-output stability

AbstractWe prove an operator-valued Laplace multiplier theorem for causal translation-invariant linear operators which provides a characterization of continuity from $$H^\alpha ({\mathbb {R}},U)$$ H α ( R , U ) to $$H^\beta ({\mathbb {R}},U)$$ H β ( R , U ) (fractional U-valued Sobolev spaces, U a complex Hilbert space) in terms of a certain boundedness property of the transfer function (or symbol), an operator-valued holomorphic function on the right-half of the complex plane. We identify sufficient conditions under which this boundedness property is equivalent to a similar property of the boundary function of the transfer function. Under the assumption that U is separable, the Laplace multiplier theorem is used to derive a Fourier multiplier theorem. We provide an application to mathematical control theory, by developing a novel input-output stability framework for a large class of causal translation-invariant linear operators which refines existing input-output stability theories. Furthermore, we show how our work is linked to the theory of well-posed linear systems and to results on polynomial stability of operator semigroups. Several examples are discussed in some detail.

Schwarz-Pick lemma for (α,β)-harmonic functions in the unit disc

We obtain Schwarz–Pick lemma for (α,β)-harmonic functions u in the disc, where α and β are complex parameters satisfying ℜα+ℜβ>−1. We prove sharp estimate of ‖Du(0)‖ for such functions in terms of Lp norm of the boundary function. Also, we give asymptotically sharp estimate of ‖Du(z)‖. This estimate is generalized to higher order derivatives. Our results extend earlier results for α-harmonic and Tα-harmonic functions.

Adaptive Nonsingular Fast Terminal Sliding Mode-Based Direct Yaw Moment Control for DDEV under Emergency Conditions

This paper presents an innovative three-level direct yaw moment control strategy for distributed drive electric vehicles (DDEV) under emergency conditions. The phase plane analysis is used at the supervisory level to design the stability boundary function taking into account the impact of the road adhesion coefficient. To guarantee the performance of finite-time convergence and singularity-free methods, the adaptive nonsingular fast terminal sliding mode control (ANFTSMC) is developed at the decision level to determine the extra yaw moment for tracking the intended side slip angle and yaw rate. Among this, the unstable domain in the phase plane is further separated into moderately and severely unstable according to the degree of vehicle instability, which is defined by the distance between the state phase point and the stability boundary. Meanwhile, the adaptive weight between the handling and stability is obtained. At the executive level, the quadratic programming algorithm is adopted to allocate four-wheel torque with the objective of optimal tire utilization rate. Finally, the co-simulation test is executed in both closed-loop and open-loop circumstances; according to the simulation results, the presented ANFTSMC method outperforms the SMC, and it can decrease the tracking error and improve the handling and stability.

Neural Network Boundary Approximation for Uncertain Nonlinear Spatiotemporal Systems and Its Application of Tracking Control.

This brief addresses the neural network (NN) approximation problem for uncertain nonlinear systems with time-varying parameters (that is, unknown nonlinear spatiotemporal systems). Due to the fact that the unknown spatiotemporal functions cannot be directly approximated by NNs, a so-called time-varying parameter extraction is given to separate time-varying parameters from uncertain nonlinear spatiotemporal functions. By using the supremum of Euler norm of the extracted time-varying parameters, the nonlinear spatiotemporal function is mapped to an unknown state-based boundary function, which can be approximated by NNs. Based on the time-varying parameter extraction, an adaptive neural tracking control law is designed for uncertain strict-feedback nonlinear spatiotemporal systems, which guarantees the convergence of the tracking error with a trajectory performance. The effectiveness of the designed method is verified by simulations.

Monitoring the Wear Trends in Wind Turbines by Tracking Fourier Vibration Spectra and Density Based Support Vector Machines

To make wind power more competitive, it is necessary to reduce turbine downtime and reduce costs associated with wind turbine operation and maintenance (O&M). Incorporating machine learning in the development of condition-based predictive maintenance methodologies for wind turbines can enhance their efficiency and reliability. This paper presents a monitoring method that utilizes Density Based Support Vector Machines (DBSVM) and the evolutionary Fourier spectra of vibrations. This method allows for the smart monitoring of the function evolution of the turbine. A complex optimal function (FO) for 5-degree order has been developed that will be the boundary function of the DBSVM to be timely determined from the Fourier spectrum through the magnitude–frequency and place of the failure occurring in the wind turbine drivetrains. The trend of the failure was constructed with the maximal values of the optimal frequency function for both yesthe cases of the upwind and downwind parts of the gearbox.

Some auxiliary estimates for solutions to non-uniformly degenerate second-order elliptic equations

We consider a class of second order elliptic equations in divergence form with non-uniform exponential degeneracy. The method used is based on the fact that the degeneracy rates of the eigenvalues of the matrix ||aij(x)|| (function λi(x)) are not the functions of unusual norm |x|, but of some anisotropic distance |x| a−. We assume that the Dirichlet problem for such equations is solvable in the classical sense for every continuous boundary function in any normal domain Ω. Estimates for the weak solutions of Dirichlet problem near the boundary point are obtained, and Green’s functions for second order non-uniformly degenerate elliptic equations are constructed.

Asymptotic solutions of differential equations with singular impulses

The paper considers impulsive systems with singularities. The main novelty is that beside the singularity of the differential equation, the impulsive equation is a singular one. The method of boundary functions is applied to obtain the main result. Examples with simulations confirming the theoretical results are given.