Small Neighborhood Research Articles

On the motion of a dynamically symmetric satellite in one case of multiple parametric resonance

The paper studies the motions of a dynamically symmetric satellite (rigid body) relative to the center of mass in the central Newtonian gravitational field on a weakly elliptical orbit in the neighborhood of its stationary rotation (cylindrical precession). We consider the values of the parameters for which, in the limiting case of a circular orbit, one of the frequencies of small linear oscillations is equal to unity and the other is equal to zero, and the rank of the coefficient matrix of the linearized equations of the perturbed motion is equal to two, as well as a small neighborhood of this resonant point in the three-dimensional space of parameters. The resonant periodic motions of the satellite, analytical in fractional powers of a small parameter (the eccentricity of the orbit of the satellite's center of mass), are constructed. A rigorous nonlinear analysis of their stability is carried out. The methods of KAM theory are used to describe two- and three-frequency conditionally periodic motions of a satellite, with frequencies of different orders in a small parameter. A number of general theoretical issues concerning the considered multiple parametric resonance in Hamiltonian systems with two degrees of freedom that are close to autonomous and periodic in time are discussed. Several qualitatively different variants of parametric resonance regions are constructed. It is shown that in the general case the nature of nonlinear resonant oscillations of the system is determined by the first approximation system in a small parameter.

Finite‐Time Decentralized Adaptive Fuzzy Control for Non‐Triangular Form Large‐Scale Time‐Delay Systems With Full State Constraints

ABSTRACTThis paper is concerned with the problem of finite‐time decentralized adaptive fuzzy fault tolerant control for a class of non‐triangular form large‐scale time delay systems with full state constraints. By using the fuzzy logic systems and domination approach, the unknown nonlinear functions are approximated and the non‐triangular form structure is tackled, respectively. The time‐varying barrier Lyapunov function (TBLF) is used to ensure that the full state constraints are satisfied. Based on the proposed TBLF and backstepping technique, an adaptive fuzzy fault‐tolerant control protocol is presented. It can assure that the errors converge to a small neighborhood of the origin in a finite time, the signals of the whole closed‐loop systems are bounded and the full state constraints are satisfied. Simulation example is presented to further demonstrate the effectiveness of the proposed approach.

Output feedback control for non-strict feedback nonlinear systems: an adaptive fuzzy backstepping scheme

The adaptive fuzzy tracking control design issue is considered in this paper for a class of non-strict feedback nonlinear systems subject to external disturbances. A fuzzy high-gain state observer is constructed to reconstruct the unmeasurable states of the system by leveraging the universal approximation property of fuzzy logic systems for arbitrary unknown nonlinear functions. Within the framework of backstepping control design and in conjunction with adaptive techniques, an adaptive fuzzy control approach is presented. Subsequently, to work out the inherent ‘complexity explosion’ problem of the proposed control approach, dynamic surface control technique is introduced, leading to a simplified adaptive fuzzy output feedback control scheme. Stability analysis shows that the two proposed control schemes can ensure that all signals of the closed-loop system are semi-globally uniformly ultimately bounded, meanwhile the system tracking error can converge to a small neighborhood around the origin. Ultimately, a numerical simulation example is provided to validate the feasibility of the proposed control scheme.

Predefined-time event-triggered adaptive neural practical tracking control for flexible-joint robot

This paper researches the predefined-time event-triggered adaptive neural practical tracking control problem for flexible-joint robot system. An improved predefined-time command filter is utilized to get rid of the “explosion of complexity” problem, and the filter errors can be eliminated by an improved error compensation mechanism. Moreover, as an effective approximation tool, radial basis function neural networks are exploited to tackle the nonlinear terms existing in flexible-joint robot system. Finally, the communication burden of the system is reduced by using event-triggered technology, and an advanced adaptive predefined-time event-triggered controller is designed. The actual controller in the control scheme is updated only when it meets the conditions of the event-triggered mechanism. For flexible-joint robot system, the resulting control scheme makes the tracking error approach to a small neighborhood of zero, and all signals of the closed-loop system remain bounded within the predefined time. The effectiveness of the proposed controller is directly illustrated by the simulation results.

Hidden-like Attractors in a Class of Discontinuous Dynamical Systems

In continuous dynamical systems, a hidden attractor occurs when its basin of attraction does not connect with small neighborhoods of equilibria. This research aims to investigate the presence of hidden-like attractors in a class of discontinuous systems that lack equilibria. The nature of non-smoothness in Filippov systems is critical for producing a wide variety of interesting dynamical behaviors and abrupt transient responses to dynamic processes. To show the effects of non-smoothness on dynamic behaviors, we provide a simple discontinuous system made of linear subsystems with no equilibria. The explicit closed-form solutions for each subsystem have been derived, and the generalized Poincaré maps have been established. Our results show that the periodic orbit can be completely established within a sliding region. We then carry out a mathematical investigation of hidden-like attractors that exhibit sliding-mode characteristics, particularly those associated with grazing-sliding behaviors. The proposed system evolves by adding a nonlinear function to one of the vector fields while still preserving the condition that equilibrium points do not exist in the whole system. The results of the linear system are useful for investigating the hidden-like attractors of flow behavior across a sliding surface in a nonlinear system using numerical simulation. The discontinuous behaviors are depicted as motion in a phase space governed by various hidden attractors, such as period doubling, period-m segments, and chaotic behavior, with varying interactions with the sliding mode.

Adaptive neural control for a class of random nonlinear Markov jump multi-agent systems with full state constraints

This paper proposes a consensus control protocol based on the adaptive backstepping technique for a class of random Markov jump multi-agent systems (MASs) with full state constraints. Each agent is described by the high-order random nonlinear uncertain system driven by random differential equations, where the random noise is the second-order stationary stochastic process. First, a distributed tracking controller is designed for Markov jump MASs, effectively handling the interaction and coupling terms between agents. Second, an appropriate tan-type barrier Lyapunov function is selected to keep the agents’ states from the violation of constraint boundaries, and the unknown nonlinear terms with Markov jump parameters are approximated by neural networks (NNs) theory. Moreover, to address the differential explosion problem, the extended state observer (ESO) is first introduced instead of employing NNs approximation or command filtering techniques. Finally, the exponentially noise-to-state stability in mean square is proved rigorously through the Lyapunov method, which guarantees all signals of the closed-loop system are bounded in probability and the tracking error converges to a small neighborhood around zero. Simulations are given to demonstrate the feasibility of theoretical results.

A small neighborhood fabric recommender system based on user historical behavior and preference

In the current landscape, textile companies need rapid, precise, and personalized assistance, especially as digitalization and information, such as e-commerce and websites, are developing rapidly. Textile enterprises can mine user preferences to make personalized recommendations of appropriate textile fabrics; this is not only in keeping with current trends, but more importantly, can control production costs and improve user satisfaction. To support the transformation of textile enterprises to a small-batch and multi-variety business model, this paper proposes a fabric recommendation system; specifically, a fabric recommender system based on user historical behavior and preference is proposed. The proposed method is mainly based on the integration of preference, user activity, and rating; firstly, according to the fabric products purchased by the user, the features of the fabric are mined using a neural network to obtain the user’s preferences; secondly, neighbors with similar user behaviors are found according to similarity in users’ activity; and finally, understanding of the fabric is enhanced through a matrix based on the fabric ratings of the user. A focus on recommendation algorithm parameterization, including selection, thresholding, and neighborhood optimization, elevates the recommendation quality. A user–fabric dataset was used for experimental verification, and included the user’s purchase score of the fabric and the image of the fabric. Comparative analyses demonstrate superior precision with fewer neighborhoods, achieving a score of up to 0.93. Our research provides insights into user behavior and personalization, guiding future recommender system design and optimization.

Fixed-Time Event-Triggered Control of Nonholonomic Mobile Robots with Uncertain Dynamics and Preassigned Transient Performance

In this paper, a novel adaptive control scheme is proposed for the path-following problem of a nonholonomic mobile robot with uncertain dynamics based on barrier functions. To optimize communication resources, we integrate an event-triggered mechanism that avoids Zeno behavior and ensures that the tracking error of the closed-loop system converges to a small neighborhood around zero within a fixed time, while consistently satisfying predefined transient performance requirements. Extensive simulation studies demonstrate the effectiveness of the proposed approach and validate the theoretical results.

On an abrasion-motivated fractal model

Abstract In this paper, we consider a fractal model motivated by the abrasion of convex polyhedra, where the abrasion is realised by chipping small neighbourhoods of vertices. After providing a formal description of the successive chippings, we show that the net of edges converge to a compact limit set under mild assumptions. Furthermore, we study the upper box-counting dimension and the Hausdorff dimension of the limiting object of the net of edges after infinitely many chipping.

Orbital motion control of an electrically charged spacecraft

In this paper, the orbital motion of an electrically charged spacecraft in the gravitational and magnetic fields of the Earth is investigated. The “direct magnetic dipole” is considered as a model of the geomagnetic field. The nonlinear non-autonomous system of differential equations of motion of the spacecraft center of mass in the Cartesian and spherical coordinate systems is derived. The analytical study of the influence of the Lorentz force on the orbital motion of a charged spacecraft is carried out. The approximate solution of the differential system is found. The results of numerical simulation of the spacecraft orbital motion based on the derived system of differential equations are presented. The analytical and numerical solutions are compared. The problem of stabilizing the spacecraft’s center of mass in the orbital plane is considered. Feedback control methods based on the use of jet engines are proposed. The technical justification of the proposed control methods is carried out. As a result, stabilization of an electrically charged spacecraft in a small neighborhood of the plane of the initial orbit is achieved. The motion of a spacecraft with a variable electric charge is considered. Methods of controlling orbital motion due to low thrust as a result of the Lorentz force effect are proposed.

Large-Kernel Central Block Masked Convolution and Channel Attention-Based Reconstruction Network for Anomaly Detection of High-Resolution Hyperspectral Imagery

In recent years, the rapid advancement of drone technology has led to an increasing use of drones equipped with hyperspectral sensors for ground imaging. Hyperspectral data captured via drones offer significantly higher spatial resolution, but this also introduces more complex background details and larger target scales in high-resolution hyperspectral imagery (HRHSI), posing substantial challenges for hyperspectral anomaly detection (HAD). Mainstream reconstruction-based deep learning methods predominantly emphasize spatial local information in hyperspectral images (HSIs), relying on small spatial neighborhoods for reconstruction. As a result, large anomalous targets and background details are often well reconstructed, leading to poor anomaly detection performance, as these targets are not sufficiently distinguished from the background. To address these limitations, we propose a novel HAD network for HRHSI based on large-kernel central block masked convolution and channel attention, termed LKCMCA. Specifically, we first employ the pixel-shuffle technique to reduce the size of anomalous targets without losing image information. Next, we design a large-kernel central block masked convolution to make the network pay more attention to the surrounding background information, enabling better fusion of the information between adjacent bands. This, coupled with an efficient channel attention mechanism, allows the network to capture deeper spectral features, enhancing the reconstruction of the background while suppressing anomalous targets. Furthermore, we introduce an adaptive loss function by down-weighting anomalous pixels based on the mean absolute error. This loss function is specifically designed to suppress the reconstruction of potentially anomalous pixels during network training, allowing our model to be considered an excellent background reconstruction network. By leveraging reconstruction error, the model effectively highlights anomalous targets. Meanwhile, we produced four benchmark datasets specifically for HAD tasks using existing HRHSI data, addressing the current shortage of HRHSI datasets in the HAD field. Extensive experiments demonstrate that our LKCMCA method achieves superior detection performance, outperforming ten state-of-the-art HAD methods on all datasets.

Finite-time event-triggered tracking control for quadcopter attitude systems with zero compensation technology

This paper primarily investigates the event-triggered tracking control problem for quadcopter attitude systems, utilizing finite-time zero compensation technology. Unlike existing research results, a zero compensation technology is proposed to solve non-affine control input problems such as saturation, dead zones, and gaps. The command filtered compensation technology is used to solve ’differential explosion’ and filtering errors. A novel Tanh type filter and a neural network are employed to approximate virtual control signals and account for un-modeled dynamics, respectively. Moreover, the finite-time convergence theory is used to prove that the state, tracking error, and filtered error compensation signals in the entire closed-loop system converge to an arbitrarily small neighborhood of the equilibrium origin. Finally, the advantages of the proposed control algorithm in improving tracking accuracy and reducing communication load were demonstrated through simulation.

Local Directional Difference and Relational Descriptor for Texture Classification

The local binary pattern (LBP) has been widely used for extracting texture features. However, the LBP and most of its variants tend to focus on pixel units within small neighborhoods, neglecting differences in direction and relationships among different directions. To alleviate this issue, in this paper, we propose a novel local directional difference and relational descriptor (LDDRD) for texture classification. Our proposed LDDRD utilizes information from multiple pixels along the radial direction. Specifically, a directional difference pattern (DDP) is first extracted by performing binary encoding on the differences between the central pixel and multiple neighboring pixels along the radial direction. Furthermore, by taking the central pixel as a reference, we extract the directional relation pattern (DRP) by comparing binary encodings representing different directions. Finally, we fuse the above DDP and DRP to form the LDDRD feature vector. Experimental results on six texture datasets reveal that our proposed LDDRD is effective and outperforms eight representative methods.

Relay Switching–Based Event‐Triggered Finite‐Time Tracking Control for Nonholonomic Systems: Theory and Experiment

ABSTRACTThis paper investigates the event‐triggered finite‐time trajectory tracking controller based on a type of chained‐form nonholonomic systems under unknown disturbances by utilizing relay switching technology. A key design idea is that the entire control design is grouped into two separated control stages to produce different finite‐time tracking controllers with correspondingly event‐triggered control rules. By using some nonlinear design methods, a relay switching–based event‐triggered finite‐time tracking control method is adopted to assure that the resulting closed‐loop tracking error system converges to an arbitrarily small neighborhood around zero within a finite time. All closed‐loop error system states keep bounded throughout the entire process. Simulation and experiment results demonstrate the rationality of the designed tracking control strategy.

Fuzzy adaptive asynchronous sampled-data consensus control for nonlinear multi-agent systems under DoS attacks

This article investigates the problem of fuzzy adaptive resilient asynchronous sampled-data consensus control (SDCC) for a class of uncertain nonlinear strict-feedback multi-agent systems (MASs) under denial-of-service (DoS) attacks and with a directed graph. Firstly, the upper bounds on the sampling intervals and a distributed sampled-data observer are proposed to estimate the leader's output and its high-order derivatives under DoS attacks. Then, the sufficient conditions to ensure the asymptotic convergence of the designed distributed sampled-data observer are established. Based on the distributed sampled-data observer and backstepping control design technique, a distributed fuzzy adaptive resilient control algorithm is developed. It is proved that the proposed control scheme can guarantee that the controlled MASs are stable, and the consensus errors converge to a small neighbourhood of zero. Finally, a simulation example on heterogeneous vehicular platoons verifies the feasibility of the proposed control scheme.

Event-Triggered Backstepping Control of Fractional-Order Chaotic Systems with Dead Zone Via Disturbance Observer

This paper comes up with an adaptive event-triggered tracking control scheme for a kind of fractional-order strict feedback nonlinear systems with actuator dead-zone inputs and uncertain external disturbances. The presented strategy can overcome the defect in standard backstepping control scheme which leads to the “explosion of complexity” problem of virtual signals, and strengthen the transmission efficiency by an event-triggered scheme. An error compensation mechanism is presented for promoting the tracking accuracy and reducing the effect filter error. The designed controller guarantees that the tracking error converges into a small neighborhood near the origin, and all closed-loop signals are bounded. Moreover, Zeno behavior will be avoided. The numerical simulation is given to verify the accuracy and effectiveness of the designed technique.

An adaptive dynamic surface control strategy for suppressing pathological oscillations in a neural mass model

Pathological oscillations that have a frequency in the [Formula: see text] band are widely recognized to be involved in Parkinson’s disease. Now, we present an adaptive dynamic surface control strategy for suppressing pathological oscillations that exist in the Parkinsonian state. First, the interactions between the subthalamic nucleus and external globus pallidus are fully considered and establish a neural mass model of Parkinson’s disease. Next, by reasonable state transformation, suppressing pathological oscillations can be converted into a tracking control study of a pure-feedback nonlinear system. Moreover, the dynamic surface control technique adopted reduces the dimensionality of the neural network input and effectively eliminates the complexity explosion problem commonly associated with existing methods. By Lyapunov stability analysis, it can be obtained that all the signals of the resulting closed-loop system are bounded, and the tracking error converges to a small neighborhood of zero. Finally, the simulation results demonstrate the effectiveness of the designed control strategy. This work may provide an effective approach to closed-loop deep brain stimulation optimization for the alleviation of the Parkinsonian state.

The Parameter Optimization of Support Vector Machine with Genetic Algorithm in Risk Early Warning Models

Machine Learning algorithms are widely used by lenders in risk early warning models. With Machine Learning, the risk levels of individual and corporate customers are determined at the account and customer level. Lenders want to manage risk by evaluating the payment performance of customer or account with the help of Machine Learning algorithms. Banks, which have an important place among lenders, develop risk early warning models with the help of learning algorithms using customer information. In the development process of risk early warning models, while banks generally use customer information and credit bureau information for the individual segment, they use financial, non-financial and behaviour-based information for the corporate segment. In this study, it is planned to develop a risk early model for customers in corporate service segment. For the customers of corporate service segment, Balance Sheet and Income Statement items were used and the financial ratios were calculated for risk early warning models. In the development of risk early warning models, Mutual Information method was used as a novel feature selection approach and Support Vector Machine method (linear function, radial basis function and sigmoid function) was used as a supervised learning approach. By changing the neighbourhood metric (k), important patterns were discovered with the Mutual Information method in feature selection process. The optimal C and gamma parameters for Support Vector Machine models have been tried to be determined with the Genetic Algorithm, which is among the Meta-Heuristic algorithms. In order to find the optimal metrics in this study, the metric values for all parameters of the SVM model (function specific) have been kept quite wide. In this dataset of corporate service customers, the small neighbourhood metric has been found to have a significant impact on model learning and performance.

Event-Triggered Fuzzy Adaptive Predefined-Time Control for Fractional-Order Nonlinear Systems with Time-Varying Deferred Constraints and Its Application

This paper focuses on the fuzzy adaptive predefined-time control for fractional-order nonlinear systems with time-varying deferred constraints. First, a modified dynamic surface control technique is introduced to address the problem of computational complexity exposed in the backstepping framework, and the interval type-2 fuzzy logic systems are applied to model the unknown nonlinearities of the systems. Next, a shifting function and the barrier Lyapunov function with variational barrier bounds are formulated to deal with the constraints issue. Particularly, the constraint conditions can be satisfied within a predetermined time, even if they are transgressed initially. Furthermore, a switching threshold event-triggered controller is devised to balance the control energy and communication resources. With the help of the predefined-time stability criterion, it is proven that the presented predefined-time event-triggered controller can ensure that all the signals involved in the closed-loop system are bounded and the tracking error fluctuates to a small neighborhood of the origin in a predefined-time interval. Finally, two simulation examples are provided to confirm the effectiveness of the put-forward control algorithm.

Practical tracking control for a class of uncertain MIMO nonlinear systems with unmatched disturbances

This paper studies the output tracking control problem for a class of uncertain MIMO nonlinear systems. The motivation comes from how to deal with unknown coupling system dynamics between subsystems and achieve the desired tracking when the system has parameter uncertainties and external disturbances. The difficulty is to guarantee that tracking errors enter an arbitrarily prescribed neighbourhood within a finite time. Based on the construction of a time-varying dynamic gain associated with tracking errors and the effective manipulation of nonlinear parametrization, a novel robust feedback controller is built up to ensure the boundedness of all closed-loop signals and the convergence of tracking errors to a small neighborhood approaching the origin in a finite time. Finally, the feasibility of control strategy is verified by numerical and practical examples.