Search Results (13)

This paper presents a novel dynamic adaptive event-triggered mechanism (DAETM) for addressing actuator saturation in leader–follower fractional-order nonlinear multi-agent networked systems (FONMANSs). By utilizing a sector-bounded condition approach and a convex hull representation technique, the proposed method effectively addresses the effects of actuator saturation. This results in less conservative linear matrix inequality (LMI) criteria, guaranteeing asymptotic consensus among agents within the FONMANS framework. The proposed sufficient conditions are computationally efficient, requiring only simple LMI solutions. The effectiveness of the approach is validated through practical applications, such as synchronous generators within a FONMANS framework, where it demonstrates superior performance and robustness. Additionally, comparative studies with Chua’s circuit system enhance the robustness and efficiency of control systems compared to existing techniques. These findings highlight the method’s potential for broad application across various multi-agent systems, particularly in scenarios with limited communication and actuator constraints. The proposed approach enhances system performance and provides a robust, adaptive control solution for dynamic and uncertain environments. Full article

Extraction of vectorized building outlines from high-resolution remote sensing images is highly useful for various application fields, such as map creation and urban planning. However, this process is often complicated by external factors, such as trees and shadows, which cause issues, such as excessive node redundancy, jagged lines, and unclear corner points. In this study, a multilevel regularization method was designed for building outlines, including the “overall–local–detail” levels. First, overall regularization was performed by combining the minimum bounding rectangle of the building outline with the Hausdorff distance method. Next, based on the convex hull of the building outline and the distribution characteristics of nodes along the outline, the building outline was divided into multiple line chains and classified for local regularization. Finally, the details of the building outline were processed, with the parallel and perpendicular characteristics enhanced to obtain the final regularization results. The experimental results showed that the proposed method effectively enhances the edge representation accuracy of building outlines and significantly improves the accuracy and regularity of building edges. Furthermore, it strengthens the orthogonal characteristics of building outlines, providing more accurate representations of true building outlines. Full article

This paper considers the regional consensus problem for multi-agent systems with actuator saturation. By utilizing the theory of convex set, a novel multiple nonlinear feedback control protocol is presented, which can effectively reduce the conservatism in dealing with saturated nonlinear input. In order to obtain a larger estimate on the domain of consensus, the composite Laplacian quadratics function is constructed to derive sufficient conditions for the consensus of multi-agent systems. In addition, an alternative convex hull representation is employed to further enlarge the above-mentioned domain of consensus. Finally, a numerical simulation case study illustrates the validity as well as the superiority of the proposed approaches. Full article

The event-triggered consensus of multi-agent systems received extensive attention in academia and industry perspectives since it ensures all agents eventually converge to a stable state while reducing the utilization of network communication resources effectively. However, the practical limitation of the actuator could lead to a saturation phenomenon, which may degrade the systems or even induce instability. This paper plans to offer a detailed review of some recent results in the event-triggered consensus of multi-agent systems subject to actuator saturation. First, the multi-agent system model with actuator saturation constraints is given, and the basic framework of the event-triggering mechanism is introduced. Second, representative results reported in recent valuable papers are reviewed based on methods for dealing with saturated terms, including low-gain feedback, sector-bounded conditions, and convex hull representations. Finally, some challenging topics worthy of research efforts are dicussed for future research. Full article

Point clouds provide a compact representation of 3D shapes however, the imperfections in acquisition processes corrupt point clouds by noise and give rise to a decrease in their power for representing 3D shapes. Learning-based denoising methods operate displacement prediction and suffer from shrinkage and outliers. In addition, they require pre-aligned datasets. In this paper, we present a self-supervised learning-based method, Canonical Mapping and Denoising Network (CMD-Net), and address category-level 3D shape denoising through canonicalization. We formulate denoising as a 3D semantic shape correspondence estimation task where we explore ordered 3D intrinsic structure points. Utilizing the convex hull of the explored structure points, the corruption on objects’ surfaces is eliminated. Our method is capable of canonicalizing noise-corrupted clouds under arbitrary rotations, therefore circumventing the requirement on pre-aligned data. The complete model learns to canonicalize the input through a novel transformer that serves as a proxy in the downstream denoising task. The analyses on the experiments validate the promising performance of the presented method on both synthetic and real data. We show that our method can not only eliminate corruption, but also remove clutter from the test data. We additionally create a novel dataset for the problem in hand and will make it publicly available in our project web-page. Full article

At the heart of both lossy compression and clustering is a trade-off between the fidelity and size of the learned representation. Our goal is to map out and study the Pareto frontier that quantifies this trade-off. We focus on the optimization of the Deterministic Information Bottleneck (DIB) objective over the space of hard clusterings. To this end, we introduce the primal DIB problem, which we show results in a much richer frontier than its previously studied Lagrangian relaxation when optimized over discrete search spaces. We present an algorithm for mapping out the Pareto frontier of the primal DIB trade-off that is also applicable to other two-objective clustering problems. We study general properties of the Pareto frontier, and we give both analytic and numerical evidence for logarithmic sparsity of the frontier in general. We provide evidence that our algorithm has polynomial scaling despite the super-exponential search space, and additionally, we propose a modification to the algorithm that can be used where sampling noise is expected to be significant. Finally, we use our algorithm to map the DIB frontier of three different tasks: compressing the English alphabet, extracting informative color classes from natural images, and compressing a group theory-inspired dataset, revealing interesting features of frontier, and demonstrating how the structure of the frontier can be used for model selection with a focus on points previously hidden by the cloak of the convex hull. Full article

Polar performance diagrams are commonly used to predict the performance of a sailing vessel under given wind conditions. They are, in particular, an essential part of robotic sailing vessels and a basis for weather routing algorithms. In this paper we introduce a new framework for scientific work with such diagrams, which we make available as an open source Python package. It contains a model for the creation of polar performance diagrams from measurement data and supports different representations of polar performance diagrams for different tasks. The framework also includes several methods for the visualisation of polar performance diagrams, for example for scientific publications. Additionally, the presented framework solves basic tasks for the future development of weather-routing algorithms in a far more general manner than other methods did previously: it provides the calculation of costs of a sailing trip using custom cost functions, suggestions of optimal steering using convex hull calculations and a more flexible calculation of isochrone points, using custom weather models. Altogether, the presented framework allows future researchers to more easily handle polar performance diagrams. The corresponding Python package is compatible with various established file formats. Full article

The Hough transform is commonly used for detecting linear features within an image. A line is mapped to a peak within parameter space corresponding to the parameters of the line. By analysing the shape of the peak, or peak locus, within parameter space, it is possible to also use the line Hough transform to detect or analyse arbitrary (non-parametric) curves. It is shown that there is a one-to-one relationship between the curve in image space, and the peak locus in parameter space, enabling the complete curve to be reconstructed from its peak locus. In this paper, we determine the patterns of the peak locus for closed curves (including circles and ellipses), linear segments, inflection points, and corners. It is demonstrated that the curve shape can be simplified by ignoring parts of the peak locus. One such simplification is to derive the convex hull of shapes directly from the representation within the Hough transform. It is also demonstrated that the parameters of elliptical blobs can be measured directly from the Hough transform. Full article

The evaluation of geometric defects is necessary in order to maintain the integrity of structures over time. These assessments are designed to detect damages of structures and ideally help inspectors to estimate the remaining life of structures. Current methodologies for monitoring structural systems, while providing useful information about the current state of a structure, are limited in the monitoring of defects over time and in linking them to predictive simulation. This paper presents a new approach to the predictive modeling of geometric defects. A combination of segments from point clouds are parametrized using the convex hull algorithm to extract features from detected defects, and a stochastic dynamic model is then adapted to these features to model the evolution of the hull over time. Describing a defect in terms of its parameterized hull enables consistent temporal tracking for predictive purposes, while implicitly reducing data dimensionality and complexity as well. In this study, two-dimensional (2D) point clouds analogous to information derived from point clouds were firstly generated over simulated life cycles. The evolutions of point cloud hull parameterizations were modeled as stochastic dynamical processes via autoregressive integrated moving average (ARIMA) and vectorized autoregression (VAR) and compared against ground truth. The results indicate that this convex hull approach provides consistent and accurate representations of defect evolution across a range of defect topologies and is reasonably robust to noisy measurements; however, assumptions regarding the underlying dynamical process play a significant the role in predictive accuracy. The results were then validated on experimental data from fatigue testing with high accuracy. Longer term, the results of this work will support finite element model updating for predictive analysis of structural capacity. Full article

SG-Bézier curves have become a useful tool for shape design and geometric representation in computer aided design (CAD), owed to their good geometric properties, e.g., symmetry and convex hull property. Aiming at the problem of approximate degree reduction of SG-Bézier curves, a method is proposed to reduce the n-th SG-Bézier curves to m-th (m < n) SG-Bézier curves. Starting from the idea of grey wolf optimizer (GWO) and combining the geometric properties of SG-Bézier curves, this method converts the problem of multi-degree reduction of SG-Bézier curves into solving an optimization problem. By choosing the fitness function, the approximate multi-degree reduction of SG-Bézier curves with adjustable shape parameters is realized under unrestricted and corner interpolation constraints. At the same time, some concrete examples of degree reduction and its errors are given. The results show that this method not only achieves good degree reduction effect, but is also easy to implement and has high accuracy. Full article

Although shape similarity is one fundamental element in coastline generalization quality, its related research is still inadequate. Consistent with the hierarchical pattern of shape recognition, the Dual-side Bend Forest Shape Representation Model is presented by reorganizing the coastline into bilateral bend forests, which are made of continuous root-bends based on Constrained Delaunay Triangulation and Convex Hull. Subsequently, the shape contribution ratio of each level in the model is expressed by its area distribution in the model. Then, the shape similarity assessment is conducted on the model in a top–down layer by layer pattern. Contrast experiments are conducted among the presented method and the Length Ratio, Hausdorff Distance and Turning Function, showing the improvements of the presented method over the others, including (1) the hierarchical shape representation model can distinguish shape features of different layers on dual-side effectively, which is consistent with shape recognition, (2) its usability and stability among coastlines and scales, and (3) it is sensitive to changes in main shape features caused by coastline generalization. Full article

Shape similarity measurement model is often used to solve shape-matching problems in geospatial data matching. It is widely used in geospatial data integration, conflation, updating and quality assessment. Many shape similarity measurements apply only to simple polygons. However, areal entities can be represented either by simple polygons, holed polygons or multipolygons in geospatial data. This paper proposes a new shape similarity measurement model that can be used for all kinds of polygons. In this method, convex hulls of polygons are used to extract boundary features of entities and local moment invariants are calculated to extract overall shape features of entities. Combined with convex hull and local moment invariants, polygons can be represented by convex hull moment invariant curves. Then, a shape descriptor is obtained by applying fast Fourier transform to convex hull moment invariant curves, and shape similarity between areal entities is measured by the shape descriptor. Through similarity measurement experiments of different lakes in multiple representations and matching experiments between two urban area datasets, results showed that the method could distinguish areal entities even if they are represented by different kinds of polygons. Full article

A novel Symmetric Sparse Representation (SSR) method has been presented to solve the band selection problem in hyperspectral imagery (HSI) classification. The method assumes that the selected bands and the original HSI bands are sparsely represented by each other, i.e., symmetrically represented. The method formulates band selection into a famous problem of archetypal analysis and selects the representative bands by finding the archetypes in the minimal convex hull containing the HSI band points (i.e., one band corresponds to a band point in the high-dimensional feature space). Without any other parameter tuning work except the size of band subset, the SSR optimizes the band selection program using the block-coordinate descent scheme. Four state-of-the-art methods are utilized to make comparisons with the SSR on the Indian Pines and PaviaU HSI datasets. Experimental results illustrate that SSR outperforms all four methods in classification accuracies (i.e., Average Classification Accuracy (ACA) and Overall Classification Accuracy (OCA)) and three quantitative evaluation results (i.e., Average Information Entropy (AIE), Average Correlation Coefficient (ACC) and Average Relative Entropy (ARE)), whereas it takes the second shortest computational time. Therefore, the proposed SSR is a good alternative method for band selection of HSI classification in realistic applications. Full article