Region Of Attraction Research Articles

Fostering Tourism Through Regional Culture in the Russian–Chinese Borderland: A Case Study of Zabaykalsky Krai and Northeast China

The article focuses on the cultural and civilisational potential of Russian eastern borders and China border regions. The issues raised in this article seem to be topical in the context of two circumstances: first, tourist contacts have undergone significant transformations in the context of the COVID-19 pandemic, and second, the aggravating situation with the emergence of barriers to entry into the European tourism space makes China one of the most attractive regions for tourism development. The concept of ‘border’ appears as a unique sociocultural space where regional culture functioning is mediated by the influence of three cultural dimensions (national, local and foreign). In the era of digitalisation, online platforms act as a modern space for the concentration and accumulation of tourist content. Updating the work on online platforms can become one of the ways of solving the identified problems in the border tourism sector. The article gives a possible solution to the above issues based on the original model of ‘regional cultures dialogueness in the borderland’, its integration into the concept of tourism development in the border areas. The authors suggest recommendations on the vector of modern state policy regarding the development of tourism initiatives in the Russian–Chinese border area.

Study of self-assembly between two magnetic particle chains in magnetorheological fluids

The self-assembly behavior of individual magnetic particles in magnetorheological liquids has been extensively analyzed in previous studies, but the self-assembly behavior between chains of magnetic particles has rarely been investigated. In this paper, the self-assembly mechanism between chains of magnetic particles is investigated using simulation and experimental methods. Firstly, a two-dimensional coupling simulation numerical model of particle-magnetic field-flow field is constructed by analyzing the magnetic force, fluid force and contact interaction force between magnetic particles. The accuracy of the simulation model was verified through experiments. Then the attraction and repulsion dividing line of two magnetic particle chains are analytically calculated by simulation combined with parametric scanning. And analyze the law of the influence of the number of magnetic particles between magnetic particle chains on the attraction and repulsion dividing line. Finally, the different self-assembly behaviors that occur when magnetic particle chains are in different regions of attraction and repulsion between them are experimentally verified. Thus, this study provides new insights into the self-assembly mechanism between chains of magnetic particles in magnetorheological fluids in terms of the effect of the number of magnetic particles on the attraction–repulsion dividing line.

Dynamics of the system of delay differential equations with nonlinearity having a simple behavior at infinity

In this paper, we study the dynamics of a system of nonlinear differential equations with delay. We find stable equilibrium states and regions of attraction to them in the phase space of the system, as well as stable and unstable homogeneous and inhomogeneous cycles. We find conditions on the parameters of the system for multistability. We show that the coupling parameter has a decisive influence on the dynamics of the system. We find regions of the parameters of the system and extensive sets of initial conditions such that if we take these values of the parameters and any initial conditions from these sets, the system will have simple dynamics.

Sampled-Data Exponential Synchronization of Complex Dynamical Networks with Saturating Actuators.

This paper investigates the problem of exponential synchronization control for complex dynamical systems (CDNs) with input saturation. Considering the effects of transmission delay, a memory sampled-data controller is designed. A modified two-sided looped functional is constructed that takes into account the entire sampling period, which includes both current state information and delayed state information. This functional only needs to be positive definite at the sampling instants. Sufficient criteria and the controller design method are provided to ensure the exponential synchronization of CDNs with input saturation under the influence of transmission delay, as well as the estimation of the basin of attraction. Additionally, an optimization algorithm for enlarging the region of attraction is proposed. Finally, a numerical example is presented to verify the effectiveness of the conclusion.

Study of sterically crowded alkanes: assessment of non-empirical density functionals including double-hybrid cost-effective methods.

We theoretically study the homolytic dissociation reactions of sterically crowded alkanes of increasing size, carrying three different (bulky) substituents such as tert-butyl, adamantane, and [1.1.1]propellanyl, employing a family of parameter-free functionals ranging from semi-local, to hybrid and double-hybrid models. The study is complemented with the interaction between a pair of HC(CH3)3 molecules at repulsive and attractive regions, as an example of a system composed by a pair of weakly bound sterically crowded alkanes. We also assessed the effect of incorporating reliable dispersion corrections (i.e., D4 or NL) for all the functionals assessed, as well as the use of a tailored basis set (DH-SVPD) for non-covalent interactions, which provides the best trade-off between accuracy and computational cost for a seemingly extended applications to branched or crowded systems. Overall, the PBE-QIDH/DH-SVPD and r2SCAN-QIDH/DH-SVPD methods represent an excellent compromise providing relatively low, and thus very competitive, errors at a fraction of the cost of other quantum-chemical methods in use.

Large‐signal stability analysis for hybridized vehicular power supply systems of rolling stocks

AbstractHybridized vehicular power supply (HVPS) are acquiring widespread adoption in various applications such as providing power for passenger or heavy‐duty electric vehicles, more‐electric ships, electrified rolling stocks, and more. Stability analysis is a critical issue for HVPS, but it presents significant challenges due to their prominent high‐dimensional and nonlinear characteristics. This paper presents a large‐signal stability analysis scheme for HVPS of rolling stocks, enabling the assessment of system stability under sudden load changes. Based on the state‐space averaging method, a mathematical model for the large‐signal behavior of the system is established. Subsequently, the small‐signal stability parameter range of the system is determined by analyzing the eigenvalues of the Jacobian matrix. To further analyze the stability of the system during large‐signal disturbances, a nonlinear decoupling transformation approach is employed to decompose the original high‐order state equations into multiple lower‐order equations. For the decoupled lower‐order subsystems, their stability is analyzed using phase portrait, and the region of attraction (ROA) is determined using the inverse trajectory method. Based on the stability analysis results, the controller is enhanced to bring the points outside the ROA back within it, thereby mitigating the transient instability phenomenon of the system. The effectiveness of the proposed method was demonstrated using two case studies.

Consecutive attractive local regions – bidirectional long short-term memory for trip destination prediction

We propose a sequence-to-sequence model to capture a partial trajectory that contains a few attractive local regions and forecast its destination. Therefore, the main goal of this work is to predict the destination, given the trip’s trajectory, effectively by learning from its attractive local sub-trajectory only. Conceptually, the proposed model incorporates Bidirectional Long Short-Term Memory (BiLSTM) for finding frequent trip trajectories and a Consecutive Attractive Local Regions (CALR) mechanism for only taking their few attractive local regions, called CALR-BiLSTM. Existing related works focused on observing whole regions of each trip trajectory at once to decide its attractive ones from a Global Attention Mechanism (GAM). However, GAM may hold similar attractive sub-trajectories for different destinations, which leads to worse predictions. To overcome the issue, the proposed model observes the entire trip trajectory part by part within a small window, such as focusing on a few regions that are attractive. In this work, we demonstrated the proposed model on large public datasets. As a result, we can enjoy the proposed model as the winner against the state-of-the-art models. Moreover, we present ablation studies on various recurrent neural networks and attention mechanisms to ensure the proposed model is in the right settings.

Multiple Sliding Modes Enlarge Basins of Attraction in Switched Control Systems

This paper investigates the role of hidden dynamics in influencing the stability of sliding solutions within control-switched systems. By employing cell-mapping methods, we provide numerical evidence that incorporating hidden dynamics on the switching manifold can extend the sliding dynamics, resulting in a significant expansion of the system’s region of attraction. As representative examples, we considered control systems with stable and unstable dynamics converging around multiple equilibrium points.

Fault‐tolerant control of unmanned marine vehicles with unknown parametric dynamics via integral sliding mode output feedback control

AbstractThis paper focuses on fault‐tolerant control (FTC) for unmanned marine vehicles (UMVs) subject to unknown parametric dynamics, thruster faults, and external disturbances. A novel FTC strategy based on the integral sliding mode output feedback method is proposed. Based on a high gain compensator and output information, a novel integral sliding mode fault‐tolerant controller is constructed to guarantee the dynamic positioning (DP) of UMVs. An attraction region that is related to the known positive constants with respect to dynamic uncertainties has been revealed for the first time. Finally, the closed‐loop stability can be guaranteed from the every initial time in despite of unknown parametric dynamics, thruster faults, and external disturbances. Simulation though a typical floating production ship model has verified the effectiveness of the proposed method.

Physics-informed neural networks for phase locked loop transient stability assessment

A significant increase in renewable energy production is necessary to achieve the UN’s net-zero emission targets for 2050. Using power-electronic controllers, such as Phase Locked Loops (PLLs), to keep grid-tied renewable resources in synchronism with the grid can cause fast transient behavior during grid faults leading to instability. However, assessing all the probable scenarios is impractical, so determining the stability boundary or region of attraction (ROA) is necessary. However, using EMT simulations or Reduced-order models (ROMs) to accurately determine the ROA is computationally expensive. Alternatively, Machine Learning (ML) models have been proposed as an efficient method to predict stability. However, traditional ML algorithms require large amounts of labeled data for training, which is computationally expensive. This paper proposes a Physics-Informed Neural Network (PINN) architecture that accurately predicts the nonlinear transient dynamics of a inverter with a PLL-based controller under fault with less labeled training data. The proposed PINN algorithm can be incorporated into conventional simulations, accelerating EMT simulations or ROMs by over 100 times. The PINN algorithm’s performance is compared against a ROM and an EMT simulation in PSCAD for the CIGRE benchmark model C4.49, demonstrating its ability to accurately approximate trajectories and ROAs of a inverter with a PLL-based controller under varying grid impedance.

Expanding the Areas of Attraction of Solutions to Singularly Perturbed Equations

In this paper, a singularly perturbed equation of the first order is considered, the concept of a region of attraction (DO) of the solution of a singularly perturbed equation to the solution of an unperturbed equation is introduced, and the existence of an OA is proved. The problem has been set about the possibility of expanding the areas of attraction of VCA solutions. It has been proven that if there is a region of attraction, then it can be expanded to the boundary of the region under consideration. In the proof, geometric constructions were used, using the level line of conjugate-harmonic functions, the method of successive approximations and methods of asymptotic estimates.

Estimating the region of attraction of integral delay equations

Abstract We present estimates of the region of attraction of a class of non-linear integral delay equations. The approach follows the same lines as the Lyapunov method by the first approximation for estimating the attraction region of ordinary and delay differential equations, which uses Lyapunov functions or Lyapunov functionals associated with the linear part of the non-linear equations. The results are illustrated by application problems to the propagation of electric pulses in the heart dynamics and non-linear predictor control.

A robust interpolated model predictive control based on recurrent neural networks for a nonholonomic differential-drive mobile robot with quasi-LPV representation: computational complexity and conservatism

This paper presents an improved Model Predictive Control (MPC) for path tracking of a nonholonomic mobile robot with a differential drive. Nonlinear dynamics and nonholonomic constraints make the optimisation problem of MPC for the robot challenging. Nonlinear dynamics of the robots are expressed by a Linear Parameter Varying (LPV), and a Recurrent Neural Network (RNN) solves the constrained optimisation problem, providing optimal velocities. Moreover, an interpolation-based approach has been introduced to augment the region of attraction. The algorithm ensures stability in the presence of bounded disturbances through the inclusion of free control moves in the control law. The controller efficiency has been evaluated in two scenarios in a hospital setting. The simulation results illustrate that the proposed method performs better than nonlinear MPC and standard LPV-based MPC in terms of computational cost, disturbance rejection, and region of attraction.

Conditions for ultimate boundedness of solutions and permanence for a hybrid Lotka–Volterra system

In the paper, a generalized Lotka–Volterra – type system with switching is considered. The conditions for the ultimate boundedness of solutions and the permanence of the system are studied. With the aid of the direct Lyapunov method, the requirements for the switching law are established to guarantee the necessary dynamics of the system. An attractive compact invariant set is constructed in the phase space of the system, and a given region of attraction for this set is provided. A distinctive feature of the work is the use of a combination of two different Lyapunov functions, each of which plays its own special role in solving the problem.

Estimating the region of attraction of wind integrated power systems based on improved expanding interior algorithm

AbstractThis paper proposes an improved expanding interior algorithm (EIA) to estimate the region of attraction (ROA) of power systems with wind power generation based on sum of squares (SOS) programming. An ordinary differential equation (ODE) model is derived for the doubly‐fed induction generator‐based wind turbine (DFIGWT), which is named as an enhanced synchronous‐generator‐mimicking (ESGM) model. The ESGM model bridges the gap between the requirement of an ODE model in ROA estimation and the conventional differential‐algebraic equation (DAE) model of the DFIGWT system. The ESGM model is able to accurately reflect the low frequency dynamics of the DFIGWT. Moreover, an improved EIA is designed to estimate the ROA based on SOS programming, which has higher efficiency than the existing ROA estimation algorithms based on SOS programming. It is able to adaptively search for the Lyapunov function and obtain an optimal estimation of the ROA in an iterative process. The accuracy and efficiency of this algorithm are verified in three test systems composed of DFIGWTs and synchronous generators (SGs). The morphological changes in the ROA of the test systems caused by the penetration of DFIGWT are examined.

Active Flutter Suppression: Quantification of Performance Loss Due to Actuator Saturation

Active flutter suppression technologies have the potential to lead to major weight savings while keeping the envisaged flight envelope for the future generation of commercial aircraft. Since the stabilization of aeroelastic systems undergoing flutter instabilities is strongly affected by actuators’ characteristics and delays in the closed loop, the degradation of closed-loop performance due to actuators’ nonlinearities must be thoroughly understood. Comparisons between the region of attraction and the controllable region can support the quantification of performance loss due to common actuators’ nonlinearities, such as amplitude and rate limits. At first, this paper illustrates a numerically robust algorithm for the full characterization of the controllable region of a generic unstable system under input amplitude and rate constraints. Secondly, the concept of region of attraction is expanded to assess the boundedness of the closed-loop response in the presence of input saturation and atmospheric disturbances. These concepts are here employed to define two nonlinear performance measures that quantify the performance loss due to actuators’ saturation in an unstable aeroelastic system stabilized by a flutter suppression controller. The approach is demonstrated on a realistic aeroelastic system for which different H2 and H∞ output feedback controllers are synthesized to augment the damping of the critical flutter mode.

Trajectory-based clustering for enhanced attractive region mining in urban taxi services

ABSTRACT Trajectory data, increasingly available due to location tracking technologies, holds immense potential for intelligent traffic management and urban planning. Traditional 'attractive region' mining methods often rely on density-based clustering, neglecting the inherent path information within trajectories. To address this, we propose a novel graph-based approach for attractive region discovery. By transforming trajectory data into graphs, we effectively leverage path and connectivity information for clustering with locality-sensitive hashing. Our study introduces the pARM, pgARM, and hgARM algorithms, demonstrating their superiority over GridDBScan through experiments on real-world datasets. We employ Davies–Bouldin metric and visualization techniques to highlight the robustness of our approach, especially for datasets with varied degree distributions. Although our method may have slightly longer processing times for smaller grid sizes, it achieves execution times comparable to GridDBScan for larger grids. We rigorously analyze performance variations within our algorithms using execution time, clustering coefficient, and modularity scores, providing guidance for their optimal application.

Stabilisation of four types of underactuated systems: a FAS approach

ABSTRACT In this paper, four general types of time-varying underactuated systems (UASs) are proposed and investigated with the fully-actuated system (FAS) approach. The proposed UASs consist of both the first-order and the second-order ones, and cover a very wide range of UASs. FAS models for all these types of UASs are obtained under very mild assumptions, and corresponding homeomorphism or diffeomorphism transformations and sets of feasibility are also established. Governed by the FAS theory, once a FAS model of a system is obtained, a stabilising controller for the system can then be easily designed. Particularly, in the case that the set of feasibility coincides with the whole initial value space, a global FAS model is produced for which (and also the original system) global exponential stabilisation is immediately achieved. Otherwise, a sub-FAS with a feasible set is produced for which a sub-stabilising controller can be immediately designed. Meanwhile, a subset in the system initial value space, which is called the region of exponential attraction (REA), is characterised, such that all the solutions of converted sub-FAS starting from this domain are driven exponentially to the origin within the feasible set. Furthermore, in the case that the set of feasibility, or the REA, contains the origin as only a boundary point, the system possesses a ‘nonholonomic’ feature. Several examples are proposed to demonstrate the proposed approach and the power of the FAS approach.

A unified controller of global trajectory tracking and posture regulation for a car‐like mobile robot

SummaryThis work proposes a smooth time‐varying controller for trajectory tracking and posture regulation problems of car‐like mobile robots (CLMR). Currently, few studies focus on the control problems of CLMR's kinematic model. Global trajectory tracking or global posture stabilization controller for CLMR has not yet been proposed. In this study, we propose a global trajectory tracking controller for CLMR for the first time. By setting a specific reference trajectory, the controller is generalized to the posture stabilization task. Obstacle avoidance is also taken into consideration in posture stabilization task. Unlike the prototypical method of transforming the model into a nonholonomic chained‐form system, the proposed method is designed based on the original tracking error equation. Therefore our approach does not have singularities and has a global attraction region. Furthermore, the global convergence of the proposed controllers is strictly proved using the proof by contradiction and Barbalat's lemma. Finally, simulated and actual experiments on a car‐like robot demonstrate the effectiveness of the proposed control scheme.

Prospects for the development of individual tourism in Normandy

In this article, on the basis of statistical data and through the use of applied research methods, the main characteristics of Normandy as an attractive tourist region in the North-West of France were presented and analyzed. The article also presented some provisions of the strategic program for the development of individual tourism in Normandy, its goals and measures to achieve these goals. General conclusions are given on the current state of affairs in Normandy in the field of tourism.