Region Of Attraction Research Articles

Natural tourist resources in the Stara planina tourist region (Bulgaria)

Abstract The Stara planina tourist region is one of the most attractive regions for tourism in Bulgaria and one of the few that have almost year-round tourist activities. The outline of the area includes the mountain of the same name, but also the Pre-Balkan. This fact predetermines the exceptional richness and diversity of natural tourist resources. Here are some of the largest broad-leaved forests in the country, waterfalls, bizarre rock formations, etc. The relatively well-preserved natural environment is a prerequisite for the presence of exceptional biodiversity, as well as a significant number of protected areas. The region is specialized mainly in mountain tourism, including recreation, mountain trekking, rural and ecotourism. Due to the scarce tourist infrastructure, ski tourism still lags behind in its development compared to other mountain regions in the country. Very often, the Stara planina Region is primarily identified with its cultural and historical heritage, while its natural features remain in the background. Regardless of this, and as a result of the more intense tourist load, the problem of protecting natural tourist resources from the growing anthropogenic pressure is gaining special relevance. There is also an urgent need to identify and evaluate the prospects for sustainable development of the tourism industry in the region. The purpose of the present study is to valorize the natural tourist resources of the Stara planina tourist region and to provide guidelines for their sustainable use.

Inertial wave attractors in librating cuboids

Perturbed rapidly rotating flows are dominated by inertial oscillations, with restricted group velocity directions, due to the restorative nature of the Coriolis force. In containers with some boundaries oblique to the rotation axis, the inertial oscillations may focus upon reflections, whereby their energy increases whilst their wavelength decreases and their trajectories focus onto attractor regions. In a linear inviscid setting, these attractors are Delta-like distributions. The linear inviscid setting is obtained formally by setting both Ekman number ${E}$ (ratio of inertial to viscous time scales) and Rossby number ${Ro}$ (non-dimensional amplitude of the forcing that drives the inertial oscillations) to zero. These settings raise fundamental questions, in particular concerning the nature of energy dissipation in the vanishing Ekman number regime. Here, we consider a simple container geometry, a rectangular cuboid, in which the direction of the rotation axis is oblique to four of its walls, subject to librational forcing (small-amplitude harmonic oscillations of the rotation rate). This geometry allows for accurate and efficient direct numerical simulations of the three-dimensional incompressible Navier–Stokes equations with no-slip boundary conditions using a spectral-Galerkin spatial discretisation along with a third-order temporal discretisation. Solutions with Ekman and Rossby numbers as small as ${E}={Ro}=10^{-8}$ reveal many details of how the inertial oscillations focus, at the libration frequency considered, onto attractors, and how the focusing leads to increased localised nonlinear and dissipative processes as ${E}$ and ${Ro}$ are reduced. Even for extremely small forcing amplitudes, nonlinear effects have important dynamic consequences for the attractors.

Circle-Inspired Sine Cosine Optimization-Enabled CRF-RNN and ZFNet for Brain Tumor Segmentation and Classification Using MRI Images

The segmentation and classification of brain tumor are a attractive regions, which distinguish tumor as well as nontumor cells for identifying a level of tumor. Segmentation and classification from MRI images is a great challenge due to their altering image sizes and vast databases. Various schemes are designed for the segmentation and classification of the brain tumor, but these methods failed to offer better classification accuracy and decision-making. Here, Circle-inspired sine cosine Optimization_conditional random field-recurrent neural network (CISCO-CRF-RNN) and CISCO-Zeiler and Fergus network (CISCO-ZFNet) are introduced for brain tumor segmentation and classification. A pre-processing phase in this research is executed by the median filter to eliminate noises from an image. The segmentation is done by CRF-RNN, which is trained by CISCO. Furthermore, CISCO is newly introduced by incorporation of Circle-Inspired Optimization Algorithm (CIOA) and Sine Cosine Algorithm (SCA). Thereafter, image augmentation is performed utilizing some image augmentation techniques, and thereafter, features namely statistical features, Convolutional Neural Network (CNN) features, haralick features, pyramid histogram of orientation gradients (PHoG), and Local Vector Pattern (LVP) are extracted. Finally, the classification of brain tumor is accomplished utilizing ZFNet, which is tuned using CISCO. In addition, CISCO-CRF-RNN obtained maximal segmentation accuracy of 90.6% whereas CISCO-ZFNet achieved maximum pixel accuracy, negative predictive value (NPV), positive predictive value (PPV), and True positive rate TPR of 92.5%, 89.2%, 90.1% and 93% as well as minimum FNR of 15%.

Estimation and Expansion of Vehicle Stability Region With Sums of Squares Programming

The vehicle stability region can be used to evaluate vehicle stability performance and lay the foundation for vehicle safety improvement. It can be obtained via the region of attraction (RoA) based on sums of squares (SOS) programming. However, it is usually conservative, and the computational burden is large. This article focuses on the above issues and proposes a well-developed method for RoA estimation, with application to the estimation and expansion of the vehicle stability region. For RoA estimation, an improved SOS program is formulated, and its optimization objective combined with the customized algorithm significantly reduces conservatism. In addition, the feasibility prejudgment strategy and the dynamic search range are proposed in the algorithm. As a result, the computational burden is greatly reduced, which also indirectly helps reduce conservatism. Then, a more accurate vehicle stability region is obtained with less time consumption, and a map-based controller is proposed to improve vehicle stability. Better stability performance and larger stability regions are guaranteed under different scenarios due to the adaptive adjustment of controller gains. Finally, simulations and hardware-in-the-loop experiments with an embedded vehicle controller are performed to verify the effectiveness of our method.

Evaluating bulk flow estimators for CosmicFlows–4 measurements

ABSTRACT For over a decade there have been contradictory claims in the literature about whether the local bulk flow motion of galaxies is consistent or in tension with the ΛCDM model. While it has become evident that systematics affect bulk flow measurements, systematics in the estimators have not been widely investigated. In this work, we thoroughly evaluate the performance of four estimator variants, including the Kaiser maximum likelihood estimator (MLE) and the minimum variance estimator (MVE). We find that these estimators are unbiased, however their precision may be strongly correlated with the survey geometry. Small biases in the estimators can be present leading to underestimated bulk flows, which we suspect are due to the presence of non-linear peculiar velocities. The uncertainty assigned to the bulk flows from these estimators is typically underestimated, which leads to an overestimate of the tension with ΛCDM. We estimate the bulk flow for the CosmicFlows–4 data and use mocks to ensure the uncertainties are appropriately accounted for. Using the MLE we find a bulk flow amplitude of 408 ± 165 kms−1 at a depth of $49\, \mathrm{Mpc} h^{-1}$, in reasonable agreement with ΛCDM. However using the MVE which can probe greater effective depths, we find an amplitude of 428 ± 108 kms−1 at a depth of $173\, \mathrm{Mpc} h^{-1}$, in tension with the model, having only a 0.11 per cent probability of obtaining a larger χ2. These measurements appear directed towards the Great Attractor region where more data may be needed to resolve tensions.

Key economic sectors for green job creation in Poland – an empirical analysis

In this study, we employed a stepwise empirical approach to identify economic sectors and analyze the regional potential for green job (GJ) creation in Poland. We used the operating register of economic entities (REGON) and Polish Labor Force Survey (BAEL) data for the period between 2015 and 2022. The changes in REGON reflect a proxy of changes in GJ stock in sectors of economic activity (PKD-2007) and regions. We estimated trends and spatial diversification of green employment. The results revealed that Mazowieckie, Wielkopolskie, Małopolskie, and Śląskie are the most attractive regions for GJ creation. The polarization of green employment declined during the analyzed period, but spatial disparities were still significant. Most sectors noted increases in GJ, except for agriculture, where the downward trend in employment has a significant influence on the green labour market. Our findings may be useful when formulating policy recommendations for educational institutions, employment institutions, local governments, government institutions, investors, and employers.

Effects of PLL Frequency Limiters on Synchronization Stability of Grid Connected VSC and Strategy to Realize Global Stability

This paper investigates the synchronization stability of voltage source converter (VSC) connected to infinite bus system with frequency limiter of phase-locked loop (PLL). First, three different types of PLL frequency limiters are modelled based on piecewise-smooth dynamical system (PSDS). Then the effects of different frequency limiters and frequency limit values on the region of attraction (ROA) of the system are studied and the properties of the PSDSs are analyzed. It is found that PLL with anti-windup limiter with back calculation can achieve global stability with appropriate limit value, and the principle of setting limit value based on a specific ROA estimation is proposed. Based on ROA estimation with Lyapunov function, a method of setting frequency limit value which guarantees global stability is proposed. The validity of the proposed strategy is verified through MATLAB/Simulink simulation.

Event-triggered neural network control using quadratic constraints for perturbed systems

This paper investigates the event-triggered control problem for perturbed systems under neural network controllers. We propose a novel event-triggering mechanism, based on local sector conditions related to the activation functions, to reduce the computational cost associated with the neural network evaluation. It avoids redundant computations by updating only a portion of the layers instead of evaluating periodically the whole neural network. Sufficient conditions in terms of matrix inequalities are established to design the parameters of the event-triggering mechanism and compute an inner-approximation of the region of attraction for the perturbed feedback system. The theoretical conditions are obtained by using a quadratic Lyapunov function and an abstraction of the activation functions via quadratic constraints to decide whether the outputs of the layers should be transmitted through the network or not. Such conditions allow us to reduce the computational activity on the neural network while preserving the stability and performance level of the perturbed feedback system. To illustrate the efficacy of our approach, we consider the nonlinear inverted pendulum system stabilized by a trained neural network.

Stabilizing model predictive control synthesis using integral quadratic constraints and full‐block multipliers

SummaryIn this paper, we discuss how to synthesize stabilizing model predictive control (MPC) algorithms based on convexly parameterized integral quadratic constraints (IQCs), with the aid of general multipliers. Specifically, we consider Lur'e systems subject to sector‐bounded and slope‐restricted nonlinearities. As the main novelty, we introduce point‐wise IQCs with storage in order to accordingly generate the MPC terminal ingredients, thus enabling closed‐loop stability, strict dissipativity with regard to the nonlinear feedback, and recursive feasibility of the optimization. Specifically, we consider formulations involving both static and dynamic multipliers, and provide corresponding algorithms for the synthesis procedures. The major benefit of the proposed approach resides in the flexibility of the IQC framework, which is capable to deal with many classes of uncertainties and nonlinearities. Moreover, for the considered class of nonlinearities, our method yields larger regions of attraction of the synthesized predictive controllers (with reduced conservatism) if compared to the standard approach to deal with sector constraints from the literature.

Fully distributed adaptive practical fixed-time consensus protocols for multi-agent systems

This paper investigates the practical fixed-time consensus problem for a multi-agent system in networks with an undirected topology. Both node-based and edge-based fully distributed adaptive protocols are proposed to achieve the practical fixed-time consensus for the single integrator-type multi-agent systems, i.e., fixed-time attractiveness of a residual set as well as asymptotic consensus. Most notably, the settling time estimate can be computed without using any global information, which is distinctive from the existing fixed-time protocols. Furthermore, a scaling technique is applied for the proposed protocol such that the fixed-time attraction region can be contracted by only tuning a scaling parameter and the original settling time estimate remains unchanged. Finally, a numerical simulation example is given to validate the proposed protocols.

On the global stabilization of 6‐DOF quadrotors: A direct Lyapunov approach

AbstractNumerous linear and nonlinear controller structures are available to stabilize 6‐DOF quadrotors, however, those structures are capable of stabilizing the quadrotors in a local region only containing the hovering configuration. This article focuses on the design of a nonlinear controller to achieve the stabilization in large for these unmanned aerial vehicles in hovering configuration at the desired attitude. In this manner, a specific set of state variables is introduced to avoid the singularity problems. Afterwards, a candidate Lyapunov function is considered and the stability is proved based on that function by solving a set of ordinary and partial differential equations, the so‐called matching conditions. Then, the asymptotic stability of the desired configuration in 6‐DOF is proved using LaSalle's invariant set principle with the region of attraction containing almost all state space. Numerical simulation results are included to validate the feasibility of the proposed almost globally stabilizing controller.

Stability analysis of sampled-data control systems with input saturation: A hybrid system approach

This work addresses the stability analysis of sampled-data control systems subject to variable sampling intervals and input saturation. From a hybrid system representation, stability conditions based on quadratic timer-dependent Lyapunov functions are proposed. Considering affine and generic polynomial timer-dependence, these conditions are cast in semidefinite and sum-of-squares optimization problems to provide maximized estimates of the region of attraction or to provide a lower bound for the maximum allowable intersampling time considering a given set of admissible initial conditions.

Robust Stability of Neural-Network-Controlled Nonlinear Systems With Parametric Variability

Stability certification and identification of a safe and stabilizing initial set are two important concerns in ensuring operational safety, stability, and robustness of dynamical systems. With the advent of machine-learning tools, these issues need to be addressed for the systems with machine-learned components in the feedback loop. To develop a general theory for stability and stabilizability of neural network (NN)-controlled nonlinear systems subject to bounded parametric variations, a Lyapunov-based stability certificate is proposed and is further used to devise a maximal Lipschitz bound for a class of stabilizing NN controllers, and also a corresponding maximal Region of Attraction (RoA) within a user-specified safety set. To compute a robustly stabilizing NN controller that also maximizes the system’s long-run utility, a stability-guaranteed training (SGT) algorithm is proposed. The effectiveness of the proposed framework is validated through an illustrative example.

A Terminal Set Feasibility Governor for Linear Model Predictive Control

The Feasibility Governor (FG) is an add-on unit for Model Predictive Controllers (MPC) that increases the closed-loop region of attraction by manipulating the applied reference to ensure the underlying optimal control problem is always feasible. The FG requires an estimate of the feasible set of the optimal control problem that underlies the MPC; obtaining this estimate can be computationally intractable for high-dimensional systems. This paper proposes a modified FG that bypasses the need for an explicit estimate, instead relying entirely on the MPC terminal set. The proposed FG formulation is proven to be asymptotically stable, exhibits zero-offset tracking, satisfies constraints, and achieves finite-time convergence of the reference. Numerical comparisons featuring an MPC with a long prediction horizon show that the FG+MPC system can achieve comparable closed-loop performance to long-horizon MPC at a significantly reduced computational cost by suitably detuning the terminal controller to enlarge the terminal set.

An analytical approach for the stability analysis of power networks through Kuramoto oscillators model

In recent years, ensuring stability in power networks has posed a significant challenge for network control engineers, primarily due to the substantial growth in power demand and the complexities involved in integrating renewable energy sources. This study endeavours to augment the existing research by presenting theoretical findings in a practical manner through the introduction of a novel Lyapunov function and the application of LaSalle’s invariance principle to establish an unequivocal and accurate synchronization condition in power networks. The study’s salient contributions include (I) the Fresh approach of utilizing a second-order configuration of asymmetrically networked, dissimilar oscillators; (II) the incorporation of lossy power networks, culminating in non-identical phase delays in the analytical model of the oscillating network; and (III) the introduction of an entirely original Lyapunov function to provide a precise and unambiguous estimation for the region of attraction in power networks. Analytical findings substantiate that network synchronization is assured by the algebraic connectivity of the network graph exceeding a particular threshold value. The study’s transient stability conditions have been authenticated via numerical simulations of the IEEE 39-bus system.

Evolution of phase diagrams of polymer adsorption over attractive surfaces as a function of flexibility and solvent quality

ABSTRACT We describe the equilibrium conformations of a polymer near an attractive surface for different conditions in solvent quality and polymer stiffness. Using molecular dynamics techniques in a canonical ensemble, we show the evolution of the phase diagrams as function of temperature and surface interaction strength. Phase diagrams show an ampler variety of possible conformations due to changes in solvent quality compared to stiffness for which variations in conformations appear mainly in the degree of adsorption. We show that the adsorption transition is independent of solvent quality and stiffness. When both parameters change simultaneously, solvent effects are stronger than the stiffness secluding the stiff conformations to regions of low temperature and high surface attraction. A remarkable observation is that the radius of gyration perpendicular component to the surface, , signals the adsorption transition at coincidental points for each system independently of solvent and stiffness variations in all simulations, which may be of aid in locating this transition in other systems.

A Novel Method for Estimating the Region of Attraction for DC Microgrids via Brayton-Moser’s Mixed Potential Theory

To avoid instability caused by abrupt load changes or contingencies, the region of attraction (ROA) estimation is significant for large-signal stability analysis of the power system. This letter proposes a novel method to estimate ROA of DC microgrids containing constant power loads (CPLs). Compared with the existing methods, an obvious advantage of the proposed method can reduce computations greatly, which is applicable to large-scale DC power grids. Finally, the feasibility of the proposed method is verified by case studies.

Ion pair and larger ion cluster formation in water interfacial regions: An atomic force microscopy study

Interfacial regions attached to hydrophobic and hydrophilic surfaces have very low relative permittivities (ε ∼ 3–5), and these low values induce the formation of ion pairs. A detailed description of ion pairing will be possible only after the development of adequate experimental probing methods. The scheme described in this work detects the ion pair (or multistage ion association) formation in water solutions in the interfacial region. Forces acting on the tip when immersed in the interfacial region attached to hydrophilic substrates, such as mica where ε < 7, are attractive (AFM tip dielectric constant = 7). These attractive force steps with extensions equal or smaller than the Bjerrum length at hydrophilic substrates are associated with ion pair formation in interfacial regions. Measurements show that the interfacial water molecular arrangement and ion pairs form an ordered structure (ε < 7) induced by mica interfacial charges. The interfacial region attached to hydrophobic substrates, however, form separated arrangements of ion pairs and water molecular structures as observed by the repulsive steps (ε > 7) intercalated in between attractive regions (ε < 7).

Local Stabilization of Constrained N-TS Fuzzy Systems Based on a Weighted Ranking Protocol

In this article, relaxed local stabilization criteria of constrained N-TS fuzzy systems are provided by developing a weighted ranking protocol. Different from the recent criteria reported in the literature, a set of operating modes is produced by employing the weighted ranking information of the available normalized fuzzy weighting functions. With regard to each enabled operating mode, its proprietary boundary information constraint is fully considered by means of introducing a class of cascade-type free variables, and thus the conservatism can be reduced to a large extent than before. More importantly, the applied variable weights for adjusting the range of different operating modes play an important role in further enlarging the estimated attraction regions. Finally, the superiority of the proposed approach is tested and verified by giving several comparisons on two key indicators for the same benchmark example.

Statistical Investigation about the SDRE Optimality for Satellites with Nonlinearities

The Attitude Control System (ACS) of a Satellite can be designed with success by linear control theory if the satellite has slow angular motions. However, for fast maneuvers, the linearized models are not able to represent the effects of the nonlinear terms. One candidate technique to design the ACS of the satellite under fast maneuvers is the State-Dependent Riccati Equation (SDRE), which provides an effective algorithm for synthesizing nonlinear feedback control taking into account the nonlinearities. Nonetheless, much criticism has been leveled against the SDRE method since it does not assure global asymptotic stability (GAS), because there are situations in which global asymptotic stability cannot be achieved (e.g., systems with multiple equilibrium points). One way to study the GAS is by estimating the region of attraction (ROA) which in turn is fundamental to investigate the performance of the controller designed by the SDRE method The Brazilian National Institute for Space Research (INPE) is responsible to build a Remote-Sensing Satellites, called Amazonia-1. The ACS of the Amazonia-1 satellite must be stabilized in three axes so that the optical payload can point to the desired target. In this paper, one investigates the performance of the Amazonia-1 ACS using a statistical test (unpaired t-test) that compares the optimality inside the ROA controlled by LQR and SDRE. By several simulations running a full Monte Carlo perturbation satellite model one observes a significant difference between the optimality of the two controllers in favor of SDRE when nonlinearities are accounted for.