Region Of Attraction Research Articles

Adaptive synapse-based neuron model with heterogeneous multistability and riddled basins.

Biological neurons can exhibit complex coexisting multiple firing patterns dependent on initial conditions. To this end, this paper presents a novel adaptive synapse-based neuron (ASN) model with sine activation function. The ASN model has time-varying equilibria with the variation of externally applied current and its equilibrium stability involves transitions between stable and unstable points through fold and Hopf bifurcations, resulting in complex distributions of attractive regions with heterogeneous multi-stability. Globally coexisting heterogeneous behaviors are studied by bifurcation diagram, phase portrait, dynamical distribution, and basin of attraction. The results show that the number of coexisting heterogeneous attractors can be up to 12, but for a simple neuron model, such a large number of coexisting heterogeneous attractors has not been reported in the relevant literature. Most interestingly, the ASN model also has riddled-like complex basins of attraction and four illustrative examples are depicted by the phase portraits with small changes of the initial conditions. Besides, the ASN model is implemented using a simple microcontroller platform, and various heterogeneous coexisting attractors are acquired experimentally to validate the numerical results.

Online modeling of environmental constraint region for complex-shaped parts assembly

Purpose The paper aims to propose a method to build environmental constraint region online in complex-shaped peg-in-hole assembly tasks. Design/methodology/approach Compared with conventional way which using computer-aided design (CAD) models of assembly parts to construct the environmental constraint region offline, the paper provides an online approach that consists of three aspects: modeling assembly parts through visual recognition, decomposing complex shapes into multiple primitive convex shapes and a numerical algorithm to simulate the peg-in-hole insertion contact. Besides, a contrast experiment is performed to validate the feasibility and effectiveness of the method. Findings The experiment result indicates that online construction takes less time than the offline way under the same task conditions. Furthermore, due to the CAD models of the parts are not required to be known, the method proposed in the paper has a broader application in most assembly scenarios. Originality/value With the improvement of customization and complexity of manufactured parts, the assembly of complex-shaped parts has drawn greater attention of many researchers. The assembly methods based on attractive region in environment (ARIE) have shown great performance to achieve high-precision manipulation with low-precision systems. The construction of environmental constraint region serves as an essential part of ARIE-based theory, directly affect the formulation and application of assembly strategies.

Estimation of non-symmetric and unbounded region of attraction using shifted shape function and R-composition

Sum-of-squares programming is widely used for region of attraction (ROA) estimations of asymptotically stable equilibrium points of nonlinear polynomial systems. However, existing methods yield conservative results, especially for non-symmetric and unbounded regions. In this study, a cost-effective approach for ROA estimation is proposed based on the Lyapunov theory and shape functions. In contrast to existing methods, the proposed method iteratively places the center of a shifted shape function (SSF) close to the boundary of the acquired invariant subset. The set of obtained SSFs yields robust ROA subsets, and R-composition is employed to express these independent sets as a single but richer-shaped level set. Several benchmark examples show that the proposed method significantly improves ROA estimations, especially for non-symmetric or unbounded ROA without a significant computational burden.

Development of Regional Labor Markets in Ukraine as a Tool to Regulate Internal Migration and Reduce Social Vulnerability

Purpose: The article explores links between the attractiveness of regional labor markets and internal migration as a change in the usual place of residence in Ukraine. Methodology: Based on the migration theory of “push-pull” a study of the attractiveness of regional labor markets as determinants of the intensification of internal migration in 24 regions of Ukraine (2010–2020) was conducted with the use of integrated assessment and balance econometric modeling. Findings: The study found that the internal migration activity in Ukraine is of urbanistic nature because the development of rural-urban area migration vectors dominates in the country. The most attractive regions in the focus of internal emigration and immigration processes are defined based on the developed rankings of the regions’ attractiveness by the system of labor market and employment development indicators. Research limitations: This article studies a specific country and its regions, along with the local labor market. One should be careful when generalizing the results to other regional labor markets. Originality/value: The level of regional labor markets’ attractiveness correlated with internal migration activity. The attractive regional labor market, high IT market development level, and increasing innovative-technological capacity proved the main attraction factors of these regions.

Finite-time and fixed-time stability analysis for time-varying systems: A dual approach

In this paper we present a new dual approach to investigating the stability of the system of two nonautonomous ODE with the right-hand side being only Lebesgue measurable with respect to time t. We define a new dual Lapunov function S which depends on three variables, and we give sufficient conditions for finite and fixed-time stability for the system using a dual Hamilton-Jacobi inequality and taking advantage of a class of functions M and MB. This method allows simultaneous investigation of the finite and fixed-time stability of the primary and the dual equation. We give some examples to illustrate the results obtained. As an application of this dual approach, we define the region of attraction and illustrate with an example.

A deterministic gradient-based approach to avoid saddle points

AbstractLoss functions with a large number of saddle points are one of the major obstacles for training modern machine learning (ML) models efficiently. First-order methods such as gradient descent (GD) are usually the methods of choice for training ML models. However, these methods converge to saddle points for certain choices of initial guesses. In this paper, we propose a modification of the recently proposed Laplacian smoothing gradient descent (LSGD) [Osher et al., arXiv:1806.06317], called modified LSGD (mLSGD), and demonstrate its potential to avoid saddle points without sacrificing the convergence rate. Our analysis is based on the attraction region, formed by all starting points for which the considered numerical scheme converges to a saddle point. We investigate the attraction region’s dimension both analytically and numerically. For a canonical class of quadratic functions, we show that the dimension of the attraction region for mLSGD is $\lfloor (n-1)/2\rfloor$ , and hence it is significantly smaller than that of GD whose dimension is $n-1$ .

Nonlinear Analysis of Stability and Safety of Optimal Velocity Model Vehicle Groups on Ring Roads

In this work, we study a group of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> homogeneous vehicles travelling on a ring road by describing the collective vehicle dynamics via the so-called Optimal Velocity Model (OVM). We analyze the stability of the equilibrium motion regime in which all vehicles drive at the same speed and keep the same headway. First, stability is studied through linearization, thereby highlighting the roles of the model parameters. Next, we tackle the full nonlinear model and we determine ellipsoidal estimates of the equilibrium’s region of attraction by defining and solving suitable Linear Matrix Inequalities (LMIs). Finally, safety aspects are discussed, incorporated in our LMI formulation as lower bounds of the inter-vehicle distances, and illustrated via simulations.

Peculiarities of International Competition in the Market of Tourism and Hospitality

The global hospitality and tourism market is being transformed through several core factors: new consumer needs of the industry, pandemic, increased competition, in particular the emergence of new regional tourism markets and new companies. The aim of the article is to investigate the competitiveness of the global hospitality and tourism market based on the example of key attractive tourism regions: Africa, the Americas, Asia, the Pacific, the Middle East and Europe. The methodology is based on a statistical analysis of regional hospitality and tourism markets by key indicators of their competitiveness in 2010‒2021. The results show a significant contraction of the global hospitality and tourism market, with transformations in regional markets (Asia due to rising travel costs and restrictions, the Middle East due to rising costs of tourism services). The European hospitality and tourism market is found to be stable due to a slight increase in the cost of travel services and weaker regulatory restrictions introduced during the pandemic. The structure of the industry has changed between 2020 and 2021, with a growing share of regional markets in Europe, resulting in a change in international competition between regional tourism and hospitality markets. The key competitive advantages of European countries in the field of tourism are historical and cultural heritage, developed tourism infrastructure, level of service, safety, cost of tourism services, including transport and accommodation facilities. Despite the development of new regional tourism markets (Asia, Pacific, Middle East) due to increased prosperity and improved infrastructure, the pandemic has caused these destinations to stagnate due to increased costs of tourism services.

On the synchronization of selfexcited and hidden attractors

Many nonlinear systems have complex behaviors where selfexcited and hidden attractors exist and some times coexist. We investigate the synchronization problem for these type systems under two different coupling configurations: drive-response and bidirectional. In the first scheme, the coupling term in the response subsystem can be design as an output feedback controller to achieve synchronization; while in the latter, since the states of both systems depend on their interaction, the coupling terms are designed in terms of their differences. As observed before synchronized behavior on a hidden attractor is very difficult to achieve. In this sense our results show that for the drive-response configuration is relatively simple to impose a synchronized behavior; however, on hidden attractors the region of attraction of the synchronized solution reduces to that of the hidden attractor. Additionally, in a bidirectional configuration the region of attraction of the synchronized behavior basically disappears making the design of a static coupling considerably more difficult. We illustrate our results with numerical simulations of systems with hidden and selfexcited attractors.

Weldability of Nickel/Aluminum Dissimilar Materials Laser Welding Part I: Microstructure Development, Solidification Behavior and Mechanical Properties of Polycrystalline Nickel-based Superalloy

Weldability-related issues, including asymmetrical weld pool shape, γ phase multicomponent microstructure development, solidification behavior and mechanical properties, of γʹʹ precipitation-strengthened polycrystalline nickel-based superalloy are experimentally analyzed during keyhole laser welding repair. The crucial relationship between them provides weldability improvement opportunities and defect-free high quality weld for feasible aerospace materials laser processing. Attractive neck transition region of weld is more vulnerable to coarser dendrite than bottom part in the vicinity of fusion boundary, and this location is also liable to abundant Laves/γ eutectic phase formation because of heat and solute accumulation. The dominant chemical inhomogeneity brings about microstructure anomalies and irregular morphology to deteriorate hot cracking resistance. Because of thermometallurgical factors of selective alloying partition in the molten pool, partition-resistant Cr is chemically accumulated in dendrite core, while partition-susceptible Ti, Al, Mo and Nb are enriched in high-supersaturation interdendrite region, which consequently result in serious segregation and extensive Nb-rich intermetallic phase formation across solidification interface. Dendrite refinement and aggressive Laves/γ eutectic phase formation suppression are not simultaneously satisfied by low heat input under nonequilibrium solidification conditions. Therefore, mechanical properties are only partially improved by diffusion-limited microstructure refinement as result of phase instability. In other words, reductions of tensile strength and ductility are attributed to brittle Laves/γ eutectic phase formation during terminal stage of solidification. The severity of eutectic reaction thermodynamically depends on nail-shaped keyhole profile, solidification conditions and solute redistribution ahead of solid/liquid interface. Additionally, viable control of weld metallurgical and mechanical properties progressively encourages optimal combination of laser power and welding speed to interdendritically minimize disadvantages of eutectic phase formation by a variety of welding conditions optimization.

A Feasibility Governor for Enlarging the Region of Attraction of Linear Model Predictive Controllers

This article proposes a method for enlarging the region of attraction of linear model predictive controllers (MPC) when tracking piecewise-constant references in the presence of pointwise-in-time constraints. It consists of an add-on unit, the feasibility governor (FG), that manipulates the reference command so as to ensure that the optimal control problem that underlies the MPC-feedback law remains feasible. Offline polyhedral projection algorithms based on multiobjective linear programming are employed to compute the set of feasible states and reference commands. Online, the action of the FG is computed by solving a convex quadratic program. The closed-loop system is shown to satisfy constraints, be asymptotically stable, exhibit zero-offset tracking, and display finite-time convergence of the reference.

Post-capture detumble trajectory stabilization for robotic active debris removal

Recent increase in space debris combined with the increase in the number of satellites launched has created an increased risk of collisions. The effects of the increased risk can be seen in the form of an increased number of near misses in recent years. The use of robotic manipulators has been suggested for Active Debris Removal (ADR) to reduce the risk of potential future collisions that generate more debris in the orbits around Earth. Compared to other ADR methods, robotic manipulators provide increased versatility as they can be reused for On-Orbit Servicing as well as On-Orbit Assembly missions. A robotic ADR operation consists of three phases: Approach, Capture, and Detumble. This paper provides a method for performing feedback-based stabilization of post-capture detumble trajectories of the chaser-debris system. The approach presented here uses Time-Varying Linear Quadratic Regulator (TVLQR) for stabilization along the detumble trajectory. The contributions of this paper are as follows: A quaternion-based linearization method for multibody systems with a free-floating base, TVLQR for stabilizing the optimal detumble trajectory, and a probabilistic Region of Attraction analysis of the resulting closed-loop system. The estimated Region of Attraction could serve as the goal for the capture controller thus allowing for controller composition through ADR phases while guaranteeing stability and successful detumble.

Stability-certified reinforcement learning control via spectral normalization

In this study, two types of methods from different perspectives based on spectral normalization (SN) are described for ensuring the stability of a feedback system controlled by a neural network (NN). The first one is that the L2 gain of the feedback system is bounded less than 1 to satisfy a stability condition derived from the small-gain theorem. When explicitly including the stability condition, the first type of method may provide an insufficient performance on the NN controller due to its strict stability condition. To overcome this difficulty, the second type of method is proposed, ensuring local stability with a larger region of attraction. In this second type, the stability is ensured by solving linear matrix inequalities after training the NN controller. SN improves the feasibility of the a posteriori stability test by constructing tighter local sectors. Numerical experiments show that the second type of method provides sufficient performance compared with the first one and ensures sufficient stability compared with existing reinforcement learning algorithms.11Project page: https://sites.google.com/g.ecc.u-tokyo.ac.jp/stability-certified-rl-via-sn.

Cryptic genetic divergence of the red dwarf rasbora, Microrasbora rubescens, in and around Inle Lake: implications for the origin of endemicity in the ancient lake in Myanmar.

Inle Lake, an ancient lake located in the Shan Plateau of Myanmar, is a biogeographically attractive region with high fish endemism. Some endemic species inhabit the lake as well as the surrounding areas. The genetic and ecological relationships between populations in the lake and surrounding areas provide important insights into the process underlying ichthyofaunal formation in Inle Lake. In this study, the authors focused on red dwarf rasbora Microrasbora rubescens, an endemic genus and species in this region, and estimated its population structure and evolutionary scenario based on genome-wide polymorphism, mtDNA and geometric morphometric analyses using samples from Inle Lake and three areas surrounding the lake. The results showed that M. rubescens comprises at least three genetically divergent lineages (Inle, Heho and Hopong) with distinct geographic structures consistent with nuclear and mtDNA data. In contrast, there was no clear regional differentiation in morphology. The divergence time estimation based on mtDNA suggests that the Hopong lineage diverged at 2.7 Ma and the Inle and Heho lineages diverged at 1.9Ma - consistent with the nuclear DNA results. The deep divergence observed in the endemic species supports the ancient history of ichthyofaunal development in this region. The distinct regional differentiation and morphological conservatism of this species might have been shaped by niche conservatism in stagnant water environments that limit dispersal and morphological diversification. Future comprehensive genetic and morphological analyses and comparisons for other native species should reveal the geographic and ecological processes that shaped the ichthyofauna in this region.

Efficient Region of Attraction Characterization for Control and Stabilization of Load Tap Changer Dynamics

In this article, we study the monitoring and control of long-term voltage stability considering load tap changer (LTC) dynamics. We show that under generic conditions, the LTC dynamics admit a unique stable equilibrium. For the stable equilibrium, we characterize an explicit inner approximation of its largest region of attraction (ROA). Compared to existing results, the computational complexity of the ROA characterization is drastically reduced. We propose a quadratically constrained linear program formulation for the ROA characterization problem. In addition, we formulate a second-order cone program for online voltage stability monitoring and control exploiting the proposed ROA characterization. We demonstrate the efficacy of the proposed formulations on the ROA characterization and stability monitoring and control using a standard IEEE test system.

On Compatibility and Region of Attraction for Safe, Stabilizing Control Laws

A novel control method is proposed to ensure compatibility of safe, stabilizing control laws, i.e., simultaneous satisfaction of asymptotic stability and constraint satisfaction for nonlinear affine systems. The results are dependent on an asymptotically stabilizing control law and a zeroing control barrier function (ZCBF), but do not require a control Lyapunov function (CLF). Sufficient conditions for a region of attraction are defined for which the proposed control safely stabilizes the system, while preserving the decrescent Lyapunov function of the original stabilizing control law. The proposed methodology for nonlinear affine systems requires checking conditions of the system dynamics over a substantial portion of the state space, which may be computationally expensive. To facilitate the search for compatibility, we extend the results to a class of nonlinear systems including mechanical systems for which a novel controller is designed to guarantee passivity, safety, and stability. Numerical examples are used to demonstrate the proposed technique.

Linear Tracking MPC for Nonlinear Systems—Part I: The Model-Based Case

We develop a tracking model predictive control (MPC) scheme for nonlinear systems using the linearized dynamics at the current state as a prediction model. Under reasonable assumptions on the linearized dynamics, we prove that the proposed MPC scheme exponentially stabilizes the optimal reachable equilibrium w.r.t. a desired target setpoint. Our theoretical results rely on the fact that, close to the steady-state manifold, the prediction error of the linearization is small and hence, we can slide along the steady-state manifold towards the optimal reachable equilibrium. The closed-loop stability properties mainly depend on a cost matrix which allows us to trade off performance, robustness, and the size of the region of attraction. In an application to a nonlinear continuous stirred tank reactor, we show that the scheme, which only requires solving a convex quadratic program online, has comparable performance to a nonlinear MPC scheme while being computationally significantly more efficient. Further, our results provide the basis for controlling nonlinear systems based on data-dependent linear prediction models, which we explore in our companion paper.

Photostable NIR-II Pigments from Extended Rylenecarboximides.

A series of near-infrared (NIR) organic absorbers, named FNs and FPs, have been obtained with absorption maxima from 870 nm to 1100 nm and thus falling into the attractive second near-infrared region (NIR-II). The synthesis of their extended aromatic cores utilized an initial aryl-amination between 4-aminonaphthalene-1,8-dicarboximide (NMI-NH2 ) or 9-aminoperylene-3,4-dicarboximide (PMI-NH2 ) with chloro-substituted 9,10-anthraquinones followed by a novel base-induced cyclodehydrogenation. A NIR-II pigment, compound FPP, was obtained through de-alkylation of a soluble precursor. The synthesis of this photostable pigment is high-yielding and avoids column chromatographic purification which is important for many applications.

A Fractional-Order Epidemic Model with Quarantine Class and Nonmonotonic Incidence: Modeling and Simulations.

In any outbreak of infectious disease, the timely quarantine of infected individuals along with preventive measures strategy are the crucial methods to control new infections in the population. Therefore, this study aims to provide a novel fractional Caputo derivative-based susceptible-infected-quarantined-recovered-susceptible epidemic mathematical model along with a nonmonotonic incidence rate of infection. A new quarantined individual compartment is incorporated into the susceptible-infected-recovered-susceptible compartmental model by dividing the total population into four subpopulations. The nonmonotonic incidence rate of infection is considered as Monod–Haldane functional type to understand the psychological effects in the population. Qualitative analysis of the study shows that the model solutions are well-posed i.e., they are nonnegative and bounded in an attractive region. It is revealed that the model has two equilibria, namely, disease-free (DFE) and endemic (EE). The stability analysis of equilibria is investigated for local as well as global behaviors. Mathematical analysis of the model reveals that DFE is locally asymptotically stable when the basic reproduction number ({R}_{0}) is lower than one. The basic reproduction number {R}_{0} is computed using the next-generation matrix method. The existence of EE is shown and it is investigated that EE is locally asymptotically stable when {R}_{0}>1 under some appropriate conditions. Moreover, the global stability behaviors of DFE and EE are analyzed under some conditions using {R}_{0}. Finally, some numerical simulations are performed to interpret the theoretical findings.

Event‐triggered control of quasi‐LPV systems with communication delays

AbstractThis paper addresses the dynamic periodic event‐triggered control for local stabilization of nonlinear networked control systems with communication delays. Based on a polytopic quasi‐linear parameter‐varying (quasi‐LPV) model of the nonlinear plant and the Lyapunov–Krasovskii stability theory, a local stability analysis condition is established. Then a constructive co‐design condition is proposed to jointly design the state‐feedback control law and the trigger rule. The local asymptotic stability of the closed‐loop equilibrium point of interest is ensured with a guaranteed region of attraction where trajectories remain inside even in the presence of communication delays. An optimization procedure is proposed to perform the co‐design considering the objectives of enlarging the guaranteed region of attraction and reducing the number of transmissions. Numerical examples indicate a trade‐off between these two objectives. Also, the examples illustrate the effectiveness of the proposed dynamic event‐triggered control co‐design approach over both its static counterpart and periodic time‐triggering mechanisms.