Domain Of Attraction Research Articles

The steady states of isotone electric systems

The steady states of an isotone electric system are described by an isotone function with respect to the componentwise order. When there are steady states, we highlight a dominant steady state and we study its domain of attraction for the fixed point iteration method.

Fault-tolerant attitude coordination control for multiple flexible spacecraft using vector measurements

This paper addresses the control problems of distributed attitude coordination for multiple flexible spacecraft based on the feedback of inertial vector measurements. It is assumed that the angular velocity information is not available, and the modal variable cannot be measured. The orientation error model with vector measurements is introduced. And then the distributed attitude synchronization control scheme is presented without actuator faults or disturbances. It is guaranteed that the desired equilibrium is locally asymptotically stable and the undesired equilibrium is unstable. Meanwhile, the domain of attraction is given by inequality constraints. In the case that there exist actuator faults and external disturbances, a robust fault-tolerant control strategy is developed to realize attitude synchronization. The hyperbolic tangent function in place of sign function is adopted to eliminate external disturbances. Meanwhile, the adaptive laws are proposed to estimate actuator faults. The salient feature of these control approaches is that no modal variable observers are utilized and the control schemes are robust to the inertia uncertainty of spacecraft. Finally, numerical simulations are implemented to manifest the validity of the presented control schemes.

On the convergence of Shannon entropy of distribution functions in the max domain of attraction of max-stable laws

On the convergence of Shannon entropy of distribution functions in the max domain of attraction of max-stable laws

On the density arising from the domain of attraction of an operator interpolating between sum and supremum: The α-Sun operator

We explore the analytic properties of the density function h(x;γ,α), x∈(0,∞), γ>0, 0<α<1 which arises as a normed limit from the domain of attraction problem for an operator interpolating between the supremum and sum as applied to a sequence of i.i.d. non-negative random variables. The parameter α controls the interpolation between these two cases, while γ further parametrises the type of distribution from which the underlying random variables are drawn. It is known that in the normed limit, for α=0 the Fréchet density arises, whereas for α=1 the limit is a stable random variable which has the well-known identification with a particular Fox H-function. It is known [21] that for intermediate α an entirely new distribution function appears, which is not one of the extensions to the hypergeometric function considered to date. Here we derive series, integral and continued fraction representations of this latter function.

Functional limit theorems for random walks perturbed by positive alpha-stable jumps

Let ξ1, ξ2,… be i.i.d. random variables of zero mean and finite variance and η1, η2,… positive i.i.d. random variables whose distribution belongs to the domain of attraction of an α-stable distribution, α∈(0,1). The two collections are assumed independent. We consider a Markov chain with jumps of two types. If the present position of the Markov chain is positive, then the jump ξk occurs; if the present position of the Markov chain is nonpositive, then the jump ηk occurs. We prove functional limit theorems for this and two closely related Markov chains under Donsker’s scaling. The weak limit is a nonnegative process (X(t))t≥0 satisfying a stochastic equation dX(t)=dW(t)+dUα(LX(0)(t)), where W is a Brownian motion, Uα is an α-stable subordinator which is independent of W, and LX(0) is a local time of X at 0. Also, we explain that X is a Feller Brownian motion with a ‘jump-type’ exit from 0.

Distributed-Delay-Dependent Stabilization for Networked Interval Type-2 Fuzzy Systems With Stochastic Delay and Actuator Saturation

In this article, a distributed-delay-dependent method is proposed to deal with the stabilization for interval type-2 Takagi–Sugeno fuzzy systems subject to stochastic network delay and actuator saturation. To deal with the stochastic feature of network-induced delays, their probability density function is utilized to establish the distributed delay model, which is more practical than the traditional time-varying network delay model. Meanwhile, in order to enlarge the estimation of the domain of attraction, a polytopic strategy composed of a state vector and a distributed-delay-dependent vector is proposed to treat the saturation nonlinearity. By constructing a distributed-delay-dependent Lyapunov–Krasovskii functional, new and less conservative conditions are achieved to guarantee the stability of the established closed-loop system. Additionally, two simulation examples are carried out to illustrate the advantages of the proposed strategy.

Quantitative and Intuitive VSG Transient Analysis With the Concept of Damping Area Approximation

The inherent large damping effect in virtual synchronous generator (VSG) control brings great challenges to its transient analysis. The recent studies mainly focus on qualitative explanation of damping effect, lacking an intuitive and quantitative assessment method. In this letter, the concept of damping area is introduced to visualize the transient damping energy in a tailored phase portrait, which facilitates the physical and intuitive understanding of damping effects. On top of that, the damping area approximation method is further proposed to evaluate attraction domain quantitatively, and its conservativeness for VSG control is proved in theory and validated by experiments. The proposed method evaluates the impact of damping on attraction domain quantitatively and intuitively, and it may provide some insights into the VSG transient stability analysis.

Efficient min–max MPC: Achieving a large domain of attraction with short horizon

AbstractThis article considers the regulation problem of a constrained linear system with bounded disturbance. The objective is to overcome the offline and online problems of the standard dual‐mode min–max model predictive control (MPC). The offline problem is related to the construction of a polyhedral terminal set, which is prohibitively complex especially for high order systems. We propose to replace the polyhedral set with the ellipsoidal one, which is much easier to construct. The online problem is related to the computational burden, which grows exponentially with the prediction horizon . We show how to employ a new terminal cost function, that results in a new min–max MPC with a large domain of attraction even with or . Hence the computational complexity is drastically reduced. Two numerical examples with comparison to earlier solutions from the literature illustrate the effectiveness of the proposed approach.

Investigating Feature Selection Techniques to Enhance the Performance of EEG-Based Motor Imagery Tasks Classification

Analyzing electroencephalography (EEG) signals with machine learning approaches has become an attractive research domain for linking the brain to the outside world to establish communication in the name of the Brain-Computer Interface (BCI). Many researchers have been working on developing successful motor imagery (MI)-based BCI systems. However, they still face challenges in producing better performance with them because of the irrelevant features and high computational complexity. Selecting discriminative and relevant features to overcome the existing issues is crucial. In our proposed work, different feature selection algorithms have been studied to reduce the dimension of multiband feature space to improve MI task classification performance. In the procedure, we first decomposed the MI-based EEG signal into four sets of the narrowband signal. Then a common spatial pattern (CSP) approach was employed for each narrowband to extract and combine effective features, producing a high-dimensional feature vector. Three feature selection approaches, named correlation-based feature selection (CFS), minimum redundancy and maximum relevance (mRMR), and multi-subspace randomization and collaboration-based unsupervised feature selection (SRCFS), were used in this study to select the relevant and effective features for improving classification accuracy. Among them, the SRCFS feature selection approach demonstrated outstanding performance for MI classification compared to other schemes. The SRCFS is based on the multiple k-nearest neighbour graphs method for learning feature weight based on the Laplacian score and then discarding the irrelevant features based on the weight value, reducing the feature dimension. Finally, the selected features are fed into the support vector machines (SVM), linear discriminative analysis (LDA), and multi-layer perceptron (MLP) for classification. The proposed model is evaluated with two benchmark datasets, namely BCI Competition III dataset IVA and dataset IIIB, which are publicly available and mainly used to recognize the MI tasks. The LDA classifier with the SRCFS feature selection algorithm exhibits better performance. It proves the superiority of our proposed study compared to the other state-of-the-art BCI-based MI task classification systems.

Using Cluster Theory to Calculate the Experimental Structure Factors of Antibody Solutions

Monoclonal antibody solutions are set to become a major therapeutic tool in the years to come, capable of targeting various diseases by clever design of their antigen binding site. However, the formulation of stable solutions suitable for patient self-administration typically presents challenges, as a result of the increase in viscosity that often occurs at high concentrations. Here, we establish a link between the microscopic molecular details and the resulting properties of an antibody solution through the characterization of clusters, which arise in the presence of self-associating antibodies. In particular, we find that experimental small-angle X-ray scattering data can be interpreted by means of analytical models previously exploited for the study of polymeric and colloidal objects, based on the presence of such clusters. The latter are determined by theoretical calculations and supported by computer simulations of a coarse-grained minimal model, in which antibodies are treated as Y-shaped colloidal molecules and attractive domains are designed as patches. Using the theoretically predicted cluster size distributions, we are able to describe the experimental structure factors over a wide range of concentration and salt conditions. We thus provide microscopic evidence for the well-established fact that the concentration-dependent increase in viscosity is originated by the presence of clusters. Our findings bring new insights on the self-assembly of monoclonal antibodies, which can be exploited for guiding the formulation of stable and effective antibody solutions.

Stability analysis and estimation of domain of attraction for hydropower station with surge tank

The surge tank is extensively used pressure reduction facility in the hydropower station, and its stability of the water level oscillation (WLO) has always been a significant issue in academia and engineering. The stability of the WLO in the nonlinear hydropower station with surge tank (HSST) system is closely related to the external disturbance. This paper aims to study the stability and domain of attraction in the HSST system. Firstly, the nonlinear mathematical model of the HSST system is established. The critical stable cross-sectional area (CSCA) of surge tanks is investigated based on Lyapunov's first method. Subsequently, the estimation of domain of attraction is conducted based on Lyapunov's second method. Finally, the global asymptotic stability of the HSST system under Thoma stable area is analyzed. of surge tanks. The results show that when the surge tank area is smaller than Thoma stable area, the HSST system is unstable, so the CSCA is large than Thoma stable area. When the surge tank area is larger than Thoma stable area, the HSST system is locally asymptotically stable. The general method for constructing Lyapunov function is presented. The domain of attraction of the WLO is drawn, which defines the disturbance range of asymptotic stability of the HSST system. The domain of attraction rises with the increase of the surge tank area. When the surge tank area is taken as Thoma stable area, the system is not asymptotically stable under any disturbance. The proposed conclusions can provide theoretical reference for the design of surge tanks in practical engineering.

Power Feasible Region Ensuring Transient Stability of Droop-Based Multiconverters DC System

This article systematically focuses on the transient stability problem of droop-based multiconverters dc (MCdc) system caused by large power disturbances. Therefore, a new and effective transient stability analysis method is proposed. In the present method, it starts with reduced-order nonlinear mathematical modeling, followed by Lyapunov energy function building, and then the inscription of the largest estimated domain of attraction (LEDA) and the power feasible region (PFR). First, a state-variable equivalent transformation method is proposed. With this method, the droop-based MCdc system can be modeled as an equivalent single-converter (ESC) model without ignoring any coupling effects between the control state-variables. Second, a Takagi–Sugeno fuzzy model of the ESC is developed, which is able to construct the LEDA. Third, to ensure the transient stability of the MCdc system under large power disturbance, the concept of PFR is proposed. Furthermore, a PFR inscription algorithm is given based on the LEDA. In addition, the influence of control parameters on the PFR is analyzed, which will provide guidelines for the optimization of the PFR. Finally, the time domain experiments are carried out on the RT-BOX hardware-in-the-loop experimental platform to verify the effectiveness of the above theoretical analysis.

Design of asynchronous switched Takagi–Sugeno model‐based H∞ filters with nonlinear consequent parts for switched nonlinear systems

SummaryThis paper investigates the design of asynchronous switched nonlinear filters for a class of continuous‐time nonlinear switched systems with mismatching switching laws and norm‐bounded disturbances. In this context, the switched nonlinear system is modelled as a switched Takagi–Sugeno (T‐S) model with nonlinear consequent parts, that is, where unmeasured nonlinear terms are kept in the nonlinear consequent parts in order to circumvent the occurrence of unmeasured premise variables, which is usually faced in conventional T‐S modeling without nonlinear consequent parts. In this framework, asynchronous switched T‐S filters with unmeasured nonlinear consequent parts are proposed to estimate unmeasured and/or disturbed system's outputs, even when the filter's switching law mismatches the switched nonlinear system's one, which can be in practice unknown or imprecisely measured. Based on a candidate multiple Lyapunov function, combined with a criterion, conditions are proposed in terms of Linear Matrix Inequalities for the design of the considered asynchronous switched T‐S filters with unmeasured nonlinear consequent parts. Compared with previous related works, these conditions have the advantage of being dwell‐time‐independent and less conservative, thanks to the incremental quadratic constraints employed to deal with the unmeasured nonlinear consequent parts. Furthermore, acknowledging that T‐S models are only representing nonlinear ones on subsets of their state space, an optimization procedure to estimate the filtering error's domain of attraction is developed. Two illustrative examples are considered to validate the proposed results. An academic one is presented to illustrate the improvements brought in terms of conservatism by the proposed switched T‐S filter design methodology with regards to previous related studies. Then, a case study illustrates the effectiveness of this proposal from a switched nonlinear mass‐spring system inspired from related literature.

Adaptive fuzzy observer based non-quadratic control for nonlinear system subject to actuator faults and saturation

This paper provides a new non-quadratic stabilization conditions based on adaptive fuzzy observer for a class of Takagi-Sugeno (T-S) fuzzy systems subject to external disturbances and both actuator faults and saturation. Firstly, an observer based fault tolerant control (FTC) is proposed, not only to estimate both system states and actuator faults but also to compensate for the actuator faults and to stabilize the faulty system with input constraints. The saturation effect is transformed into dead-zone nonlinearity and the generalized sector bound condition is used to estimate the attraction domain. To less the conservatism of the quadratic Lyapunov technique, a proper integral structure based on the non-quadratic function is investigated. The H∞ criteria is considered and the robust stabilization conditions of the faulty closed-loop system are expressed as a linear matrix inequalities (LMIs) optimization problem. Finally, the robustness and the advantages of the proposed approach are demonstrated through a mixed CSTR and a numerical example.

Resilience of Pyrenean Forests after Recurrent Historical Deforestations

The long-term resilience of Pyrenean forests in the face of historical anthropogenic clearing remains largely unknown. In this paper, a high-resolution (decadal to subdecadal) paleoecological study of mid-elevation Pyrenean forests is presented that encompasses the last two millennia. This long-term record was obtained after sediment coring, dating (varve counting) and pollen analysis of annually laminated (varved) sediments from Lake Montcortès, situated at 1027 m elevation, in the transition between the Mediterranean and montane forest belts. This allowed the definition of three major deforestation/recovery cycles during the Roman, Medieval and Modern times. Each DR cycle is characterized considering three different levels: overall forest trends, forest type and individual taxa. Overall, the studied forests exhibited high resilience, as they recovered almost completely after each deforestation event (bulk resilience). The critical point of no return (tipping point) beyond which forests would have irreversibly disappeared from the region was never reached, even after deforestation magnitudes above 60%. The different forest types identified (conifer, sclerophyll and deciduous) persisted over time, showing similar heterogeneous patterns with minor spatial reorganizations (mosaic resilience). Individually, the main forest taxa underwent minor variations in their relative abundances, always within the same attraction domains (community resilience). The high levels of resilience documented in these Pyrenean forests are attributed to the action of metapopulation and metacommunity processes and mechanisms in a highly dynamic patchy environment. Conservation actions should be focused on the maintenance of these spatial patterns and the associated ecological dynamics.

Fighting in Cyberspace: Internet Access and the Substitutability of Cyber and Military Operations

Pundits debate whether conflict in cyberspace is more likely to trigger or preempt conflict in other domains. We consider a third possibility. Rather than directly complementing or substituting for traditional forms of conflict, the Internet could separately affect both virtual and kinetic dispute behavior. Specifically, we argue that a country’s increasing Internet access causes it to engage in aggressive cyberspace behavior more often. At the same time, economic and social changes associated with the information age reduce the utility of pursuing more traditional forms of conflict. Cyberspace offers an attractive domain in which to shape the balance of power, interests, and information in a technological era, while territorial conquest has become somewhat anachronistic. We test our theory using an innovative estimation approach, applied to panel data on cyber versus conventional disputes. Our findings confirm this indirect substitutability between cyber and conventional conflict.

DC operating points of nonlinear circuits and generalized Carleman linearization

PurposeThe purpose of this paper is to present a procedure for approximating DC operating points of nonlinear circuits. The presented approach can also be applied in case of multiple DC operating points.Design/methodology/approachA generalized Carleman linearization is used, which transforms an algebraic nonlinear equation into an equivalent infinite-dimensional linear system. In general, no close-form solution can be given for the infinite-dimensional linear system. Hence, the infinite-dimensional linear system is approximated by a finite one over a predefined interval using a self-consistent technique. The presented procedure allows to approximate all possible DC operating points within a predefined interval. To isolate all DC operating points, the initial interval is gradually divided into subintervals.FindingsIt is shown that the presented approach is not restricted to the polynomial case and allows to approximate all DC operating points. The presented approach can be applied in case of multiple DC operating points and does not depend on the domain of attraction of the DC operating points.Originality/valueA new procedure for the approximation of DC operating points of nonlinear circuits based on a generalized Carleman linearization is presented. This approach can be applied in case of multiple DC operating points and is independent of the domain of attraction. Further, this generalized approach is not restricted to the polynomial case and can be applied to a variety of circuits.

Large-Signal Stability Analysis for Inverter-Based Dynamic Microgrids Reconfiguration

Compared to conventional microgrids (MGs) with pre-defined and static topology, dynamic MGs feature varying electric boundaries and enhanced operational resiliency. This paper evaluates the operation stability of inverter-based dynamic MGs in terms of fulfilling the requested MGs topology change and associated network reconfiguration, which falls into the category of large-signal stability analysis. A complete nonlinear state-space model of inverter-based dynamic MGs is derived, where coordinated controls among inverters along with the effect of communication delays have been considered. In response to reconfiguration demands, an evaluation scheme is developed to determine whether the system could perform seamless topology variation without losing synchronism. Specifically, the system’s stability region is quantified by the domain of attraction (DoA) around the desired operating point using Takagi-Sugeno fuzzy modeling (T-S multimodeling). The large-signal stability of a multi-bus inverter-based dynamic MG with both interface inverters and sectionalizing switches have been analyzed. The stability regions estimated under different scenarios of topology variation have been validated using time-domain simulation in MATLAB/Simulink. The developed evaluation scheme is used to quantify the effects of control gain designs and communication delays on system large-signal stability.

Stabilization of the Moving Front Solution of the Reaction-Diffusion-Advection Problem

We consider the initial-boundary value problem of reaction-diffusion-advection that has a solution of a front form. The statement comes from the theory of wave physics. We study the question of the solution stabilizing to the stationary one. Proof of the stabilization theorem is based on the concepts of upper and lower solutions and corollaries from comparison theorems. The upper and lower solutions with large gradients are constructed as modifications of the formal moving front asymptotic approximation in a small parameter. The main idea of the proof is to show that the upper and lower solutions of the initial-boundary value problem get into the attraction domain of the asymptotically stable stationary solution on a sufficiently large time interval. The study conducted in this work gives an answer about the non-local attraction domain of the stationary solution and can give some stationing criteria. The results are illustrated by computational examples.

Impact of correlated Gaussian colored noises on stability and stationary probability density for the randomly forced two-species competitive Gompertz model

In this paper, random factors described by correlated Gaussian colored noises are introduced into a two-species competition model with Gompertz growth. Firstly, stochastic stability is studied with the help of singular boundary theory. After that, the stationary probability density of the limiting system is given explicitly and then the extrema of invariant measure are discussed in detail. Finally, the average time of system escaping from the attraction domain is calculated using mean first passage time, and noise enhanced stability is observed. Our results show that random factors are more likely to make the system lose its original stability. Instead, the sample trajectories will stay near the maximum of the stationary probability density for a long time. Importantly, noise intensity and correlation degree are destructive, which can expand the distribution range of population density, weaken the stability of the system, and then easily lead to ecological imbalance. Conversely, the role of correlation time and proper competition between species is constructive and conducive to coexistence.