Notion Of Stability Research Articles

A Cooperative Implementation of Mesh Stability in Vehicular Platoons

This work studies the problem of mesh stability in connected and automated vehicles. Mesh stability, also known as 2D string stability, refers to studying how disturbances propagate in vehicular platoons in both longitudinal and lateral direction. As opposed to available decentralized results only relying on on-board sensing, the distinguishing feature of this work is a cooperative version of mesh stability, where on-board sensing is augmented by vehicle-to-vehicle communication. This cooperative version dramatically improves the state-of-the-art decentralized performance: for longitudinal control, a new cooperative non-identical protocol (i.e. with non-identical control gains) is proposed that improves the state-of-the-art decentralized non-identical protocol in terms of scalability of the control gains and strong notion of string stability. For lateral control, after showing that the non-identical approach is not necessary, a cooperative non-identical protocol is proposed to achieve another strong notion of string stability. Robustness of the proposed implementation against vehicle-to-vehicle communication delays and actuation time lags is considered. Numerical experiments, also performed with the vehicle simulator CarSim, validate the robustness and effectiveness of the proposed protocol.

Stability in mechanics and dynamics; a brief historical tour from Newton to modern tools, including Riemannian structures and entropy

AbstractThis article presents some historical developments in the theory of stability in mechanics from a dynamical systems point of view, focusing on mathematical methods from the earliest developments (Newton) and explaining some classical and some recent methods used, including Riemannian structures, entropy and notions of stability in dynamics.

Stability analysis of stochastic gradient descent for homogeneous neural networks and linear classifiers

We prove new generalization bounds for stochastic gradient descent when training classifiers with invariances. Our analysis is based on the stability framework and covers both the convex case of linear classifiers and the non-convex case of homogeneous neural networks. We analyze stability with respect to the normalized version of the loss function used for training. This leads to investigating a form of angle-wise stability instead of euclidean stability in weights. For neural networks, the measure of distance we consider is invariant to rescaling the weights of each layer. Furthermore, we exploit the notion of on-average stability in order to obtain a data-dependent quantity in the bound. This data-dependent quantity is seen to be more favorable when training with larger learning rates in our numerical experiments. This might help to shed some light on why larger learning rates can lead to better generalization in some practical scenarios.

Lipschitz structural stability of group actions with the shadowing property

In this paper, we introduce a notion of Lipschitz structural stability for finitely generated group actions on compact metric spaces, and prove that if a finitely generated group action on a compact manifold is expansive and has the shadowing property then it is Lipschitz structurally stable. For this we first extend the notion of hyperbolic metric for homeomorphisms to our setting, and show that a finitely generated group action admits a hyperbolic metric if and only if it is expansive. Applications are given for north-south and symbolic dynamics.

Hedonic coalition formation games: Nash stability under different membership rights

Purpose - We study hedonic coalition formation games in which each agent has preferences over the coalitions she is a member of. Hedonic coalition formation games are used to model economic, social, and political instances in which people form coalitions. The outcome of a hedonic coalition formation game is a partition. We consider stability concepts of a partition that are based on a single-agent deviation under different membership rights, that is, we study Nash stability under different membership rights. We revisit the conditions that guarantee the existence of Nash stable partitions and provide examples of hedonic coalition formation games satisfying these conditions. Methodology – While analyzing a stability notion for hedonic coalition formation games, two crucial points are considered: i) who can deviate from the given partition, ii) what are the allowed movements for the deviator(s), i.e., what deviators are entitled to do. For the first point, the deviation of a single agent is considered for Nash stabilities. For the second point, the allowed movements for deviators are determined by specifying membership rights, that is, membership rights describe whose approval is needed for a particular deviation. So, we reconsider stability concepts by using membership rights based on individual deviations, i.e., we consider Nash stability under different membership rights for hedonic coalition formation games. Findings- A classification of stability concepts based on a single-agent deviation for hedonic coalition formation games are provided by employing membership rights. The conditions in the literature guaranteeing the existence of Nash stable partitions for all membership rights are revisited. For each condition, an example of a hedonic coalition formation game satisfying the condition is given. Hence, a complete analysis of sufficient conditions for all Nash stability concepts are provided. Conclusion- To choose the correct stability notion one first should understand the membership rights in the environment that she studies. Then, for hedonic coalition formation problems, the appropriate Nash stability notion consistent with the ongoing membership rights should be chosen when single-agent deviation is considered. Keywords: Coalition formation, Hedonic games, Nash stability, membership rights, separable preferences JEL Codes: C71, C78, D71

Extended Stability and Control Strategies for Impulsive and Fractional Neural Networks: A Review of the Recent Results

In recent years, cellular neural networks (CNNs) have become a popular apparatus for simulations in neuroscience, biology, medicine, computer sciences and engineering. In order to create more adequate models, researchers have considered memory effects, reaction–diffusion structures, impulsive perturbations, uncertain terms and fractional-order dynamics. The design, cellular aspects, functioning and behavioral aspects of such CNN models depend on efficient stability and control strategies. In many practical cases, the classical stability approaches are useless. Recently, in a series of papers, we have proposed several extended stability and control concepts that are more appropriate from the applied point of view. This paper is an overview of our main results and focuses on extended stability and control notions including practical stability, stability with respect to sets and manifolds and Lipschitz stability. We outline the recent progress in the stability and control methods and provide diverse mechanisms that can be used by the researchers in the field. The proposed stability techniques are presented through several types of impulsive and fractional-order CNN models. Examples are elaborated to demonstrate the feasibility of different technologies.

Well-posedness for a stochastic Camassa–Holm type equation with higher order nonlinearities

This paper aims at studying a generalized Camassa–Holm equation under random perturbation. We establish a local well-posedness result in the sense of Hadamard, i.e., existence, uniqueness and continuous dependence on initial data, as well as blow-up criteria for pathwise solutions in the Sobolev spaces Hs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H^s$$\\end{document} with s>3/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$s>3/2$$\\end{document} for x∈R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$x\\in \\mathbb R$$\\end{document}. The analysis on continuous dependence on initial data for nonlinear stochastic partial differential equations has gained less attention in the literature so far. In this work, we first show that the solution map is continuous. Then we introduce a notion of stability of exiting time. We provide an example showing that one cannot improve the stability of the exiting time and simultaneously improve the continuity of the dependence on initial data. Finally, we analyze the regularization effect of nonlinear noise in preventing blow-up. Precisely, we demonstrate that global existence holds true almost surely provided that the noise is strong enough.

Ritualized world relations: a Confucian critique of Rosa’s limitations on resonance

Hartmut Rosa argues that our modern and post-modern societies can be understood through the notion of dynamic stabilization—institutions require growth to maintain themselves. Part of the impetus behind the acceleration that drives dynamic stabilization is the desire to make the world more available, attainable, and accessible. On both the institutional and individual levels, this is translated into making the world more within our reach, more engineerable, predictable, and controllable. Paradoxically, success in these areas is often accompanied by the world becoming increasingly silent, cold, and unresponsive. We feel alienated or that our world relation has failed. Rosa’s solution is to reestablish resonance with the world. In this paper, we argue that his notion of resonance depends on a degree of atomic agency that muffles its own efficacy. The Confucian notion of ritual offers a more dispersed notion of agency. Rather than seeing oneself, others, and the world as distinct agents or indivisible entities, a ritualized approach sees them as mutually constitutive. It is true even on the level of agency, which drastically changes our relationship with the world.

Logahoric Higgs torsors for a complex reductive group

In this article, a logahoric Higgs torsor is defined as a parahoric torsor with a logarithmic Higgs field. For a connected complex reductive group G, we introduce a notion of stability for logahoric $$\mathcal {G}_{\varvec{\theta }}$$ -Higgs torsors on a smooth algebraic curve X, where $$\mathcal {G}_{\varvec{\theta }}$$ is a parahoric group scheme on X. In the case when the group G is the general linear group $$\textrm{GL}_n$$ , we show that the stability condition of a parahoric torsor is equivalent to the stability of a parabolic bundle. A correspondence between semistable logahoric $$\mathcal {G}_{\varvec{\theta }}$$ -Higgs torsors and semistable equivariant logarithmic G-Higgs bundles allows us to construct the moduli space explicitly. This moduli space is shown to be equipped with an algebraic Poisson structure.

Stability and disruptive speech

Stability and disruptive speech

Approach to the synthesis of an aperiodic robust automatic control system based on the gradient-speed method of Lyapunov vector functions

One of the actual problems for the theory and practice of control of dynamic objects is the development of methods for research and synthesis of control systems of multidimensional objects. The paper proposes a universal approach to construct Lyapunov vector functions directly from the equation of state of control system and a new gradient-speed method of Lyapunov vector functions to study aperiodic robust stability of linear control system with m inputs and n outputs. The study of aperiodic robust stability of automatic control systems is based on the construction of Lyapunov vector functions and gradient-speed dynamic control systems. The basic statements of Lyapunov's theorem about asymptotic stability and notions of stability of dynamic systems are used. The representation of control systems as gradient systems and Lyapunov functions as potential functions of gradient systems from the catastrophe theory allow to construct the full-time derivative of Lyapunov vector functions always as a sign-negative function equal to the scalar product of the velocity vector on the gradient vector. The conditions of aperiodic robust stability are obtained as a system of inequalities on the uncertain parameters of the automatic control system, which are a condition for the existence of the Lyapunov vector-function. A numerical example of synthesis of aperiodic robustness of a multidimensional control object is given. The example shows the main stages of the developed synthesis method, the study of the system stability at different values of the coefficients k, confirming the consistency of the proposed method. Transients in the system satisfy all requirements

INVESTIGATION OF THE IMPLEMENTATION OF LEADER-FOLLOWER FORMATION CONTROL TO BIPEDAL LOCOMOTION

Robot that uses bipedal locomotion such as humanoid robot has a unique appeal in which the robot can perform many duties/works that cannot be done by wheeled robots due to spatial and environmental constraints. Related literature were about biped robots and robot arm that uses the concept of central pattern generator (CPG). Biped robots that use CPG (technically a neural oscillators) do not need any mathematical model of the robot itself. The controller “exploits” the dynamics of the robot to achieve an efficient way to drive the robot’s joints. The driving frequency from this type of controller is thus heavily influenced by the dynamics of the robot it controls. One disadvantage of this method is that we cannot adjust the walking/movement parameter easily. Inspired by the idea of central pattern generator where one central “brain” controls the movement of the joints of the robot and the fact that the system uses neural oscillators reach some kind of “consensus”, we are interested to study the feasibility of the implementation of leader – follower formation control based on consensus algorithm to bipedal locomotion system. The method studied in this report is to force the dynamic model of the double pendulum to match the kinematic model of the double integrator agent that uses consensus algorithm in forming formation. The walking/movement parameters of the robot using the proposed method are defined by one central “brain”, and then the joints are working in consensus way to achieve the target joints’ trajectories specified by the “brain”. The study also concludes the notion of stability of the system driven by this controller which strongly related to the consensus ability in the context of Multi – Agent System.

Blind matching algorithm based proxy distribution against internet censorship

AbstractProxy based censorship circumvention technique is treated as one of the most promising approaches to fighting against Internet censorship, and its practical applications like the onion router and Lantern have been widely utilized. However, the proxy distribution, as a basic and core issue, still remains unsolved due to (i) the finiteness and non‐renewable nature of proxy resources, (ii) the heterogeneity of clients and proxies requirements, and (iii) the existence of secondary censorship. In this paper, a win‐win driven proxy distribution mechanism for proxy based censorship circumvention systems is designed by leveraging the blind matching theory. Specifically, a combinational manner is developed to measure the quality of service (QoS) requirements of clients in terms of normalized bandwidth and reliability, and security requirements of proxies in terms of credits and suspicion. Then, by introducing the concept of virtual currency, the proxy distribution issue is formulated as two‐sided combinatorial problems from the perspective of clients and proxies, respectively. To solve the complex NP‐hard combinatorial problems in a win‐win manner without unilateral dominance, a two‐sided many‐to‐many context‐free matching game is constructed, in which the aspiration levels and agreement functions are defined to capture the security and QoS concerns of clients and proxies. Further, a modified notion of pairwise stability is exploited as the solution concept, and a client‐proxy blind matching algorithm with market and information decentralization is proposed to obtain the ε‐pairwise stable solution, where clients and proxies make encounters randomly and update their aspiration levels through a stochastic learning process. Finally, theoretical analysis and numerical results are carried out to validate the properties and performance of the proposed algorithm including stability, complexity, and convergence.

THEORETICAL AND PRACTICAL ASPECTS OF MANAGEMENT OF THE FINANCIAL STABILITY OF THE ENTERPRISE

The article considers the basic scientific approaches to the economic contents of the notions of financial stability, mechanism of enterprise management. Offered interpretations of the concept of the mechanism of financial stability enterprise management and main stages of the process of its formation. The activity of the Ukrainian enterprise "Stalkonstruktsia" LLC is characterized. It was determined that during 2019-2021, the company's balance sheet is completely liquid, which indicates a sufficient amount of funds to repay current liabilities. The indicators of the business activity of "Stalkonstruktsia" LLC in 2019-2021 positively characterize the company's activity, namely, the company uses its own capital effectively, we observe an increase in the turnover rate of stocks, finished products, accounts payable and an increase in the efficiency of their use, which is positively reflected in the business activity of the company. It was concluded that the enterprise needs to use more long-term debt financing in its economic activities, which will increase the return on equity.

Arithmetic statistics and diophantine stability for elliptic curves

We study the growth and stability of the Mordell–Weil group and Tate–Shafarevich group of an elliptic curve defined over the rationals, in various cyclic Galois extensions of prime power order. Mazur and Rubin introduced the notion of diophantine stability for the Mordell–Weil group an elliptic curve $$E_{/{{\mathbb {Q}}}}$$ at a given prime p. Inspired by their definition of stability for the Mordell–Weil group, we introduce an analogous notion of stability for the Tate–Shafarevich group, called -stability. From the perspective of Iwasawa theory, it benefits us to introduce a stronger notion of diophantine stability for the Mordell–Weil group. It is shown that any non-CM elliptic curve of rank 0 defined over the rationals is strongly diophantine stable and -stable at $$100\%$$ of primes p. Next, we show that standard conjectures on rank distribution give lower bounds for the proportion of rational elliptic curves E that are strongly diophantine stable at a fixed prime $$p\ge 11$$ . Related questions are studied for rank jumps and growth of ranks Tate–Shafarevich groups on average in prime power cyclic extensions.

Lyapunov stability of the subgradient method with constant step size

We consider the subgradient method with constant step size for minimizing locally Lipschitz semi-algebraic functions. In order to analyze the behavior of its iterates in the vicinity of a local minimum, we introduce a notion of discrete Lyapunov stability and propose necessary and sufficient conditions for stability.

On stability for generalized linear differential equations and applications to impulsive systems

In this paper, we are interested in investigating notions of stability for generalized linear differential equations (GLDEs). Initially, we propose and revisit several definitions of stability and provide a complete characterization of them in terms of upper bounds and asymptotic behaviour of the transition matrix. In addition, we illustrate our stability results for GLDEs to linear periodic systems and linear impulsive differential equations. Finally, we prove that the well-known definitions of uniform asymptotic stability and variational asymptotic stability are equivalent to the global uniform exponential stability introduced in this article.

On [formula omitted]-manifolds stability for impulsive delayed SIR epidemic models

In this paper, we study an impulsively extended delayed SIR (Susceptible-Infected-Recovered) epidemic model for the spread of infectious diseases. The impulsive control model is represented by a neural network system with reaction-diffusion terms and impulses at fixed instants of time. The notion of stability of specific manifolds defined by continuous functions is introduced to the model under consideration. Using the Lyapunov impulsive approach, we derive criteria for the global practical exponential stability of the defined manifolds of solutions. Since the stability of manifolds concepts generalize the stability of separate state notions, our results are more general and they extend some existing stability results for non-impulsive and impulsive SIR epidemic models. An example is considered to show the effectiveness of our results.

The Graph Model for Conflict Resolution and Credible Maximin Stability

In strategic conflicts, the behavior of decision makers (DMs) is affected by their beliefs about how their opponents will respond, how they will counter respond, and more generally by the number of action-reaction steps they consider. In this article, we propose several notions of stability with variable horizon that vary in whether the focal DM and her opponents are allowed to make moves that are immediately disadvantageous, called unilateral disimprovements. Credible maximin stability reflects the assumption that opponents will attempt to deter a focal DM from a move by imposing the strongest possible sanction. We analyze the effects of varying the horizon on this form of stability, and on the relationships among the solution concepts that result. Requiring the focal DM to make only unilateral improvements does not influence the stability of states, but restricting opponents’ responses to unilateral improvements reduces the set of stable states. An application to a water-pricing conflict illustrates the analysis of a graph model using credible maximin stabilities.

On the notions of normality, locality, and operational stability in ADRC

On the notions of normality, locality, and operational stability in ADRC