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Related papers: Lyapunov Approach to Consensus Problems

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Polyhedral Lyapunov functions can approximate any norm arbitrarily well. Because of this, they are used to study the stability of linear time varying and linear parameter varying systems without being conservative. However, the…

Optimization and Control · Mathematics 2021-03-08 Dimitris Kousoulidis , Fulvio Forni

We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable…

Dynamical Systems · Mathematics 2013-06-12 A. Gorban , I. Tyukin , E. Steur , H. Nijmeijer

We propose consensus propagation, an asynchronous distributed protocol for averaging numbers across a network. We establish convergence, characterize the convergence rate for regular graphs, and demonstrate that the protocol exhibits better…

Information Theory · Computer Science 2007-07-13 Ciamac C. Moallemi , Benjamin Van Roy

We propose a technique for the design and analysis of adaptation algorithms in dynamical systems. The technique applies both to systems with conventional Lyapunov-stable target dynamics and to ones of which the desired dynamics around the…

Optimization and Control · Mathematics 2007-05-23 Tyukin Ivan , Danil Prokhorov , Cees van Leeuwen

In this paper, finite-time state consensus problems for continuous-time multi-agent systems are discussed, and two distributive protocols, which ensure that the states of agents reach an agreement in a finite time, are presented. By…

Dynamical Systems · Mathematics 2007-05-23 Long Wang , Feng Xiao

This paper fully studies distributed optimal consensus problem in non-directed dynamical networks. We consider a group of networked agents that are supposed to rendezvous at the optimal point of a collective convex objective function. Each…

Optimization and Control · Mathematics 2017-12-22 Amir Adibzadeh , Amir A. Suratgar , Mohammad B. Menhaja , Mohsen Zamani

Stochastic optimal control problems have a long tradition in applied probability, with the questions addressed being of high relevance in a multitude of fields. Even though theoretical solutions are well understood in many scenarios, their…

Statistics Theory · Mathematics 2024-05-28 Sören Christensen , Claudia Strauch , Lukas Trottner

Representation of a swarm of independent robotic agents under graph-theoretic constructs allows for more formal analysis of convergence properties. We consider the local and global convergence behavior of an N-member swarm of agents in a…

Adaptation and Self-Organizing Systems · Physics 2010-10-26 Gregory K. Fricke , Bruce W. Rogers , Devendra P. Garg

In this paper, we focus on the topic Synchronization and consensus of Complex Networks and their relationships. It is revealed that two topics are closely relating to each other and all results given in \cite{Li1,Li2} and many other papers…

Adaptation and Self-Organizing Systems · Physics 2018-10-01 Tianping Chen

We introduce a simple dynamic model of opinion formation, in which a finite population of individuals hold vector-valued opinions. At each time step, each individual's opinion moves towards the mean opinion but is then perturbed…

Probability · Mathematics 2026-03-27 Edward Crane , Stanislav Volkov

We study the convergence properties of the original and away-step Frank-Wolfe algorithms for linearly constrained stochastic optimization assuming the availability of unbiased objective function gradient estimates. The objective function is…

Optimization and Control · Mathematics 2025-04-08 Natthawut Boonsiriphatthanajaroen , Shane G. Henderson

The majority of machine learning methods can be regarded as the minimization of an unavailable risk function. To optimize the latter, given samples provided in a streaming fashion, we define a general stochastic Newton algorithm and its…

Statistics Theory · Mathematics 2023-06-30 Claire Boyer , Antoine Godichon-Baggioni

Switching between finitely many continuous-time autonomous steepest descent dynamics for convex functions is considered. Convergence of complete solutions to common minimizers of the convex functions, if such minimizers exist, is shown. The…

Optimization and Control · Mathematics 2018-08-06 Rafal Goebel , Ricardo Sanfelice

We consider a matching system where items arrive one by one at each node of a compatibility network according to Poisson processes and depart from it as soon as they are matched to a compatible item. The matching policy considered is a…

Probability · Mathematics 2020-11-10 Matthieu Jonckheere , Pascal Moyal , Claudia Ramírez , Nahuel Soprano-Loto

This paper is concerned with the study of synchronization and consensus phenomena in complex networks of diffusively-coupled nodes subject to external disturbances. Specifically, we make use of stochastic Lyapunov functions to provide…

Systems and Control · Computer Science 2016-03-22 Giovanni Russo , Rovert Shorten

In this note we investigate the problem of global exponential synchronization of multi-agent systems described by nonlinear input affine dynamics. We consider the case of networks described by undirected connected graphs possibly without…

Optimization and Control · Mathematics 2024-11-01 Vincent Andrieu , Daniele Astolfi , Alexandre Cellier-Devaux

Stability of stationary solutions of parabolic equations is conventionally studied by linear stability analysis, Lyapunov functions or lower and upper functions. We discuss here another approach based on differential inequalities written…

Functional Analysis · Mathematics 2012-06-26 A. G. Ramm , V. Volpert

In this paper, we present estimates for solutions and for the attraction domain of the trivial solution for systems with delayed and nonlinear weighted homogeneous right-hand side of positive degree. The results are achieved via a…

Systems and Control · Electrical Eng. & Systems 2021-01-27 Gerson Portilla , Irina Alexandrova , Sabine Mondié

This article investigates the consensus tracking problem of multi-agent systems under jointly connected topology through automated synthesis of Lyapunov functions. Based on the proposed distributed nonlinear control protocol, several…

Optimization and Control · Mathematics 2026-05-28 Shuyuan Zhang , Lei Wang , Qing-Guo Wang

We present an analytical-numerical method providing robust upper estimates for the topological entropy or, more generally, uniform volume growth exponents of differentiable mappings. By introducing varying metrics, we simplify the analysis…

Dynamical Systems · Mathematics 2025-03-17 Mikhail Anikushin , Andrey Romanov