The study of complex networks with multi-weights has been a hot topic recently. For a network with a single weight, previous studies have shown that they can promote synchronization. But for complex networks with multi-weights, there are no rigorous analysis to show that synchronization can be reached faster. In this paper, the complex network is allowed to be directed, which will make the synchronization analysis difficult for multiple couplings. In virtue of the normalized left eigenvectors (NLEVec) corresponding to the zero eigenvalue of coupling matrices, we prove that if the Chebyshev distance between NLEVec is less than some value, which is defined as the allowable deviation bound, then the synchronization and control will be realized with sufficiently large coupling strengths, i.e., all coupling matrices do accelerate synchronization. Moreover, adaptive rules are also designed for the coupling strength.
In this note, we study the prescribed-time (PT) synchronization of multiweighted and directed complex networks (MWDCNs) via pinning control. Unlike finite-time and fixed-time synchronization, the time for synchronization can be preset as needed, which is independent of initial values and parameters like coupling strength. First and foremost, we reveal the essence of PT stability by improper integral, L'Hospital rule and Taylor expansion theory. Many controllers established previously for PT stability can be included in our new model. Then, we apply this new result on MWDCNs as an application. …
We study synchronization and consensus in a group of dynamical systems coupled via multiple directed networks. We show that even though the coupling in a single network may not be sufficient to synchronize the systems, combination of multiple networks can contribute to synchronization. We illustrate how the effectiveness of a collection of networks to synchronize the coupled systems depends on the graph topology. In particular, we show that if the graph sum is a directed graph whose reversal contains a spanning directed tree, then the network synchronizes if the coupling is strong enough. This…
This study deals with analysis and control of cooperative synchronization for identical agents interacting on a directed graph topology. The agents are considered to have general continuous linear time-invariant dynamics with homogeneous communication and/or control delays. An LMI approach based on a Lyapunov-Krasovskii functional is proposed, together with the synchronizing region concept, which decouples the single-agent dynamics from the detailed graph topology. Moreover, the conventional notion of synchronizing region is here extended by an LMI relaxation utilizing quasi-convex characteris…
We study the problem of robust global synchronization of pulse-coupled oscillators (PCOs) over directed graphs. It is known that when the digraphs are strongly connected, global synchronization can be achieved by using a class of deterministic set-valued reset controllers. However, for large-scale networks, these algorithms are not scalable because some of their tuning parameters have upper bounds of the order of O(1/N), where N is the number of agents. This paper resolves this scalability issue by presenting several new results in the context of global synchronization of PCOs with more genera…
Almost Decouplability of any Directed Weighted Network Topology
College of Electrical Engineering, Northwest University for Nationalities（西北民族大学电气工程学院）；PN Engineering College, National University of Sciences and Technology（国立科技大学工程与科学学院）
This paper studies scale-free protocol design for H2 almost state synchronization of homogeneous networks of non-introspective agents in presence of external disturbances. The necessary and sufficient conditions are provided by designing collaborative linear dynamic protocols. The design is based on localized information exchange over the same communication network, which does not need any knowledge of the directed network topology and the spectrum of the associated Laplacian matrix. Moreover, the proposed protocol is scalable and achieves H2 almost synchronization with a given arbitrary degre…
This paper studies global regulated state synchronization of discrete-time double-integrator multi-agent systems subject to actuator saturation by utilizing localized information exchange. We propose a scale-free linear protocol that achieves global regulated state synchronization for any network with arbitrary number of agents and arbitrarily directed communication graph that has a path between each agent and exosystem which generates the reference trajectory.
This paper studies synchronization of homogeneous and heterogeneous discrete-time multi-agent systems. A class of linear dynamic protocol design methodology is developed based on localized information exchange with neighbors which does not need any knowledge of the directed network topology and the spectrum of the associated Laplacian matrix. The main contribution of this paper is that the proposed protocols are scale-free and achieve synchronization for arbitrary number of agents.
This paper studies regulated state synchronization of homogeneous networks of non-introspective agents in presence of unknown nonuniform input delays. A scale-free protocol is designed based on additional information exchange, which does not need any knowledge of the directed network topology and the spectrum of the associated Laplacian matrix. The proposed protocol is scalable and achieves state synchronization for any arbitrary number of agents. Meanwhile, an upper bound for the input delay tolerance is obtained, which explicitly depends on the agent dynamics.
Synchronization is an essential property of engineered and natural networked dynamical systems. The Kuramoto model of nonlinear synchronization has been widely studied in applications including entrainment of clock cells in brain networks and power system stability. Synchronization of Kuramoto networks has been found to be challenging in the presence of signed couplings between oscillators and when the network includes oscillators with heterogeneous natural frequencies. In this paper, we study the problem of minimum-set control input selection for synchronizing signed Kuramoto networks. We fir…
This paper studies scale-free protocol design for H_\infty almost output and regulated output synchronization of heterogeneous multi-agent systems with linear, right-invertible, and introspective agents in presence of external disturbances. The collaborative linear protocol designs are based on localized information exchange over the same communication network, which do not require any knowledge of the directed network topology and spectrum of the associated Laplacian matrix. Moreover, the proposed scale-free protocols achieve H_\infty almost synchronization with a given arbitrary degree of ac…
This paper addresses the output synchronization problem for heterogeneous nonlinear multi-agent systems with distributed event-based controllers. Employing the two-step synchronization process, we first outline the distributed event-triggered consensus controllers for linear reference models under a directed communication topology. It is further shown that the subsequent triggering instants are based on intermittent communication. Secondly, by using certain input-to-state stability (ISS) property, we design an event-triggered perturbed output regulation controller for each nonlinear multi-agen…
We study asynchronous dynamics in a network of interacting agents updating their binary states according to a time-varying threshold rule. Specifically, agents revise their state asynchronously by comparing the weighted average of the current states of their neighbors in the interaction network with possibly heterogeneous time-varying threshold values. Such thresholds are determined by an exogenous signal representing an external influence field modeling the different agents' biases towards one state with respect to the other one. We prove necessary and sufficient conditions for global stabili…
This paper considers the fixed-time control problem of a multi-agent system composed of a class of Euler-Lagrange dynamics with parametric uncertainty and a dynamic leader under a directed communication network. A distributed fixed-time observer is first proposed to estimate the desired trajectory and then a fixed-time controller is constructed by transforming uncertain Euler-Lagrange systems into second-order systems and utilizing the backstepping design procedure. The overall design guarantees that the synchronization errors converge to zero in a prescribed time independent of initial condit…
This paper studies scalable global state synchronization of discrete-time double integrator multi-agent systems in presence of input saturation based on localized information exchange. A scale-free collaborative linear dynamic protocols design methodology is developed for discrete-time multi-agent systems with both full and partial-state couplings. And the protocol design methodology does not need any knowledge of the directed network topology and the spectrum of the associated Laplacian matrix. Meanwhile, the protocols are parametric based on a parameter set in which the designed protocols ca…
This paper studies global and semi-global regulated state synchronization of homogeneous networks of non-introspective agents in presence of input saturation based on additional information exchange where the reference trajectory is given by a so-called exosystem which is assumed to be globally reachable. Our protocol design methodology does not need any knowledge of the directed network topology and the spectrum of the associated Laplacian matrix. Moreover, the proposed protocol is scalable and achieves synchronization for any arbitrary number of agents.
