General Algebraic Connectivity Research Articles

Consensus of Stochastic Dynamical Multiagent Systems in Directed Networks via PI Protocols.

With the rapid development of swarm intelligence, the consensus of multiagent systems (MASs) has attracted substantial attention due to its broad range of applications in the practical world. Inspired by the considerable gap between control theory and engineering practices, this article is aimed at addressing the mean square consensus problems for stochastic dynamical nonlinear MASs in directed networks by designing proportional-integral (PI) protocols. In light of the general algebraic connectivity, consensus underlying PI protocols for a directed strongly connected network is investigated, and due to the M -matrix approaches, consensus with PI protocols for a directed network containing a spanning tree is studied. By constructing appropriate Lyapunov functions, combining with the stochastic analysis technique and LaSalle's invariant principles, some sufficient conditions are derived under which the stochastic dynamical MASs realize consensus in mean square. Numerical simulations are finally presented to illustrate the validity of the main results.

Quantized-observer based consensus for fractional order multi-agent systems under distributed event-triggered mechanism

This paper investigates the consensus problem of general nonlinear fractional order multi-agent systems in a directed network under event-triggered mechanism. First, observers are designed for every agent based on the outputs of them. Second, taking the constrains of communication bandwidth and storage space into consideration, the uniform quantizers are used for each channel. Then, the consensus criteria related with the general algebraic connectivity of communication topology under event-triggered mechanism are derived, furthermore, the Zeno behavior is excluded. Finally, an example is given to shown the effectiveness of the proposed methods.

Output-Feedback Self-Synchronization of Directed Lur'e Networks via Global Connectivity.

In this article, we generalize the results on self-synchronization of Lur'e networks diffusively interconnected through dynamic relative output-feedback from the undirected graph case in Zhang et al. 2016 to the general directed graph case. A linear dynamic self-synchronization protocol of the same structure is adopted as the one proposed in Zhang et al. 2016. That is, the Lur'e-type nonlinearity is not involved in our self-synchronization protocol. It is in fact unknown and only assumed to be incrementally sector bounded within a given sector. In the absence of a leader Lur'e system defining the synchronization trajectory, we construct a novel self-synchronization manifold in order to derive the self-synchronization error dynamics. Meanwhile, the connectivity of the general directed graph having a directed spanning tree is quantified by the global connectivity, instead of the so-called general algebraic connectivity used in the directed graph case under static relative state feedback. The global connectivity plays a crucial role in handling self-synchronization problems of directed nonlinear networks via dynamic relative output feedback, including directed networks with the Lipschitz nonlinear node dynamics, which is also discussed in this article. The protocol parameter matrix design is performed by solving the obtained LMI conditions in sequence. In addition, some discussions are complemented on the important technical details in our self-synchronization protocol design along with extensions. Finally, our theoretical results are illustrated through numerical simulations over a directed nonlinear dynamical network.

Improved leaderless consenus criteria of networked multi-agent systems based on the sampled data

ABSTRACTThis paper is concerned with leaderless consensus of networked multi-agent systems with Lipschitz-type nonlinear dynamics based on the sampled data. By introducing a weighted average state of all nodes as the virtual leader, the error variables are defined as the distance between agents and the virtual leader. The improvements are done in two directions. First, several consensus conditions are derived by linear matrix inequalities based on Finsler's lemma instead of algebraic criteria based on the general algebraic connectivity. Finsler's lemma is utilised to deal with the linear dependence of the error variables. Second, a distributed event-triggered transmission strategy under the periodic sampling scheme is proposed to reduce the communication between agents and the control updates, which only need to check the event condition at each sampling instant, avoiding the continuous monitor. With the improved strategies, one theorem and two corollaries are derived and a co-design approach of the feedback gain and the event-triggered matrix is also presented. Finally, an example is provided to validate the effectiveness of the theoretical results.

Synchronization control for reaction–diffusion FitzHugh–Nagumo systems with spatial sampled-data

To gain a better understanding the synchronization mechanism of networked neurons, this paper studies the synchronization control for a class of reaction–diffusion FitzHugh–Nagumo systems, associated with a digraph containing at least one directed spanning tree. A novel control method adopting spatial sampling strategies is proposed, in which the control inputs are constructed directly on the spatial means of system state variables on sampling subsets. After discussing the existence and uniqueness of classical solutions, we show analytically that the synchronization of the controlled systems is equivalent to that of the corresponding FitzHugh–Nagumo systems under the corresponding control inputs. Based on the study on general algebraic connectivity, a sufficient condition for the system synchronization is given, together with case simulations to illustrate the effectiveness and potential of the new control method.

Synchronization of directed switched complex networks with stochastic link perturbations and mixed time-delays

In this paper, the synchronization problem is studied for a class of directed switched complex networks. The links among the nodes are perturbed by stochastic noises and the topology varies according to certain predetermined switching rules. The coupled networks under consideration are subject to mixed delays comprising both discrete and distributed ones. A new estimate of the general algebraic connectivity is firstly given for the directed complex networks, based on which the exponential synchronization problem is analyzed by virtue of the average-dwell-time technique. Then, sufficient conditions are derived to guarantee the synchronization in mean square provided that the switching is slow on the average. Subsequently, the switched complex networks with link failures are investigated and it is shown that the synchronization can be achieved if the average link failure ratio does not exceed certain threshold. Finally, a numerical simulation example is presented to demonstrate the effectiveness of the proposed algorithm.

Consensus analysis of multiagent systems with second-order nonlinear dynamics and general directed topology: An event-triggered scheme

Event-triggered sampling control is motivated by the application of embedded microprocessors equipped in the agents with limited computation and storage resources. This paper studies the global consensus in second-order multi-agent systems with the inherent nonlinear dynamics on general directed networks using decentralized event-triggered strategy. For each agent, only utilizing local and current sampling data, the update of controllers is event-based and only triggered at their own event times. A high-performance sampling event that only needs neighbors’ states at their own discrete time instants is presented. Furthermore, we introduce two kinds of general algebraic connectivity for strongly connected networks and strongly connected components of directed networks containing a spanning tree to describe the system's ability to reach consensus. A detailed theoretical analysis on consensus is performed and two criteria are derived by the virtues of algebraic graph theory, matrix theory, and Lyapunov control approach. It is shown that the continuous communication between neighboring agents can be avoided and the Zeno-behavior of triggered time sequence is excluded during the system's whole working process. In addition, numerical simulation is given to illustrate the effectiveness of the theoretical results.

Event-triggered nonlinear consensus in directed multi-agent systems with combinational state measurements

ABSTRACTEvent-triggered sampling control is motivated by the applications of embedded microprocessors equipped in the agents with limited computation and storage resources. This paper studied global consensus in multi-agent systems with inherent nonlinear dynamics on general directed networks using decentralised event-triggered strategy. For each agent, the controller updates are event-based and only triggered at its own event times by only utilising the locally current sampling data. A high-performance sampling event that only needs local neighbours’ states at their own discrete time instants is presented. Furthermore, we introduce two kinds of general algebraic connectivity for strongly connected networks and strongly connected components of the directed network containing a spanning tree so as to describe the system's ability for reaching consensus. A detailed theoretical analysis on consensus is performed and two criteria are derived by virtue of algebraic graph theory, matrix theory and Lyapunov control approach. It is shown that the Zeno behaviour of triggering time sequence is excluded during the system's whole working process. A numerical simulation is given to show the effectiveness of the theoretical results.

Event-triggered consensus in nonlinear multi-agent systems with nonlinear dynamics and directed network topology

The event-triggered sampling control scheme is motivated by applications of embedded microprocessors with limited computation and storage resources. This paper proposes a novel framework for consensus of multiagent systems with inherent nonlinear dynamics in general directed networks by a distributed event-triggered control mechanism. A kind of high-performance event which effectively avoids continuous communications among agents is designed to analytically determine when an agent should sample its current state. Two kinds of general algebraic connectivity are introduced to respectively investigate the global consensus in strongly connected networks and a class of networks containing directed spanning trees. Sufficient conditions are derived to reach a global consensus based on algebraic graph, matrix theory, and Lyapunov control approach. A numerical example is presented to demonstrate the correctness of the theoretical results.

Second-order consensus in multi-agent systems with directed topologies and communication constraints

The paper investigates second-order consensus problem for multi-agent systems with nonlinear dynamic and directed topologies, where each agent can only communicate with its neighbors on some disconnected time intervals. A novel intermittent consensus protocol is designed by its own and the neighbor's relative local information. Based on the Lyapunov stability theory and the intermittent control method, some novel and simple criteria are derived for consensus of multi-agent systems under a fixed strongly connected topology, it is proved that consensus can be reached if the general algebraic connectivity and the measure of communication are larger than the corresponding threshold values, respectively. Finally, two numerical examples are provided to demonstrate the effectiveness of the obtained theoretical results.

Consensus of second-order multi-agent systems with delayed nonlinear dynamics and intermittent communications

This article investigates the second-order consensus problem of multi-agent systems with inherent delayed nonlinear dynamics and intermittent communications. Each agent is assumed to obtain the measurements of relative states between its own and the neighbours' only at a sequence of disconnected time intervals. A new kind of protocol based only on the intermittent measurements of neighbouring agents is proposed to guarantee the states of agents to reach second-order consensus under a fixed strongly connected and balanced topology. By constructing a common Lyapunov function, it is shown that consensus can be reached if the general algebraic connectivity and communication time duration are larger than their corresponding threshold values, respectively. Finally, simulation examples are provided to verify the effectiveness of the theoretical analysis.

Consensus in multi‐agent systems with communication constraints

AbstractThe problem of second‐order consensus is investigated in this paper for a class of multi‐agent systems with a fixed directed topology and communication constraints where each agent is assumed to share information only with its neighbors on some disconnected time intervals. A novel consensus protocol designed based on synchronous intermittent local information feedback is proposed to coordinate the states of agents to converge to second‐order consensus under a fixed strongly connected topology, which is then extended to the case where the communication topology contains a directed spanning tree. By using tools from algebraic graph theory and Lyapunov control approach, it is proved that second‐order consensus can be reached if the general algebraic connectivity of the communication topology is larger than a threshold value and the mobile agents communicate with their neighbors frequently enough as the network evolves. Finally, a numerical example is simulated to verify the theoretical analysis. Copyright © 2011 John Wiley & Sons, Ltd.