Xiaofeng Liao

Event-Triggering Sampling Based Leader-Following Consensus in Second-Order Multi-Agent Systems

In this note, the problem of second-order leader-following consensus by a novel distributed event-triggered sampling scheme in which agents exchange information via a limited communication medium is studied. Event-based distributed sampling rules are designed, where each agent decides when to measure its own state value and requests its neighbor agents broadcast their state values across the network when a locally-computed measurement error exceeds a state-dependent threshold. For the case of fixed topology, a necessary and sufficient condition is established. For the case of switching topology, a sufficient condition is obtained under the assumption that the time-varying directed graph is uniformly jointly connected. It is shown that the inter-event intervals are lower bounded by a strictly positive constant, which excludes the Zeno-behavior before the consensus is achieved. Numerical simulation examples are provided to demonstrate the correctness of theoretical results.

Event-triggered asynchronous intermittent communication strategy for synchronization in complex dynamical networks

This paper presents a new framework for synchronization of complex network by introducing a mechanism of event-triggering distributed sampling information. A kind of event which avoids continuous communication between neighboring nodes is designed to drive the controller update of each node. The advantage of the event-triggering strategy is the significant decrease of the number of controller updates for synchronization task of complex networks involving embedded microprocessors with limited on-board resources. To describe the systems ability reaching synchronization, a concept about generalized algebraic connectivity is introduced for strongly connected networks and then extended to the strongly connected components of the directed network containing a directed spanning tree. Two sufficient conditions are presented to reveal the underlying relationships of corresponding parameters to reach global synchronization based on algebraic graph, matrix theory and Lyapunov control method. A positive lower bound for inter-event times is derived to guarantee the absence of Zeno behavior. Finally, a numerical simulation example is provided to demonstrate the theoretical results.

Second-Order Global Consensus in Multiagent Networks With Random Directional Link Failure

In this paper, we consider the second-order globally nonlinear consensus in a multiagent network with general directed topology and random interconnection failure by characterizing the behavior of stochastic dynamical system with the corresponding time-averaged system. A criterion for the second-order consensus is derived by constructing a Lyapunov function for the time-averaged network. By associating the solution of random switching nonlinear system with the constructed Lyapunov function, a sufficient condition for second-order globally nonlinear consensus in a multiagent network with random directed interconnections is also established. It is required that the second-order consensus can be achieved in the time-averaged network and the Lyapunov function decreases along the solution of the random switching nonlinear system at an infinite subsequence of the switching moments. A numerical example is presented to justify the correctness of the theoretical results.

Cooperative Distributed Optimization in Multiagent Networks With Delays

In this technical correspondence, we consider a distributed cooperative optimization problem encountered in a computational multiagent network with delay, where each agent has local access to its convex cost function, and jointly minimizes the cost function over the whole network. To solve this problem, we develop an algorithm that is based on dual averaging updates and delayed subgradient information, and analyze its convergence properties for a diminishing step-size by utilizing Bregman-distance functions. Moreover, we provide sharp bounds on the convergence rates as a function of the network size and topology embodied in the inverse spectral gap. Finally, we present a numerical example to evaluate our algorithm and compare its performance with several similar algorithms.

Event-triggered synchronization strategy for complex dynamical networks with the Markovian switching topologies

This paper concerns the synchronization problem of complex networks with the random switching topologies. By modeling the switching of network topologies as a Markov process, a novel event-triggered synchronization strategy is proposed. Unlike the existing strategies, the event detection of this strategy only works at the network topology switching time instant, which can significantly decrease the communication frequency between nodes and save the network resources. Under this strategy, the synchronization problem of complex network is equivalently converted to the stability of a class of Markovian jump systems with a time-varying delay. By using the Lyapunov-Krasovskii functional method and the weak infinitesimal operation, a sufficient condition for the mean square synchronization of the complex networks subject to Markovian switching topologies is established. Finally, a numerical simulation example is provided to demonstrate the theoretical results.

On reaching group consensus for linearly coupled multi-agent networks

Abstract In this paper, the problems of group consensus for linearly coupled multi-agent networks including first-order and second-order are investigated, respectively. Based on the Laplacian matrix associated with the weighted adjacency matrix of the system, we present two novel linear protocols which can exactly reflect the interactive influence between the agents of the multi-agent network. Instead of relying on other conservative assumptions presented by the majority of the relevant research works, some promising criteria which can guarantee the reaching of group consensus of the multi-agent network are also obtained analytically. In addition, we also extend our work to study the group consensus for the multi-agent network with generally connected topology which neither needs to be strongly connected nor needs to contain a directed spanning tree. The conclusion that we have obtained should be more representative. Finally, the validity and correctness of our theoretical results are verified by several numerical simulated examples.

Leader-Following Consensus of Discrete-Time Multiagent Systems With Encoding–Decoding

The leader-following consensus of general linear discrete-time multiagent systems with a limited communication data rate and a directed fixed topology is investigated. The consensus protocol is designed for each agent, which is given in terms of states of its encoder and decoders with time-varying quantization levels. A rigorous analysis for the consensus convergence is provided. A finite lower bound of the communication data rate between each pair of adjacent agents is obtained to ensure consensus. A numerical example is presented to demonstrate the validity of the results obtained.

Leader-following consensus in second-order multi-agent systems with input time delay

This paper analytically investigates an event-triggered leader-following consensus in second-order multi-agent systems with time delay in the control input. Each agents update of control input is driven by properly defined event, which depends on the measurement error, the states of its neighboring agents at their individual time instants, and an exponential decay function. Necessary and sufficient conditions are presented to ensure a leader-following consensus. Moreover, the control is updated only when the event-triggered condition is satisfied, which significantly decreases the number of communication among nodes, avoided effectively the continuous communication of the information channel among agents and excluded the Zeno-behavior of triggering time sequences. A numerical simulation example is given to illustrate the theoretical results.

On pinning group consensus for dynamical multi-agent networks with general connected topology

In this paper, we focus on investigating group consensus of dynamical multi-agent networks via pinning scheme. The topology of the network is a general digraph, which needs neither being symmetric nor containing a spanning directed tree, and some criteria are proposed to guarantee the realization of group consensus instead of relying on other conservative assumptions presented by majority of the relevant research works, such as in-degree balance. In addition, it is interesting to find that the nodes with zero in-degree should be pinned first based on the property of M-matrix. Furthermore, an adaptive pinning control approach is developed to obtain the appropriate control gains. Finally, the effectiveness and correctness of our theoretical findings are verified by some numerical simulations.

Reinforcement Learning in Energy Trading Game Among Smart Microgrids

Reinforcement learning (RL) is essential for the computation of game equilibria and the estimation of payoffs under incomplete information. However, it has been a challenge to apply RL-based algorithms in the energy trading game among smart microgrids where no information concerning the distribution of payoffs is a priori available and the strategy chosen by each microgrid is private to opponents, even trading partners. This paper proposes a new energy trading framework based on the repeated game that enables each microgrid to individually and randomly choose a strategy with probability to trade the energy in an independent market so as to maximize his/her average revenue. By establishing the relationship between the average utility maximization and the best strategy, two learning-automaton-based algorithms are developed for seeking the Nash equilibria to accommodate the variety of situations. The novelty of the proposed algorithms is related to the incorporation of a normalization procedure into the classical linear reward-inaction scheme to provide a possibility to operate any bounded utility of a stochastic character. Finally, a numerical example is given to demonstrate the effectiveness of the algorithms.