Consensusability of discrete-time multi-agent systems

In this paper, consensus analysis and design are investigated for discrete-time multi-agent systems (MASs) with consecutive packet losses in communication links of directed communication topology. It is assumed that at each transmitted instant, the packet loss is stochastic and described by Bernoulli distribution, but during a given time window, the data could be successfully transmitted to the agent from each of its neighbors. First, we utilize the incidence matrix of a directed spanning tree of the communication topology to construct a linear transformation matrix so that the consensus problem is equivalently transformed into a mean square asymptotic stability problem of a reduced-order system. Second, by using Lyapunov–Krasovskii functional approach, we derive some sufficient conditions of consensus criterion in terms of linear matrix inequalities (LMIs). These conditions express the relationship among the control gain matrix, packet loss rate, and the number of consecutive packet losses. Based on the conditions, gain matrix in the consensus protocol is designed to guarantee the MAS with stochastic packet losses to achieve mean square asymptotic consensus. Moreover, for the special case of undirected communication topology, by using the matrix decomposition method, the variables of LMIs are transformed into the low-order conditions independent of the network size. Finally, some numerical examples are given to show the effectiveness of the proposed method.

In this article, the leader-follower consensus is investigated for discrete-time second-order multiagent systems with smart leader, where the smart leader can obtain the feedback information from its neighbours. Different from the existing results, an objective function is provided to determine whether the leader utilizes the feedback information from its neighboring agents, with the purpose of making the system have better performance. Under the directed interconnected topology, a novel distributed consensus protocol is designed for second-order discrete-time multiagent systems. Some necessary and sufficient conditions are derived for the leader-follower consensus of discrete-time second-order multiagent systems with smart leader under fixed/switching topology. Finally, two simulation examples are presented to demonstrate the feasibility of the theoretical results.

This paper investigates the problem of event-based consensus of discretetime multi-agent systems with general linear dynamics subject to actuator saturation. Leader-following and leaderless semi-global consensus are achieved by a distributed event-trigger strategy for the multi-agent systems. In spite of the input saturation constraint, it is shown that feedback control updating is unnecessary until an event is triggered. The combinational-state variables and the Riccati equation are used to construct a Lyapunov function and to design the event-triggering conditions and the low-gain control laws. Numerical examples are provided to illustrate the theoretical results. Keywords: Event-triggered control, Input saturation, Riccati equation, Semi-global consensus.

This paper aims to design a controller to handle the secure consensus problems for a class of discrete-time multi-agent systems with time delays and parameter uncertainties under false data injection attacks. To investigate the effects of false data injection attacks on multi-agent systems, the approach of linear matrix inequalities is utilized to design the control gain matrix. First, parameter uncertainties are left out to obtain the sufficient conditions guaranteeing consensus of multi-agent systems. Second, Schur complement is used to eliminate the influence of the unknown time-varying parameter uncertainties on the aforementioned conditions. Then, linear matrix inequalities are given to obtain the control gain matrix. Simulation results are presented to demonstrate the effectiveness of the proposed control approach.

Robust distributed adaptive consensus for discrete-time multiagent systems with uncertain topologies

This paper investigates the consensus problem for discrete linear multi-agent systems (MASs) in the case of Markovian packet dropouts. The agent subsystems are connected by lossy channels, which can be described by Markov process. The relationship of agent dynamics, communication network, and packet losses rate is studied, and based on which the MASs can achieve consensus by a designed distributed controller. Specifically, based on the stability of a transformed system state function under the identical packet looses, we first derive the sufficient condition of consensus for discrete-time MASs, and meanwhile design the control gain. Then, we also discuss the sufficient condition of consensus for the MASs under nonidentical packet losses. At last, the availability of the proposed results is illustrated through simulation examples.

This article is devoted to consensus control problem for discrete-time higher-order multi-agent systems. A novel distributed control protocol with one-step predictive output feedback is proposed to improve dynamic performance for consensus convergence. It is shown that consensus is reached if and only if there exists a common control gain which simultaneously stabilizes N−1 systems in a special form, where N is the number of agents. A simulation is performed to illustrate the effectiveness of the theoretical results.

Consensus of discrete-time multi-agent systems over packet dropouts channels

Leader-following almost output consensus for discrete-time heterogeneous multi-agent systems in the presence of external disturbances

This paper studies the consensus problem for discrete-time multi-agent systems with state, input and different communication delays, where the input delays can be arbitrarily large yet exactly known. Moreover, the communication delays are different for different agents and can also be arbitrarily large. A nested predictor based protocol is established to solve the problem. It is shown that both the input and communication delays can be compensated completely. Furthermore, a linear matrix inequalities based approach is provided to design the state feedback gains. Finally, a numerical example is worked out to illustrate the effectiveness of the proposed approach.

On the cluster consensus of discrete-time multi-agent systems

In this technical note, a distributed velocity-constrained consensus problem is studied for discrete-time multi-agent systems, where each agent's velocity is constrained to lie in a nonconvex set. A distributed constrained control algorithm is proposed to enable all agents to converge to a common point using only local information. The gains of the algorithm for all agents need not to be the same or predesigned and can be adjusted by each agent itself based on its own and neighbors' information. It is shown that the algorithm is robust to arbitrarily bounded communication delays and arbitrarily switching communication graphs provided that the union of the graphs has directed spanning trees among each certain time interval. The analysis approach is based on multiple novel model transformations, proper control parameter selections, boundedness analysis of state-dependent stochastic matrices1, exploitation of the convexity of stochastic matrices, and the joint connectivity of the communication graphs. Numerical examples are included to illustrate the theoretical results.

This paper studies the resilient asymptotic consensus problem for discrete-time multi-agent systems in the presence of adversaries and transmission delays. The network is assumed to have loyal agents and adversarial agents, and each loyal agent in the network has no knowledge of the network topology other than an upper bound on the number of adversarial agents in its neighborhood. For the considered networked system, only locally delayed information is available for each loyal agent, and also the information flow is directed and a control protocol using only local information is designed to guarantee the realization of consensus with respect to communication graph, which satisfies a featured network robustness. Numerical examples are finally given to demonstrate the effectiveness of theoretical results.

This paper studies the consensus problem of discrete-time single-integrator multi-agent systems with multiplicative uncertainties and bounded communication delays in switching networks. Some sufficient conditions for non-stochastic consensus are obtained by adopting the constant-gain protocol. For the case that the uncertainty is exponentially decaying (i.e. is with ), it is proved for any bounded delays, the consensus can be achieved if the switching topology is uniformly rooted. For the case that the uncertainty is polynomially decaying (i.e. is with ), under a precondition that the system state is bounded, a similar conclusion is also obtained. The convergence rate of the consensus protocol is quantified in terms of the decay rate of uncertainties. Simulation results are given to verify the correctness of the conclusion.

Multi-agent systems consist of a number of interacting autonomous agents, each of which is capable of sensing its environment (including other agents) and deciding to act in order to achieve its own objectives. In order to guarantee the overall design objectives of multi-agent systems, the behavior of individual agents and their interactions need to be regulated and coordinated [23,29,30]. The development of multi-agent systems therefore requires programming languages that facilitate the implementation of individual agents as well as mechanisms that control and regulate individual agents' behaviors. It also requires computational tools to test and verify programs that implement multi-agent systems [7].