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

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.

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.

The study of multi-agent systems (MAS) focuses on systems in which many intelligent agents interact within an environment. The agents are considered to be autonomous entities. MAS can be used to solve problems that are difficult or impossible for an individual agent to solve. The main feature which is achieved when developing MAS, if they work, is flexibility, since MAS can be added to, modified and reconstructed, without the need for detailed rewriting of the application. MAS can manifest self-organization as well as self-steering related complex behaviors even when the individual strategies of all their agents are simple. The goal of MAS research is to find methods that allow us to build complex systems composed of autonomous agents who, while operating on local knowledge and possessing only limited abilities, are nonetheless capable of enacting the desired global behaviors. We want to know how to take a description of what a system of agents should do and break it down into individual agent behaviors. This thesis investigates the problem when discrete-time MAS are consensusable under undirected graph. A discussion is provided to show how the problem differs from continuous time system. Then a consensusability condition is derived in terms of the Mahler measure of the agent system for single input single out systems (SISO) and result shows that there is an improved consensusability by a power of two. An algorithm is proposed for distributed consensus feedback control law when the consensusability holds. Also the case of output feedback is considered in which the consensusability problem becomes more complicated. To solve this we decompose the problem into two parts i.e. state feedback and state estimation. Simulation results demonstrate the effectiveness of the established results.

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 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.

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

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 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.

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.

This paper proposes a robust distributed event-triggered approach for consensus in linear multi-agent systems (MAS) with uncertain network topologies. To achieve consensus, each agent transmits its information only when a certain event-triggering condition is fulfilled. The connection weights in the network are uncertain and hence the information received by each agent is unreliable. In such an uncertain topology, the objective is to co-design robust consensus parameters (namely, the state transmission threshold and local control gains) that collectively ensure an exponential rate for consensus convergence. An objective function incorporating the transmission load and control effort is minimized to compute the design parameters. Numerical simulations quantify the effectiveness of the proposed event-triggered consensus approach in a second-order MAS.

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.

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