Leader-following Consensus Of Multi-agent Systems Research Articles

Stochastic leader-following consensus of multi-agent systems with measurement noises and communication time-delays

Abstract This work addresses the leader-following consensus control of continuous-time single-integrator multi-agents systems with measurement noises and time-delays. As often happened in practical applications, the states information received by an agent from its neighbors are assumed with time-delays and contaminated by additive or multiplicative noises. Using stochastic analysis tools and algebraic graph theory, the mean square leader-following consensus and the almost sure leader-following consensus are proposed for multi-agent systems under additive and multiplicative noises, respectively. For the case with additive noises, the sufficient conditions of the mean square and the almost sure leader-following consensus are obtained by employing the variation of constants formula. As to the case with multiplicative noises, Lyapunov functional is constructed to get the sufficient conditions for the leader-following consensus, where the agents converge to the leader with an exponential rate. These results show that for any given time-delay and noise intensity, the two consensus can be achieved under the appropriate control gains. Numerical simulations are conducted to justify the effectiveness of the proposed consensus protocols.

Distributed event-triggered observer-based tracking control of leader–follower multi-agent systems

In this paper, we consider the exponential leader-following consensus of multi-agent systems with high-dimensional active leader. To ensure the followers can track the leader as well as save the communication resource, a distributed observer-based controller based on periodic event-triggered mechanism is proposed. By using the delay-input method, the underlying leader-following consensus problem of multi-agent systems can be equivalently transformed into the asymptotical stability problem of the time-delay systems. Based on a novel time-delay analysis method, it is shown that the leader-following consensus can be reached. Secondly, to further reduce the amount of signal transmission, an event-triggered mechanism based on quantization is proposed. Thirdly, to remove the limitation that all followers know the system matrix of the leader system, an adaptive distributed observer-based controller is proposed. A numerical example is proposed to illustrate the effectiveness of the obtained result.

Mean square consensus of leader-following multi-agent systems with measurement noises and time delays

This paper investigates the mean square consensus problem of dynamical networks of leader-following multi-agent systems with measurement noises and time-varying delays. We consider that the fixed undirected communication topologies are connected. A neighbor-based tracking algorithm together with distributed estimators are presented. Using tools of algebraic graph theory and the Gronwall-Bellman-Halanay type inequality, we establish sufficient conditions to reach consensus in mean square sense via the proposed consensus protocols. Finally, a numerical simulation is provided to demonstrate the effectiveness of the obtained theoretical result.

Leader–Follower Consensus of Multiagent Systems With Energy Constraints: A Markovian System Approach

This paper is concerned with the leader-follower consensus of multiagent systems with wireless communications with the main objective of reducing the power consumption. First, by assuming that the sampling period jumps from one to another only from a given set, a new stochastic sampling approach is introduced to reduce the sampling frequency of each agent. Then, only 1-D of the sampled data is selected, and transmitted to its neighboring agents. Finally, each agent is scheduled to communicate with others intermittently. A unified Markovian system model is proposed to capture the above stochastic sampling, measurement selection scheme and intermittent transmission process, and such a novel protocol can significantly reduce the power consumption. Based on the Lyapunov stability theory and the Markovian jump system approach, the distributed consensus-based controller gain is obtained by solving an optimization problem. The advantage of the proposed consensus protocol is verified by two simulation examples. The simulation results explicitly show our result is more energy-efficient than that of existing one.

Event‐triggered consensus of non‐linear multi‐agent systems with sampling data and time delay

The sampled-data based event-triggered strategy for consensus of leader-following multi-agent systems with the input-delay and non-linear dynamics is studied. A novel event-triggered transmission strategy is proposed, where the controller of each agent updates and the sampled-data of each agent transmits to its neighbours' only at the agent's own triggering time instants. The measurement errors are defined based on the state information of the local neighbourhood and leader to design the event triggering scheme, and this scheme reduces the number of event triggering times, the controller updating and communications between agents. Moreover, in the proposed event triggered control strategy, the Zeno-behaviour is avoided. The control protocol and event triggering scheme can be simply designed by solving an LMI condition to achieve leader-following consensus asymptotically. The effectiveness of the proposed results is demonstrated via a numerical example.

Finite-time and fixed-time leader-following consensus for multi-agent systems with discontinuous inherent dynamics

ABSTRACTThis paper is concerned with finite-time and fixed-time consensus of multi-agent systems in a leader-following framework. Different from conventional leader-following tracking approaches where inherent dynamics satisfying the Lipschitz continuous condition is required, a more generalised case is investigated: discontinuous inherent dynamics. By nonsmooth techniques, a nonlinear protocol is first proposed to achieve the finite-time leader-following consensus. Then, based on fixed-time stability strategies, the fixed-time leader-following consensus problem is solved. An upper bound of settling time is obtained by using a new protocol, and such a bound is independent of initial states, thereby providing additional options for designers in practical scenarios where initial conditions are unavailable. Finally, numerical simulations are provided to demonstrate the effectiveness of the theoretical results.

Observer Design for Tracking Consensus in Second-Order Multi-Agent Systems: Fractional Order Less Than Two

This technical note studies the leader-following tracking consensus problem of a class of multi-agent systems where the dynamics of the leader is described by second-order systems. In order to track the states of the leader, observers for the followers are designed by fractional-order multi-agent systems where the relative velocity information is unavailable. It is interestingly found that the followers can track the leader with second-order dynamics even if the fractional order is less than two by only using the position information of the local neighbors, which is different from the existing results. A novel fractional-order observer is first proposed, whose order is surprisingly less than the original leader system. It is also shown that leader-following consensus can be ensured if some carefully selected followers are informed and the relative position-based protocols are appropriately designed with fractional order being between one and two. A necessary and sufficient condition for the leader-following consensus in multi-agent systems without control-input delay is proposed. The results are then extended to the case with constant control-input delay. It is found that, in both cases, the real and imaginary parts of the eigenvalues of the augmented Laplacian matrix of the topology play an important role in achieving consensus.

Time-varying leader-following consensus of high order multi-agent systems

In this paper, a time-varying leader-following consensus of multi-agent systems under fixed, connected and undirected communication topology is presented. In the proposed method, the dynamics of each agent including the followers and their corresponding leader is a linear nth order system. Moreover, the communication topology between the leader and its neighbours depends upon bounded and time-varying functions, assumed to remain connected as time passes. To tackle this problem, a set of time-varying distributed control laws for each follower agent is designed, based on algebraic graph theory, algebraic Riccati equation and Lyapunov direct method. Simulation results indicate the effectiveness of the proposed method and display convergence to consensus is achieved in a finite time via time-varying distributed control laws.

Partial component consensus of leader-following multi-agent systems

Consensus problems, as basic topics in distributed coordination of multi-agent systems, have drawn a great deal of attention from different research fields. Generally, consensus refers to the asymptotic convergence of state variables of all agents with time evolution. In this paper, a concept on partial component consensus in multi-agent system is first given, which is a weaker dynamic behavior of group than the consensus in general, and then the problem of partial component consensus in leader-following first-order multi-agent system with the directed network topology is discussed. By designing an appropriate pinning control protocol and building corresponding error system, partial component consensus in multi-agent system is transformed into the partial variable stability of the error system. Using matrix theory and stability theory, a sufficient condition is given to realize partial component consensus in multi-agent system. Numerical simulations are given to illustrate the theoretical results.

Leader-following consensus of multi-agent systems with limited data rate

This paper investigates the leader-following consensus problem of time-invariant linear multi-agent systems with limited data rate. Based on the idea of assigning a priority level for each agent of the concerned multi-agent system, a novel distributed control law has been proposed. The proposed control law has two distinctive advantages. That is, it is fully distributed in the sense that it does not rely on the eigenvalues of the Laplace matrix associated with the topology. Moreover, the required data rate is independent of the number of agents and remains small even if the number of the agents in multi-agent systems is large. An example is finally given to illustrate the effectiveness of the proposed controller.

Leader-following consensus of multi-agent system with a smart leader

In line of the research on leader-following consensus, this paper studies the consensus problem for the first-order multi-agent system with a smart leader. Different from previous works where the leader is independent of all the other agents, a kind of leader, called smart leader, is proposed, which can gain and utilize its neighboring followers' position information. Whether such information will be used in adjusting the control algorithm for the smart leader is decided by an event-trigger function. The theory and simulation results show that the proposed model can gain advantage in robustness and fault-tolerance ability with the traditional one. Moreover, a sufficient condition is provided, which can ensure that the position-tracking error and velocity-tracking error are bounded when some actuator faults occur on some of the followers in the framework of the fixed topology. In addition, similar results are also given under switching topology. Finally, some simulation examples are presented for illustration.

Event-Triggered Schemes on Leader-Following Consensus of General Linear Multiagent Systems Under Different Topologies.

This paper investigates the leader-following consensus for multiagent systems with general linear dynamics by means of event-triggered scheme (ETS). We propose three types of schemes, namely, distributed ETS (distributed-ETS), centralized ETS (centralized-ETS), and clustered ETS (clustered-ETS) for different network topologies. All these schemes guarantee that all followers can track the leader eventually. It should be emphasized that all event-triggered protocols in this paper depend on local information and their executions are distributed. Moreover, it is shown that such event-triggered mechanism can significantly reduce the frequency of control's update. Further, positive inner-event time intervals are assured for those cases of distributed-ETS, centralized-ETS, and clustered-ETS. In addition, two methods are proposed to avoid continuous communication between agents for event detection. Finally, numerical examples are provided to illustrate the effectiveness of the ETSs.

Event-Based Leader-following Consensus of Multi-Agent Systems with Input Time Delay

The event-based control strategy is an effective methodology for tackling the distributed control of multi-agent systems with limited on-board resources. This technical note focuses on event-based leader-following consensus for multi-agent systems described by general linear models and subject to input time delay between controller and actuator. For each agent, the controller updates are event-based and only triggered at its own event times. A necessary condition and two sufficient conditions on leader-following consensus are presented, respectively. It is shown that continuous communication between neighboring agents can be avoided and the Zeno-behavior of triggering time sequences is excluded. A numerical example is presented to illustrate the effectiveness of the obtained theoretical results.

Stochastic consensus of leader-following multi-agent systems under additive measurement noises and time-delays

Information exchange between agents in multi-agents systems is often inexact and delayed. This paper proposes a distributed leader-following consensus algorithm for continuous-time single-integrator multi-agent systems under measurement noises and time-delays in directed topologies. The information states received by an agent from its neighbors are delayed by uniform time-delays. In the meantime, they are corrupted by additive white noises. Based on graph theory and stochastic tools, conditions to ensure the tracking consensus in mean square for both directed fixed and switching topologies are derived. The effectiveness of the proposed algorithms is proved through some simulations.

Leader-following consensus of multi-agent systems via sampled-data control with randomly missing data

The objective of this paper is to inspect the leader-following consensus of distributed multi-agent system (MAS) under sampled-data control. The communication flow among neighbor agents is described by an undirected graph. The control protocols are designed by using sampling period technique and zero-order hold circuit along with missing data. A stochastic variable satisfying Bernoulli distributed white noise sequences is introduced to model the missing data. Moreover, by employing the input-delay approach, we transform the sampling data into time-varying delayed data and on the basis of receiving data, two sampled-data control models are proposed. Through the construction of a suitable Lyapunov–Krasovskii functional and by the utilization of integral inequalities, new delay-dependent consensus conditions for the concerned system are derived in the form of linear matrix inequalities (LMIs) which can be readily solved by utilizing any of the valid software packages. The effectiveness of the proposed algorithms is illustrated by two numerical simulations.

Leader-following consensus of multi-agent systems with delayed impulsive control

This paper is concerned with the consensus of second-order multi-agent systems with a leader and switching topologies. A delayed impulsive consensus protocol is proposed, which only depends on the agent's own information and its neighbour's partial information. Based on a Lyapunov function approach, sufficient conditions for the convergence to consensus are established, which provides the appropriate impulsive delay interval on the admissible switching topology. Finally, numerical simulations are provided to illustrate the theoretical results.

Leader-following consensus of multi-agent systems with jointly connected topology using distributed adaptive protocols

The leader-following consensus problems for multi-agent systems with a linear and Lipschitz nonlinear dynamics are considered. Distributed adaptive protocols and Lipschitz distributed adaptive protocols are respectively designed for the linear and Lipschitz nonlinear cases, under which leader-following consensus is reached for jointly connected topology. Finally, a simulation example is provided to illustrate the theoretical results.

Adaptive Leader-Following Consensus of Multi-Agent Systems with Unknown Nonlinear Dynamics

This paper deals with the leader-following consensus of multi-agent systems with matched nonlinear dynamics. Compared with previous works, the major difficulty here is caused by the simultaneous existence of nonidentical agent dynamics and unknown system parameters, which are more practical in real-world applications. To tackle this difficulty, a distributed adaptive control law for each follower is proposed based on algebraic graph theory and algebraic Riccati equation. By a Lyapunov function method, we show that the designed control law guarantees that each follower asymptotically converges to the leader under connected communication graphs. A simulation example demonstrates the effectiveness of the proposed scheme.

Consensus of leader-following multi-agent systems in time-varying networks via intermittent control

This paper is concerned with the issue of consensus for leader-following multi-agent systems, wherein the agents acting as followers update states based on the information received from the time-varying neighbors and the virtual leader. Moreover, the neighbors of an agent are divided into three types according to their relative position, which may also be changed with time. Consensus protocol is derived mainly by using intermittent control, and based on the Lyapunov stability theory, sufficient conditions for consensus are presented and proved theoretically. Finally, some numerical examples are given to demonstrate the effectiveness of the results.

Leader-following consensus of multi-agent systems under directed communication topology via distributed adaptive nonlinear protocol

In this paper, we study the leader-following consensus problem of general linear multi-agent systems under directed communication topology. To avoid using any global information, an adaptive nonlinear protocol is proposed based only on the relative state information. It is proved that, for any directed communication graph that contains a spanning tree with the root node being the leader agent, the proposed control law solves the leader-following consensus problem. A numerical example is provided to illustrate the effectiveness of the theoretical results.