Observer‐Based Consensus Tracking for Nonlinear Multi‐Agent Systems With Intermittent Communications

This paper addresses the observer‐based consensus tracking problem of multi‐agent systems with intermittent communications. The agent dynamics are modeled as general linear systems with Lipschitz nonlinearity. Under the assumption that each agent can intermittently share its relative output with neighbors, a class of an observer‐type protocol is proposed, and the consensus tracking problem can be converted further into the stability problem of the nonlinear switching systems. Using a combined tool from M matrix theory, switching theory and the averaging approach, a multi‐step algorithm is presented to construct the observer gains and protocol parameters, and the sufficient criteria established not only can ensure the state estimates convergence to the real values but also can guarantee the follower states synchronize to those of the leader. The obtained results reveal the relationships among the communication rate, the convergence rate, and the dwell time of switching topologies. Finally, the theoretical findings are validated by a numerical example.     

Consensus in multi‐agent systems with communication constraints

The 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.     

A New Observer‐Type Consensus Protocol for Linear Multi‐Agent Dynamical Systems

The consensus problem is investigated in this paper for a class of multi‐agent systems with general linear node dynamics and directed communication topologies. A new distributed observer‐type consensus protocol is designed based only on the relative output measurements of neighboring agents. Compared with existing observer‐type protocols, the one presented here does not require information about the relative states of the observers. Tools from small gain theory and matrix analysis, some sufficient conditions are obtained for achieving consensus in such multi‐agent systems where the underlying network topology contains a directed spanning tree. Finally, some numerical examples including an application in low‐Earth‐orbit satellite formation flying are provided to illustrate the theoretical results.     

Design of a class of nonlinear consensus protocols for multi‐agent systems

This paper investigates the consensus problem for multi‐agent systems and presents a class of nonlinear consensus protocols. First, we reveal some structure property of the corresponding Laplacian matrix by decomposing the interaction graph into strongly connected components. Then, by means of the input‐to‐state stability and algebraic graph theory, we propose a framework to prove consensus for multi‐agent systems with nonlinear protocols. In particular, we prove that consensus can be always reached in systems of single‐integrator agents with a directed communication topology containing a spanning tree, provided the nonlinear protocol is an odd and increasing function. The nonlinear consensus protocols proposed in this paper include the classical linear consensus protocol as a special case, and may have a wide range of applications, including consensus with faster convergence rates and with bounded control inputs. Copyright © 2012 John Wiley & Sons, Ltd.     

Consensus for multi‐agent systems under double integrator dynamics with time‐varying communication delays

In this paper, the consensus control problems for multi‐agent systems under double integrator dynamics with time‐varying communication delays are investigated. We assume that the interaction graphs among agents are directed. Two kinds of protocols are considered. One is an absolute damping protocol, and the other is a relative damping protocol. For the first protocol, Lyapunov–Razumikhin functional techniques are used. We derive sufficient conditions that guarantee that all agents asymptotically reach consensus under fixed topology and switching topology, respectively. Moreover, the allowable upper bound for communication delays is given. For the second protocol, Lyapunov–Krasovskii functional techniques are used. Linear matrix inequality (LMI)‐form sufficient conditions are obtained to guarantee the consensus problems to be solved under fixed topology and switching topology, respectively. The allowable upper bound for communication delays is given as well. The feasibilities of the demanded LMIs are also discussed. Finally, numerical simulations are provided to illustrate the effectiveness of our theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.     

Predictive Consensus for Networked Multi‐Agent Systems with Switching Topology and Variable Delay

This paper investigates consensus problems of networked linear time invariant (LTI) multi‐agent systems, subject to variable network delays and switching topology. A new protocol is proposed for such systems with matrix B that has full row rank, based on stochastic, indecomposable, aperiodic (SIA) matrix and the predictive control scheme. With the predictive scheme the network delay is compensated. Consensus analysis based on the seminorm is provided. The conditions are obtained for such systems with periodic switching topology to reach consensus. The proposed protocol can deal with time‐varying delays, switching topology, and an unstable mode. The numerical examples demonstrate the effectiveness of the theoretical results.     

Distributed consensus of delayed multi‐agent systems with nonlinear dynamics via intermittent control

In this paper, a distributed consensus of delayed multi‐agent systems with a leader is investigated, and a nonlinear protocol is proposed based on intermittent control. A notable feature of this protocol is to address second‐order consensus problems for delayed nonlinear multi‐agent systems, where agents can only communicate with each other over some disconnected time intervals. Some sufficient conditions to guarantee the consensus over fixed and switching topologies are derived. It is shown that second‐order consensus for delayed multi‐agent system with intermittent control can be achieved if the time delay is less than a critical value and the communication time duration is larger than a threshold value. In addition, some numerical examples are given to illustrate the effectiveness and feasibility of the theoretical results.     

A novel consensus algorithm for second‐order multi‐agent systems without velocity measurements

In this paper, a novel consensus protocol for second‐order multi‐agent systems is elegantly designed, and it relaxes the common requirement of the velocity information of the agents. An interesting consensus criterion is explicitly derived in terms of the proposed cooperation law provided that the dynamical equation for each agent is linear. As an extension, the proposed cooperation rule is further extended to a general scenario, where the coupling weights characterizing the relationships among the neighboring agents are time‐varying. Accordingly, two distributed cooperative algorithms (node/edge‐based scheme) are explicitly designed. Moreover, we study the case of network with switching communication setting. It shows that edge‐based law is capable with the time‐varying topology, while the node‐based scheme is not. In addition, the proposed coordination strategies are applied to the tracking problem as well. Finally, these obtained consensus results are well supported in the light of the pendulum models. Copyright © 2016 John Wiley & Sons, Ltd.     

Intermittent observer-based consensus control for multi-agent systems with switching topologies

In this paper, we focus on the consensus problem for leaderless and leader–followers multi-agent systems with periodically intermittent control. The dynamics of each agent in the system is a linear system, and the interconnection topology among the agents is assumed to be switching. We assume that each agent can only share the outputs with its neighbours. Therefore, a class of distributed intermittent observer-based consensus protocols are proposed for each agent. First, in order to solve this problem, a parameter-dependent common Lyapunov function is constructed. Using this function, we prove that all agents can access a prescribed value, under the designed intermittent controller and observer, if there are suitable conditions on communication. Second, based on the investigation of the leader-following consensus problem, we design a new distributed intermittent observer-based protocol for each following agent. Finally, we provide an illustrative example to verify the effectiveness of the proposed approach.     

Discrete‐time global leader‐following consensus of a group of general linear systems using bounded controls

This paper deals with the problem of global leader‐following consensus of a group of discrete‐time general linear systems with bounded controls. For each follower agent in the group, we construct both a bounded state feedback control law and a bounded output feedback control law. The feedback laws for each input of an agent use a multi‐hop relay protocol, in which the agent obtains the information of other agents through multi‐hop paths in the communication network. The number of hops each agent uses to obtain its information about other agents for an input is less than or equal to the sum of the number of real eigenvalues on the unit circle and the number of pairs of complex eigenvalues on the unit circle of the subsystem corresponding to the input, and the feedback gains are constructed from the adjacency matrix of the communication network. We show that these control laws achieve global leader‐following consensus when the communication topology among follower agents forms a strongly connected and detailed balanced directed graph and the leader is a neighbor of at least one follower agent. Copyright © 2017 John Wiley & Sons, Ltd.     

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.     

Observer-based consensus in networks of discrete-time switched linear dynamics under a fixed topology

This paper considers the consensus problem of discrete-time switched linear multi-agent systems under a fixed communication topology. An observer-based protocol with sampled data is proposed for solving such a problem. Assume that the digraph has a directed spanning tree and that all switched subsystem of each agent are stabilisable and detectable. It is shown that the proposed protocol solves the consensus problem when the sampling period is sufficiently small and the average dwell time of the switching signal is sufficiently large. Moreover, to reduce the conservatism, a sufficient condition for consensus is obtained to design the feedback gain matrices and the observer gain matrices by linear matrix inequalities, which guarantee that consensus can be achieved when the sampling period and the average dwell time are in the general case. Finally, the effectiveness of the theoretical results is demonstrated through an example.     

Consensus Control for Directed Networks Under Quantized Information Exchange

In this paper, without assuming balanced network topologies, we address the weighted average consensus problem for discrete‐time single‐integrator multi‐agent systems with logarithmic quantized information communication. By incorporating generalized quadratic Lyapunov function with the discrete‐time Bellman–Gronwall inequality, a new upper bound about the quantization precision parameter of the infinite‐level logarithmic quantizer is derived to design quantized protocol, under which agents in strongly connected directed networks can attain weighted average consensus. The obtained new upper bound clearly characterizes the intimate relation between the quantization precision parameter and the directed network topology. The proposed quantized protocol is particularly applicable to digital networks where balanced message passing among agents is not available.     

A Novel Leader-following Consensus of Multi-agent Systems with Smart Leader

This article studies the leader-following consensus problem for mixed-order multi-agent systems with a leader. Different from the traditional leader which is independent of all the other agents, the leader, called smart leader, can obtain and utilize the feedback information from its neighbors at some disconnected time intervals. A new distributed consensus control protocol based on intermittent control is developed for leader-following consensus with a smart leader. Moreover, the smart leader can adjust the control protocol based on the feedback information from its neighbors. With the aid of Lyapunov function, some sufficient conditions are derived for leader-following consensus of multi-agent systems with mixed-order dynamics under fixed directed topology. In addition, the similar results are obtained under switching directed topology. Finally, simulation results are provided to verify the correctness and effectiveness of theoretical results.     

Time‐varying output formation control for linear multi‐agent systems with switching topologies

Time‐varying output formation control problems for linear multi‐agent systems with switching topologies are studied, where two types of switching topologies are considered: (1) the topology is undirected and jointly connected, and 2) each topology is directed and has a spanning tree. An output formation protocol under switching topologies is constructed using the outputs of neighboring agents via dynamic output feedback. Two algorithms are proposed to design the dynamic protocols under both jointly connected topologies and switching directed topologies. Time‐varying output formation feasibility conditions are given to describe the compatible relationship among the desired time‐varying output formation, the dynamics of each agent, and the switching topologies. The stability of the closed‐loop multi‐agent systems under the proposed two algorithms is investigated based on the common Lyapunov functional theory and the piecewise Lyapunov functional theory, respectively. In the case where the topologies are jointly connected, time‐varying output formation can be achieved for multi‐agent systems using the designed protocol if the given time‐varying output formation satisfies the feasible constraint. For the case where the switching topologies are directed and have a spanning tree, the time‐varying output formation can be realized if the output formation feasibility constraint is satisfied and the dwell time is larger than a positive threshold. Moreover, approaches to determine the output formation references are provided to describe the macroscopic movement of the time‐varying output formation. Finally, numerical simulation results are presented to demonstrate the effectiveness of the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.     

Event‐triggered Guaranteed Cost Consensus of Networked Singular Multi‐agent Systems

The problem of event‐triggered guaranteed cost consensus of discrete‐time singular multi‐agent systems with switching topologies is investigated in this paper. To save the limited network communication bandwidth of multi‐agent systems, a novel event‐triggered networked consensus mechanism is proposed. Based on the graph theory and singular system theory, sufficient conditions of guaranteed‐cost consensus of discrete‐time singular multi‐agent systems are derived and given in the form of the linear matrix inequalities, respectively. A co‐design approach of the multi‐agent consensus gain matrix and the event‐triggered parameters is presented. Furthermore, based on the approach of second class equivalent transformation for singular systems, the cost function is determined, and an explicit expression of consensus functions is presented. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method.     

LQR‐based optimal topology of leader‐following consensus

In this paper, we consider the optimal topology for leader‐following consensus problem of continuous‐time and discrete‐time multi‐agent systems based on linear quadratic regulator theory. For the first‐order multi‐agent systems, we propose a quadratic cost function, which is independent of the interaction graph, and find that the optimal topology is a star topology. For the second‐order multi‐agent systems, a quadratic cost function is also constructed, whereas the optimal topology for second‐order leader‐following consensus problem is an unevenly weighted star topology. The universality of these findings means that if each follower is connected with the leader, the information exchange between followers is unnecessary and insufficient. Simulation examples are provided to illustrate the effectiveness of the theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.     

Disturbance observer–based consensus tracking for nonlinear multiagent systems with switching topologies

This paper considers the leader‐follower consensus tracking problem for nonlinear multiagent systems with external disturbances and switching topologies. A distributed disturbance observer is constructed to estimate the disturbances suffered by the followers. Then, a distributed consensus protocol is proposed for the consensus tracking problem with disturbance rejection under a fixed directed topology based on the disturbance observer. Next, this result is extended to the case in which the switching communication topology only frequently but not always contains a directed spanning tree. By selecting the parameters appropriately such that the communication time satisfies various preset conditions, it is theoretically proven that the consensus tracking with disturbance rejection can also be achieved by the multiagent systems. Finally, a simulation example is presented to demonstrate the performance of the proposed control scheme.     

Coordination of discrete‐time multi‐agent systems via relative output feedback

This paper investigates the joint effects of agent dynamic and network topology on the consensusability of linear discrete‐time multi‐agent systems via relative output feedback. An observer‐based distributed control protocol is proposed. A necessary and sufficient condition for consensusability under this control protocol is given, which explicitly reveals how the intrinsic entropy rate of the agent dynamic and the eigenratio of the undirected communication graph affect consensusability. As a special case, multi‐agent systems with discrete‐time double integrator dynamics are discussed where a simple control protocol directly using two‐step relative position feedback is provided to reach a consensus. Finally, the result is extended to solve the formation and formation‐based tracking problems. The theoretical results are illustrated by simulations. Copyright © 2010 John Wiley & Sons, Ltd.     

Distributed reliable H∞ consensus control for a class of multi‐agent systems under switching networks: A topology‐based average dwell time approach

This paper investigates the problem of distributed reliable H_∞ consensus control for high‐order networked agent systems with actuator faults and switching undirected topologies. The Lipschitz nonlinearities, several types of actuator faults, and exogenous disturbances are considered in subsystems. Suppose the communication network of the multi‐agent systems may switch among finite connected graphs. By utilizing the relative state information of neighbors, a new distributed adaptive reliable consensus protocol is presented for actuator failure compensations in individual nodes. Note that the Lyapunov function for error systems may not decrease as the communication network is time‐varying; as a result, the existing distributed adaptive control technique cannot be applied directly. To overcome this difficulty, the topology‐based average dwell time approach is introduced to deal with switching jumps. By applying topology‐based average dwell time approach and Lyapunov theory, the distributed controller design condition is given in terms of LMIs. It is shown that the proposed scheme can guarantee that the reliable H_∞ consensus problem is solvable in the presence actuator faults and external disturbance. Finally, two numerical examples are given the effectiveness of the proposed theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.