Consensus strategy for a class of multi‐agents with discrete second‐order dynamics

This paper investigates consensus strategies for a group of agents with discrete second‐order dynamics under directed communication topology. Consensus analysis for both the fixed topology and time‐varying topology cases is systematically performed by employing a novel graph theoretic methodology as well as the classical nonnegative matrix theory. Furthermore, it is shown that the necessary and sufficient condition for the agents under fixed communication topology to reach consensus is that the communication topology has a spanning tree; and sufficient conditions for the agents to reach consensus when allowing for the dynamically changing communication topologies are also given. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed results. Copyright © 2011 John Wiley & Sons, Ltd.     

Group consensus control for double‐integrator dynamic multiagent systems with fixed communication topology

The problem of group consensus is investigated in this paper, where all agents possess double‐integrator dynamics. Two different kinds of consensus protocols are proposed for networks with fixed communication topology to reach group consensus for the agents’ positions and velocities. Convergence analysis is discussed, and necessary and/or sufficient conditions are presented for multiagent systems to achieve group consensus. The first protocol leads to dynamic consensus where positions of all agents reach time‐varying consensus values. By applying the second protocol, both the agents’ positions and their velocities reach constant consensus values. That is, static consensus is achieved. Simulation examples are given to show the effectiveness of the theoretical results.Copyright © 2012 John Wiley & Sons, Ltd.     

Stable‐protocol output consensualization for high‐order swarm systems with switching topologies

Stable‐protocol (SP) output consensus analysis and design for high‐order linear time‐invariant swarm systems with switching topologies are dealt with. Firstly, on the basis of observability decomposition, a dynamic output feedback consensus protocol with switching topologies is given. Then, a necessary and sufficient condition for SP output consensus is shown, and an explicit expression of the output consensus function is presented, which is independent of switching topologies. Furthermore, necessary and/or sufficient conditions for SP output consensualization, which are independent of the number of agents, are shown respectively. Finally, a numerical example is shown to demonstrate theoretical results. Copyright © 2012 John Wiley & Sons, Ltd.     

Admissible consensus analysis for high‐order linear singular swarm systems with multiple time‐varying delays and topology variances

Admissible consensus analysis problems for high‐order linear time‐invariant singular swarm systems with multiple time delays and time‐varying interaction topologies are investigated. First, necessary and sufficient conditions for admissible consensus are presented, and admissible consensus problems are transformed into admissible problems of multiple lower dimensional singular systems. Then, on the basis of the first equivalent form, explicit expressions of consensus functions are given, where the impacts of initial states of agents and protocols, time delays and topology variances are determined, respectively. Moreover, it is shown that if interaction topologies are balanced, then swarm systems with the same initial states but different interaction topologies and different time delays have an identical consensus function. Finally, numerical simulations are given to demonstrate theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.     

Average consensus of continuous‐time multi‐agent systems with quantized communication

This paper focuses on the average consensus problem of first‐order and second‐order continuous‐time multi‐agent systems with logarithmic quantized information transmission. The balanced and strongly connected digraphs are utilized to characterize the interaction topologies between agents. Based on the state estimation, distributed state updating mechanisms are introduced for every agent such that all agents’ states achieve average consensus asymptotically. By means of differential inclusion theory, we discuss the existence and convergence property of the Krasovskii solutions to the closed‐loop system models. By designing the proper control gain parameters and quantizer accuracy, two sufficient conditions are established to guarantee the achievement of average consensus. Finally, two numerical simulations are provided to illustrate the effectiveness of theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.     

A decoupled designing approach for sampling consensus of multi‐agent systems

This paper introduces the motion‐planning approaches to solve the distributed consensus problems via sampling measurements. First, for first‐order multiagent systems, a class of sampled‐data–based algorithms are developed with arbitrary sampling periods, which solve the asymptotic consensus problem under both directed fixed and random switching topologies. Then, a new kind of distributed consensus algorithms is designed based on sampling measurements for second‐order multiagent systems. Under both the directed fixed and periodical switching topologies, asymptotic consensus problems of second‐order multiagent systems can be solved by using the proposed algorithms. Compared with existing continuous‐time consensus algorithms, one of remarkable advantages of proposed algorithms is that the sampling periods, communication topologies, and control gains are decoupled and can be separately designed, which relaxes many restrictions in controller designs. Finally, some numerical examples are given to illustrate the effectiveness of the analytical results.     

Admissible Consensus of Multi‐Agent Singular Systems

Consensus problems are studied for both continuous‐time and discrete‐time multi‐agent singular systems with time‐invariant and directed communication topologies. Under restricted system equivalence of singular agents, sufficient and necessary conditions are obtained for admissible consensus ability with static protocols, which are based on both the relative information of the dynamic states and the absolute information of the static states. For a network of continuous‐time singular systems, the existence of admissible consensualization can be cast into strong stabilizability of the agent dynamics. Once discrete‐time multi‐agent singular systems satisfy the condition of reaching nontrivial final consensus states, strong stabilizability is a sufficient condition to achieve admissible consensualization. Two algorithms are proposed to construct two protocols, which are based on a linear matrix inequality and a modified Riccati equation, respectively. Finally, the algorithms are illustrated by two simulation examples.     

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.     

Distributed consensus of discrete‐time multi‐agent systems with multiplicative noises

In this paper, we consider the consensus problem of discrete‐time multi‐agent systems with multiplicative communication noises. Each agent can only receive information corrupted by noises from its neighbors and/or a reference node. The intensities of these noises are dependent on the relative states of agents. Under some mild assumptions of the noises and the structure of network, consensus is analyzed under a fixed topology, dynamically switching topologies and randomly switching topologies, respectively. By combining algebraic graph theory and martingale convergence theorem, sufficient conditions for mean square and almost sure consensus are given. Further, when the consensus is achieved without a reference, it is shown that the consensus point is a random variable with its expectation being the average of the initial states of the agents and its variance being bounded. If the multi‐agent system has access to the state of the reference, the state of each agent can asymptotically converge to the reference. Numerical examples are given to illustrate the effectiveness of our results. Copyright © 2014 John Wiley & Sons, Ltd.     

Finite‐Time Consensus Problem for Second‐Order Multi‐Agent Systems Under Switching Topologies

This paper investigates the finite‐time consensus problem for multi‐agent systems with second‐order individual dynamics under switching topologies. A distributed continuous‐time protocol is designed to guarantee finite‐time consensus for homogeneous agents without predetermined leaders, i.e., it ensures agents asymptotically converge to an average consensus within finite time, even if the interaction topology among them is time‐varying but stepwise jointly‐connected. In particular, it introduces a distributed continuous‐time protocol to reach consensus in finite time and reduce the chattering together. Finally, the simulation results are also given to validate the proposed approach.     

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.     

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.     

Output consensus for heterogeneous multiagent systems with Markovian switching network topologies

This paper investigates the output consensus problem of heterogeneous continuous‐time multiagent systems under randomly switching communication topologies. The switching mechanism is governed by a time‐homogeneous Markov process, whose states correspond to all possible communication topologies among agents. A novel dynamic consensus controller is proposed. The controller gains are designed based on the information of the expectation graph and the solutions to regulator equations. Furthermore, a necessary and sufficient condition is presented for output consensus of the controlled multiagent system in mean square sense. Finally, a simulation example is provided to corroborate the effectiveness of the proposed controller.     

Consensus seeking of high-order dynamic multi-agent systems with fixed and switching topologies

This article studies a consensus problem for a group of high-order dynamic agents with fixed and switching topologies. Two linear consensus protocols, which only depend on the agent's own information and its neighbours' partial information, are proposed, respectively, for the group with and without communication time-delays. For the case of fixed topology and zero communication time-delay, a necessary and sufficient condition for the consensus is established. The parameter design of the protocol is also discussed. Under switching topology, the consensus is investigated for two cases: the case of zero communication time-delay and the case of nonuniform communication time-delays. For each case, a sufficient condition for the consensus is provided. Moreover, for a group of double/triple-integrator agents with fixed topology and uniform constant time-delay, some necessary and sufficient conditions for the consensus are given. Finally, numerical simulations are worked out to illustrate the effectiveness of the theoretical results.     

Guaranteed cost consensus for multi‐agent systems with switching topologies

Firstly, guaranteed cost consensus for multi‐agent systems is introduced based on state errors among neighboring agents and control inputs of all agents, where a tradeoff between the consensus regulation performance and the control effort is considered. Then, a sufficient condition for guaranteed cost consensus is given by the state‐space decomposition approach and the Lyapunov method, where an upper bound of the cost function is determined and an approach is proposed to determine the control gain. It is worth mentioning that the criterions for guaranteed cost consensus are only dependent on the maximum eigenvalue of the Laplacian matrices of switching topologies. Finally, numerical simulations are given to demonstrate theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.     

Guaranteed‐Cost Consensus Control For High‐Order Linear Swarm Systems

Guaranteed‐cost consensus analysis and design problems for high‐order linear time‐invariant swarm systems are dealt with in this paper. First, a guaranteed‐cost consensus control problem is introduced to obtain a trade‐off design object between consensus regulation performances and control energy consumptions. Then, sufficient conditions for guaranteed‐cost consensus and consensualization are presented respectively, an upper bound of the cost function is determined, and explicit expressions of consensus functions are given, which are independent of interaction topologies of swarm systems. Finally, a numerical example is shown to demonstrate theoretical results.     

Leader‐following control for multiple inertial agents

This paper investigates distributed controller design problem for a leader‐follower network in the presence of communication delays. Two main contributions are made in this work. First, the second‐order controlled consensus scheme for the weakly connected communication graph topology is proposed. A necessary and sufficient condition is given under which the exponential consensus is achieved. Meanwhile, the relationship among the agents' inertias, the allowable delay bound, the communication topology, the consensus convergence rate, and the control gains is unveiled. Second, the robustness performances of the distributed control scheme with respect to the communication failures and delays are provided. It is shown that if the communication failure rate and the topology switching frequency, respectively, satisfy the given bounds, the exponential second‐order controlled consensus can be achieved under a bounded delay. Numerical examples are given to illustrate the theoretical results. Copyright © 2010 John Wiley & Sons, Ltd.     

Observer‐based consensus control of nonlinear multiagent systems under semi‐Markovian switching topologies and cyber attacks

This article investigates the leader‐following consensus of nonlinear multiagent systems under semi‐Markovian switching topologies and cyber attacks. Unlike the related works, the communication channels considered herein are subjected to successful but recoverable attacks, and when the channels work well, the network topology is time‐varying and described by a semi‐Markovian switching topology. Due to the effect of attacks, the communication network is intermittently paralyzed. For the cases that the transition rates of semi‐Markovian switching topologies are completely known and partially unknown, observer‐based control protocols and sufficient conditions are proposed, respectively, to ensure the consensus of the systems in the mean square sense. Finally, simulation examples are given to illustrate the validity of the theoretical results.     

Distributed leader‐follower consensus for a class of semilinear second‐order multiagent systems using time scale theory

The problem of distributed leader‐follower consensus for second‐order linear multiagent systems with unknown nonlinear inherent dynamics is investigated in this paper. It is assumed that the dynamic of each agent is described by a semilinear second‐order dynamic equation on an arbitrary time scale. Using calculus on time scales and direct Lyapunov's method, some sufficient conditions are derived to ensure that the tracking errors exponentially converge to zero. Some numerical results show the effectiveness of the proposed scheme.     

Second‐order consensus for nonlinear leader‐following multi‐agent systems via dynamic output feedback control

The second‐order consensus problem of nonlinear leader‐following multi‐agent systems is investigated in this paper. To solve the case that the velocities of all agents cannot be measured and the nonlinearity is unknown, an observer‐based dynamic output feedback controller is proposed based on a non‐separation principle method. Using the feedback domination technique, it is shown that the systems output can reach consensus by choosing appropriate gains. Two examples are given to verify the efficiency of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.