Consensus Problem Of Multi-agent Systems Research Articles

Consensus condition for linear multi-agent systems over randomly switching topologies

This paper studies both continuous and discrete time consensus problems for multi-agent systems with linear time-invariant agent dynamics over randomly switching topologies. The switching is governed by a time-homogeneous Markov process, whose state corresponds to a possible interaction topology among agents. Necessary and sufficient conditions are derived for achieving consensus under a common control protocol, respectively. It is shown that the effect of switching topologies on consensus is determined by the union of topologies associated with the positive recurrent states of the Markov process. Moreover, the effect of random link failures on discrete time consensus is investigated. The implications and relationships with the existing results are discussed. Finally, the theoretical results are validated via simulations.

Finite-gain L p consensus of multi-agent systems

This paper studies consensus problems for multi-agent systems modeled by linear time-invariant systems with external disturbances under a fixed directed communication topology. It is shown that consensus can be achieved if each agent with the same disturbance signals. But the result is different for each agent with different disturbances. In this case, the finite-gain Lp consensus is introduced to describe the effects of the external disturbance on the consensus performance. A necessary and sufficient condition for reaching finite-gain Lp consensus is presented, and analytic estimation of the Lp gain is given. A distributed algorithm is proposed to ensure that the finite-gain L2 consensus can be reached with a desired L2 gain. Numerical examples are given to illustrate the given results.

Robust Consensus of Multi-Agent Systems with Nonuniform Time-Delays and Switching Topologies

This paper studies the robust consensus problem for multi-agent systems with nonuniform time-delays and switching topologies in the presence of external disturbances, where each agent has a self-delay and each delay is independent of each other. A neighbor-based rule is used for the agents with nonuniform time-delays and external disturbances. A sufficient condition is derived under which all agents achieve consensus while satisfying desired H_infinity performance. Finally, the effectiveness of the obtained theoretical results is demonstrated through numerical simulations.

Second-Order Consensus Seeking in Multi-Agent Systems With Nonlinear Dynamics Over Random Switching Directed Networks

This paper discusses the second-order local consensus problem for multi-agent systems with nonlinear dynamics over dynamically switching random directed networks. By applying the orthogonal decomposition method, the state vector of resulted error dynamical system can be decomposed as two transversal components, one of which evolves along the consensus manifold and the other evolves transversally with the consensus manifold. Several sufficient conditions for reaching almost surely second-order local consensus are derived for the cases of time-delay-free coupling and time-delay coupling, respectively. For the case of time-delay-free coupling, we find that if there exists one directed spanning tree in the network which corresponds to the fixed time-averaged topology and the switching rate of the dynamic network is not more than a critical value which is also estimated analytically, then second-order dynamical consensus can be guaranteed for the choice of suitable parameters. For the case of time-delay coupling, we not only prove that under some assumptions, the second-order consensus can be reached exponentially, but also give an analytical estimation of the upper bounds of convergence rate and the switching rate. Finally, numerical simulations are provided to illustrate the feasibility and effectiveness of the obtained theoretical results.

Robust iterative learning protocols for finite-time consensus of multi-agent systems with interval uncertain topologies

This paper is devoted to the robust finite-time output consensus problems of multi-agent systems under directed graphs, where all agents and their communication topologies are subject to interval uncertainties. Distributed protocols are constructed by using iterative learning control (ILC) algorithms, where information is exchanged only at the end of one iteration and learning is used to update the control inputs after each iteration. It is proved that under ILC-based protocols, the finite-time consensus can be achieved with an increasing number of iterations if the communication network of agents is guaranteed to have a spanning tree. Moreover, if the information of any desired terminal output is available to a portion (not necessarily all) of the agents, then the consensus output that all agents finally reach can be enabled to be the desired terminal output. It is also proved that for all ILC-based protocols, gain selections can be provided in terms of bound values, and consensus conditions can be developed associated with bound matrices. Simulation results are given to demonstrate the effectiveness of our theoretical results.

Distributed consensus of multi-agent systems with general linear node dynamics and intermittent communications

SUMMARY Without assuming that the mobile agents can communicate with their neighbors all the time, the consensus problem of multi-agent systems with general linear node dynamics and a fixed directed topology is investigated. To achieve consensus, a new class of distributed protocols designed based only on the intermittent relative information are presented. By using tools from matrix analysis and switching systems theory, it is theoretically shown that the consensus in multi-agent systems with a periodic intermittent communication and directed topology containing a spanning tree can be cast into the stability of a set of low-dimensional switching systems. It is proved that there exists a protocol guaranteeing consensus if each agent is stabilizable and the communication rate is larger than a threshold value. Furthermore, a multi-step intermittent consensus protocol design procedure is provided. The consensus algorithm is then extended to solve the formation control problem of linear multi-agent systems with intermittent communication constraints as well as the consensus tracking problem with switching directed topologies. Finally, some numerical simulations are provided to verify the effectiveness of the theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.

Leader-following consensus of multi-agent systems with switching topologies and time-delays

This paper investigates the leader-following consensus problem of multi-agent systems where the leader is static and the controlling effect of each follower depends on its own state. The control protocols are proposed for two cases: i) for network with switching topologies and undirected information flow; ii) for network with directed information flow and communication time-delays. With the aid of several tools from algebraic graph, matrix theory and stability theory, the sufficient conditions guaranteeing leader-following consensus are obtained by constructing appropriate Lyapunov functions. Simulations are presented to demonstrate the effectiveness of our theoretical results.

Distributed consensus of linear multi-agent systems with adaptive dynamic protocols

This paper considers the distributed consensus problem of multi-agent systems with general continuous-time linear dynamics for both the cases without and with a leader whose control input might be nonzero and time varying. For the case without a leader, based on the relative output information of neighboring agents, two types of distributed adaptive dynamic consensus protocols are proposed, namely, the edge-based adaptive protocol which assigns a time-varying coupling weight to each edge in the communication graph and the node-based adaptive protocol which uses a time-varying coupling weight for each node. These two adaptive protocols are designed to ensure that consensus is reached in a fully distributed fashion for all undirected connected communication graphs. It is shown that the edge-based adaptive consensus protocol is applicable to arbitrary switching connected graphs. For the case where there exists a leader whose control input is possibly nonzero and bounded, a distributed continuous adaptive protocol is designed to guarantee the ultimate boundedness of the consensus error with respect to any communication graph which contains a directed spanning tree with the leader as the root and whose subgraph associated with the followers is undirected, requiring neither global information of the communication graph nor the upper bound of the leader’s control input. A distributed discontinuous protocol is also discussed as a special case. Simulation examples are finally given to illustrate the theoretical results.

Distributed control gains design for consensus in multi-agent systems with second-order nonlinear dynamics

This paper discusses the design of distributed control gains for consensus in multi-agent systems with second-order nonlinear dynamics. First, an effective distributed adaptive gain-design strategy is proposed based only on local information of the network structure. Then, a leader–follower consensus problem in multi-agent systems with updated control gains is studied. A distributed adaptive law is then proposed for each follower based on local information of neighboring agents and the leader if this follower is an informed agent. Furthermore, a distributed leader–follower consensus problem in multi-agent systems with unknown nonlinear dynamics is investigated by combining the variable structure approach and the adaptive method. Finally, simulation examples are given to illustrate the theoretical analysis.

Finite-time consensus protocols for networks of dynamic agents by terminal iterative learning

This paper aims to address finite-time consensus problems for multi-agent systems under the iterative learning control framework. Distributed iterative learning protocols are presented, which adopt the terminal laws to update the control input and are offline feedforward design approaches. It is shown that iterative learning protocols can guarantee all agents in a directed graph to reach the finite-time consensus. Furthermore, the multi-agent systems can be enabled to achieve a finite-time consensus at any desired terminal state/output if iterative learning protocols can be improved by introducing the desired terminal state/output to a portion of agents. Simulation results show that iterative learning protocols can effectively accomplish finite-time consensus objectives for both first-order and higher order multi-agent systems.

Consensus of second-order multi-agent systems with delayed nonlinear dynamics and intermittent communications

This article investigates the second-order consensus problem of multi-agent systems with inherent delayed nonlinear dynamics and intermittent communications. Each agent is assumed to obtain the measurements of relative states between its own and the neighbours' only at a sequence of disconnected time intervals. A new kind of protocol based only on the intermittent measurements of neighbouring agents is proposed to guarantee the states of agents to reach second-order consensus under a fixed strongly connected and balanced topology. By constructing a common Lyapunov function, it is shown that consensus can be reached if the general algebraic connectivity and communication time duration are larger than their corresponding threshold values, respectively. Finally, simulation examples are provided to verify the effectiveness of the theoretical analysis.

Extensions of Invariance Principle with Applications in Multi-Agent Systems

In this paper, we develop two extensions of invariance principle for nonlinear switched systems. We first present a union invariance principle for switched systems which shows that the switched solution approaches the combined zero loci of the output functions. Then, we extend the union weak-invariance principle to an intersection invariance principle, which greatly reduces the convergence region. Our new principles include as a special case the integral invariance principle. Finally, consensus problem of multi-agent systems with jointly connected topologies is solved using the principles.

Decentralized state feedback consensus of linear multi-agent systems with input saturation

The decentralized state feedback consensus problem for multi-agent systems under actuator saturation is formulated in this paper. The entire system is decentralized in the sense that each agent can only obtain information from its neighbor agents. Firstly, a decentralized controller is designed based on graph Laplacian. The consensus problem is reduced to solve the matrix inequality problem under actuator saturation. Secondly, an optimization algorithm for feedback controller is proposed in order to achieve a large domain of attraction for the resulting closed-loop system. Finally, a numerical example is given to demonstrate the effectiveness of the design algorithm.

Adaptive Coordination Control of Multi-Agent Systems with Switching Topologies and Unknown Nonlinear Dynamics

In this paper, we study the leader-following adaptive consensus problem for multi-agent systems with unknown nonlinear dynamics. The topologies of the networks are switching. A novel adaptive consensus algorithm is proposed by using linear parameterizations of unknown nonlinear dynamics of all agents. By stability analysis and parameter convergence analysis of the proposed algorithm, adaptive consensus can be realized based on neighboring graphs. The stability analysis is based on algebraic graph theory and Lyapunov theory, the PE condition plays a key role in parameter convergence analysis. Example is given to validate the theoretical results.

Consensus of multi‐agent systems with general linear dynamics via dynamic output feedback control

This study addresses consensus problems of multi-agent systems (MASs) using dynamic output feedback control under both fixed and switching topologies. We aim to exploit the information structure for the consensusability of MASs. Necessary and sufficient conditions are presented in terms of detectability and stabilisability of the agents, graph topology, and some matrix inequality constraints. These conditions explicitly reveal how consensusability is affected by the intrinsic dynamics of the agents, the communication topology and available information. In addition, this paper provides several constructive procedures for protocol design to achieve consensus, and establishes the so-called separation principle, which simplifies the design procedure greatly.

Adaptive Consensus of High Order Multi-Agent Systems with Unknown Nonlinear Dynamics

In this paper, high order consensus problem of multi-agent systems with non-identical unknown nonlinear dynamics following an unknown and nonlinear leader is investigated in networks with fixed and switching topologies. By parameterizations of unknown nonlinear dynamics of agents in the system, neighbor-based adaptive consensus algorithms are proposed by incorporating consensus errors in addition to relative position feedback. Base on algebraic graph theory, Lyapunov theory, Riccati inequalities and PE condition, analysis of stability and parameter convergence of the proposed algorithm are conducted. Finally, a simulation in switching networks is worked out to illustrate the effectiveness of the theoretical results.

Distributed Design of Finite-time Average Consensus Protocols

In this paper, we are interested in the finite-time average consensus problem for multi-agent systems or wireless sensor networks. This issue is formulated in a discrete-time framework by utilizing a linear iteration scheme, where each node repeatedly updates its value as a weighted linear combination of its own value and those of its neighbors. Unlike most of research in literature, this work deals with the foremost step, called configuration step, during which the consensus protocol is to be set up in each agent. Designing consensus protocols can be viewed as a matrix factorization problem. For connected undirected graphs, we propose a learning method for solving such matrix factorization problem in a distributed way. More precisely, we first show how solving this problem for the particular case of strongly regular graphs. Then, a distributed gradient back-propagation algorithm is derived for the general case. The performance of the proposed algorithm is evaluated by means of simulation results.

Distributed RobustH∞Consensus Control of Multiagent Systems with Communication Errors Using Dynamic Output Feedback Protocol

This paper studies robust consensus problem for multiagent systems modeled by an identical linear time-invariant system under a fixed communication topology. Communication errors in the transferred data are considered, and only the relative output information between each agent and its neighbors is available. A distributed dynamic output feedback protocol is proposed, and sufficient conditions for reaching consensus with a prescribedH∞performance are presented. Numerical examples are given to illustrate the theoretical results.

Multi‐agent iterative learning control with communication topologies dynamically changing in two directions

This study aims to develop an iterative learning control (ILC) approach to solving finite-time output consensus problems of multi-agent systems. The communication topologies among agents are considered to dynamically change in two directions (along both time axis and iteration axis), for which a framework is presented to construct effective distributed protocols. It is shown that a protocol can be derived through ILC to enable multi-agent systems to accomplish the finite-time consensus, which moreover can possess an exponentially fast convergence speed. In particular, for any desired terminal output that is available to not all of but only a portion of agents, multi-agent systems can be guaranteed to achieve the finite-time consensus at the desired terminal output. Simulation tests are given to demonstrate the performance and effectiveness of the obtained consensus results.

Consensus Problem in Multi-Agent Systems with Communication Channel Constraint on Signal Amplitude

Consensus Problem in Multi-Agent Systems with Communication Channel Constraint on Signal Amplitude