Stochastic consensus of single‐integrator multi‐agent systems under relative state‐dependent measurement noises and time delays

This paper proposes a consensus algorithm for continuous‐time single‐integrator multi‐agent systems with relative state‐dependent measurement noises and time delays in directed fixed and switching topologies. Each agent's control input relies on its own information state and its neighbors' information states, which are delayed and corrupted by measurement noises whose intensities are considered a function of the agents' relative states. The time delays are considered time‐varying and uniform. For directed fixed topologies, condition to ensure mean square linear χ‐consensus (average consensus, respectively) are derived for digraphs having spanning tree (balanced digraphs having spanning tree, respectively). For directed switching topologies, conditions on both time delays and dwell time have been given to extend the mean square linear χ‐consensus (average consensus, respectively) of fixed topologies to switching topologies. Copyright © 2016 John Wiley & Sons, Ltd.     

Consensus of second‐order multi‐agent systems with exogenous disturbances

In this paper, the consensus of second‐order multi‐agent dynamical systems with exogenous disturbances is studied. A pinning control strategy is designed for a part of agents of the multi‐agent systems without disturbances, and this pinning control can bring multiple agents' states to reaching an expected consensus track. Under the influence of the disturbances, disturbance observers‐based control (DOBC) is developed for disturbances generated by an exogenous system to estimate the disturbances. Asymptotical consensus of the multi‐agent systems with disturbances under the composite controller can be achieved for fixed and switching topologies. Finally, by applying an example of multi‐agent systems with switching topologies and exogenous disturbances, the consensus of multi‐agent systems is reached under the DOBC with the designed parameters. Copyright © 2010 John Wiley & Sons, Ltd.     

Consensus of second‐order discrete‐time multi‐agent systems with relative‐state‐dependent noises

This paper studies the consensus problem of second‐order discrete‐time multi‐agent systems with relative‐state‐dependent noises. Directed switching topologies are considered. Firstly, for a kind of switching topology with each digraph containing a spanning tree, we give a weak consensus result on the basis of the mode‐dependent average dwell time method. Then, if all digraphs in a switching topology are strongly connected and the corresponding Laplacian matrices have a common left eigenvector for zero eigenvalue, we prove that the mean square and almost sure consensus can always be guaranteed for an arbitrary switching sequence with some constant distributed control gains, and we also give the statistic properties of the final consensus points. Numerical examples are presented to illustrate the effectiveness of our results. Copyright © 2017 John Wiley & Sons, Ltd.     

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.     

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 of heterogeneous first‐ and second‐order multi‐agent systems with directed communication topologies

In this paper, we consider the consensus problem for heterogeneous multi‐agent systems composed of some first‐order and some second‐order dynamic agents in directed communication graphs. Consensus protocols are proposed for the second‐ and first‐order dynamic agents, respectively. Under certain assumptions on the control parameters, for fixed communication topologies, necessary and sufficient conditions for consensus are given, and the consensus values of all agents are established. For switching topologies, sufficient conditions are given for all agents to reach consensus. Finally, simulation examples are presented to demonstrate the effectiveness of the proposed methods. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

Consensus of data‐sampled multi‐agent systems with Markovian switching topologies

This paper studies the consensus problem of data‐sampled multi‐agent systems with Markovian switching topologies. Two different consensus algorithms are considered. By a system transformation, the mean‐square consensus problem of multi‐agent systems is converted into the mean‐square stability problem of Markov jump systems. Necessary and sufficient conditions of mean‐square consensus are obtained. The cone complementary linearization algorithm is used to get the allowable control gain. Simulation examples are given to show the effectiveness of the results. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

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

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.     

Consensus of linear multi‐agent systems with stochastic noises and binary‐valued communications

This article studies consensus problems of discrete‐time linear multi‐agent systems with stochastic noises and binary‐valued communications. Different from quantized consensus of first‐order systems with binary‐valued observations, the quantized consensus of linear multi‐agent systems requires that each agent observes its neighbors' states dynamically. Unlike the existing quantized consensus of linear multi‐agent systems, the information that each agent in this article gets from its neighbors is only binary‐valued. To estimate its neighbors' states dynamically by using the binary‐valued observations, we construct a two‐step estimation algorithm. Based on the estimates, a stochastic approximation‐based distributed control is proposed. The estimation and control are analyzed together in the closed‐loop system, since they are strongly coupled. Finally, it is proved that the estimates can converge to the true states in mean square sense and the states can achieve consensus at the same time by properly selecting the coefficient in the estimation algorithm. Moreover, the convergence rate of the estimation and the consensus speed are both given by O(1/t). The theoretical results are illustrated by simulations.     

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.     

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.     

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 seeking via iterative learning for multi‐agent systems with switching topologies and communication time‐delays

This paper deals with the high‐precision consensus seeking problem of multi‐agent systems when they are subject to switching topologies and varying communication time‐delays. By combining the iterative learning control (ILC) approach, a distributed consensus seeking algorithm is presented based on only the relative information between every agent and its local (or nearest) neighbors. All agents can be enabled to achieve consensus exactly on a common output trajectory over a finite time interval. Furthermore, conditions are proposed to guarantee both exponential convergence and monotonic convergence for the resulting ILC processes of multi‐agent consensus systems. In particular, the linear matrix inequality technique is employed to formulate the established convergence conditions, which can directly give formulas for the gain matrix design. An illustrative example is included to validate the effectiveness of the proposed ILC‐motivated consensus seeking algorithm. Copyright © 2016 John Wiley & Sons, Ltd.     

Consensus in second‐order Markovian jump multi‐agent systems via impulsive control using sampled information with heterogenous delays

This paper investigates the consensus problem of second‐order Markovian jump multi‐agent systems with delays. Both network‐induced random delay and node‐induced state delay are considered, where the network‐induced random delay, subjected to a Markov chain, exists in the switching signal and the node‐induced state delay, related to switching topologies, is heterogeneous between any two linked agents. In order to reduce communication and control energy, an impulsive protocol is proposed, where each agent only can get delayed relative positions to neighbors and the velocity of itself at impulsive instants. By performing three steps of model transformation and introducing a mapping for two independent Markov chains, the consensus problem of the original continuous‐time system is equivalent to the stability problem of a discrete‐time expand error system with two Markovian jumping parameters and a necessary and sufficient criterion is derived. A numerical example is given to illustrate the effectiveness of the theoretical result.@@@@This work is supported by the National Natural Science Foundation of China under Grants 61374171, 61572210, and 51537003, the Fundamental Research Funds for the Central Universities (2015TS030), and the Program for Changjiang Scholars and Innovative Research Team in University (IRT1245).     

Guaranteed‐Performance Consensualization for High‐Order Lipschitz Nonlinear Multi‐Agent Systems with Balanced Directed Switching Topologies

Guaranteed‐performance consensus design problems for both the leaderless and leader‐following high‐order multi‐agent systems with balanced directed switching topologies and Lipschitz nonlinear dynamics are investigated. Consensus protocols and quadratic performance functions based on state errors are proposed to obtain the guaranteed‐performance consensus. By a state decomposition method, the consensualization problems for leaderless cases are transformed into asymptotic stability ones of a reduced‐order subsystem and the guaranteed‐performance cost is determined by the Lyapunov stability analysis of the reduced‐order subsystem, and the state error method is utilized to deal with the guaranteed‐performance consensualization problems for leader‐following cases. Then, by using the structure property of the transformation matrix and the Lipschitz condition, the impacts of Lipschitz nonlinear terms can be determined. Moreover, guaranteed‐performance consensualization criteria are presented based on linear matrix inequalities for both leaderless and leader‐following cases with directed switching topologies. Furthermore, the guaranteed‐performance costs are determined, which can respectively reflect the structures of the interaction topologies of leaderless and leader‐following cases. Finally, two numerical simulations are presented to verify the validity of theoretical results.     

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 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.     

Synchronization of General Linear Multi‐Agent Systems With Measurement Noises

This paper studies the synchronization of general linear multi‐agent systems with measurement noises in mean square. It shows that the conventional consensus protocol is efficient and robust to the additive and multiplicative measurement noises in mean square. For the additive measurement noises which are independent of the relative‐states, it shows that the multi‐agent systems can achieve synchronization in practical mean square. For the multiplicative measurement noises which are dependent of the relative‐states, it shows that the multi‐agent systems can achieve synchronization in (strict) mean square. Furthermore, the new consensus protocol is better than the conventional one at some specific situations, i.e., the multi‐agent systems with additive measurement noises can also achieve synchronization in (strict) mean square. Numerical simulations are also provided and the results show highly consistent with the theoretical results.     

Consensus analysis of continuous‐time second‐order multi‐agent systems with nonuniform time‐delays and switching topologies

In this study, consensus problems for second‐order multi‐agent systems with nonuniform and switching topologies are investigated. Each agent has a self‐delay, and each delay is independent of the others. As a measure of the disagreement dynamics, a class of positive semi‐definite Lyapunov–Krasovskii functions are introduced. Using algebraic graph theory and these Lyapunov–Krasovskii functions, sufficient conditions are derived by contradiction under which all agents asymptotically reach consensus. Finally, the effectiveness of the obtained theoretical results is demonstrated through numerical simulations.