Consensus of linear multi-agent systems based on full-order observer

This paper considers distributed consensus problem of multi-agent systems consisting of general linear dynamics with a time-invariant communication topology. A distributed full-order observer type consensus protocol based on relative output measurements of neighbor agents is proposed. It is found that the consensus problem of linear multi-agent systems with a directed communication topology having a spanning tree can be solved if and only if all subsystems are asymptotically stable. Some necessary and sufficient conditions are obtained for ensuring consensus in multi-agent systems. The design technique is based on algebraic graph theory, Riccati inequality and linear control theory. Finally, simulation example is given to illustrate the effectiveness of the theoretical results.     

Designing distributed consensus protocols for second-order nonlinear multi-agents with unknown control directions under directed graphs

This paper focuses on the leaderless and leader-following consensus problems of second-order nonlinear multi-agents under directed graphs. Both leaderless and leader-following consensus protocols are proposed for multi-agents with unknown control directions based on the Nussbaum-type gains. For the leaderless case, the proposed protocol can guarantee that the consensus errors asymptotically converge to zero. Moreover, for the leader-following case, the Lyapunov stability analysis shows that the consensus tracking errors can be made arbitrarily small by tuning the control parameters. It should also be noted that these proposed protocols do not require any information about the global communication topology and work with only the relative information of neighboring agents. Illustrative examples are given to show the effectiveness of the proposed control protocols.     

Consensus disturbance rejection with event-triggered communications

This paper considers the consensus disturbance rejection problem of networks of linear agents with event-triggered communications in the presence of matched disturbances. Based on the disturbance observer, distributed event-based consensus protocols are proposed and constructed for both the cases of neutrally stable and general linear agents. Under the proposed event-based consensus protocol, it is shown that the consensus errors are asymptotically stable and the Zeno behavior can be excluded. Compared to the previous related works, our main contribution is that the proposed event-based protocol can achieve consensus and meanwhile reject disturbance, without the need of continuous communications among neighboring agents. For the case of neutrally stable agents, the event-based protocol is fully distributed, using only the local information of each agent and its neighbors. Simulation results are presented to illustrate the effectiveness of the theoretical results.     

Robust quantized consensus of discrete multi-agent systems under input saturation

In this paper, we consider the quantized consensus problem of multiple discrete-time integrator agents which suffer from input saturation. As agents transmit state information through communication networks with limited bandwidth, the states of agents have to be quantized into a finite number of bits before transmission. To handle this quantized consensus problem, we introduce an internal time-varying saturation function into the controllers of all agents and ensure that the range of the state of each agent can be known in advance by its neighboring agents. Based on such shared state range information, we construct a quantized consensus protocol which implements a finite-bit quantization strategy to all states of agents and can guarantee the achievement of the asymptotic consensus under any given input saturation threshold. Such desired consensus can be guaranteed at as low bit rate as 1 bit per time step for each agent. Moreover, we can place an upper bound on the convergence rate of the consensus error of agents. We further improve that quantized consensus protocol to a robust version whose parameters are determined with only an upper bound on the number of agents and does not require any more global information of the inter-agent network. Simulations are done to confirm the effectiveness of our quantized consensus protocols.     

Event-triggered group consensus for multi-agent systems subject to input saturation

This paper investigates group consensus for leaderless multi-agent systems with non-identical dynamics. The consensus protocol is put forward in the form of the distributed event-triggered control subject to saturation, which depends on information from neighboring agents at event-triggered instants. In order to exclude the Zeno behavior and save resources, the given event-triggered condition is detected only at discrete sampling times, where the sampling intervals can be variable. Based on the graph theory, Lyapunov–Krasovskii functional method and by adopting the free-weighting matrix technique, some sufficient group consensus criteria in terms of linear matrix inequalities are derived. Furthermore, optimization problems aiming at maximizing the event-triggered parameter and the consensus region are proposed. Finally, numerical simulations illustrate the effectiveness of the theoretical results.     

Consensus analysis for multi-agent systems via periodic event-triggered algorithms with quantized information

In this article, a novel distributed event-triggered control protocol for the consensus of second-order multi-agent systems with undirected topology is studied. Based on the proposed control protocol, the event-triggered condition is evaluated only at every sampling instant. The control input for each agent will be updated with local information if and only if its condition is violated. Both ideal and quantized relative state measurements are considered under this framework. Some sufficient conditions for achieving consensus are derived using spectral properties of edge Laplacian matrix and the discrete-time Lyapunov function method. Finally, numerical examples are given to demonstrate the effectiveness of our theoretical results.     

Leaderless and leader-following consensus of linear multi-agent systems with distributed event-triggered estimators

This paper considers the event-triggered leaderless and leader-following consensus problems for linear multi-agent systems. By introducing event-triggered estimators, two novel control schemes are proposed. Different from the existing event-triggered controllers, which rely on the Fiedler eigenvalue of Laplacian matrix, the developed controllers only use the information from neighboring agents. Meanwhile, the adaptive trigger parameters are designed in the event-triggered mechanisms to improve the self-regulation ability of the event-triggered estimators. In addition, the leaderless consensus and the leader-following consensus can be achieved under the corresponding control protocols. Finally, two simulation examples are given to illustrate the validity of the proposed control protocols.     

Event-triggered fully distributed asymptotic consensus for leaderless multiple Euler-Lagrange systems

In this paper, the fully distributed consensus for a class of multiple Euler-Lagrange systems is investigated, where the protocol is designed under the event-triggered control framework and the dynamics of Euler-Lagrange systems are heterogeneous. Since only local information interactions at triggered instants can be used and the Euler-Lagrange systems are of relatively complex dynamics, it is challenging to achieve asymptotic consensus without using any global information (such as the Laplacian matrix information). By skillfully integrating the adaptive control, distributed control and event-triggered control techniques, a novel protocol is proposed for the investigated multiple Euler-Lagrange systems. It is proven that the asymptotic consensus can be achieved by the developed protocol. By a numerical example, the effectiveness of the developed protocol is illustrated.     

OKC协同知识建构中群体共识影响因素研究——群体结构的调节作用

本文从群体认知的视角,基于社会认知论,从认知主体、认知客体和认知情境三个层面提出了OKC协同知识建构中影响群体共识的五个因素:成员参与度、知识异质性、认知对象复杂度、沟通协调和群体结构,并构建群体共识影响模型。基于351个英文版Wikipedia样本数据,通过偏最小二乘结构方程对模型进行了实证检验。研究发现成员参与度不仅对群体共识存在直接影响,而且通过影响知识异质性和沟通协调对群体共识产生间接影响。认知对象复杂度对群体共识存在负向影响。此外,群体结构能够调节知识异质性、沟通协调与群体共识间的关系。     

Event-triggered control of leader-following and cluster consensus for MAS under directed graph with designable minimum event interval

This paper investigates the event-based consensus problems for linear multi-agent systems under directed network topology. First, a new event-triggered control method is proposed for the leader-following consensus problem of agents under directed graphs. Then this new method is applied to the cluster control problem under special topological conditions. The new event-based control scheme is better than some existing literature in the following aspects. 1) The graph only needs to contain a spanning tree instead of being required to be strongly connected graph or undirected, and the triggering function is state-dependent rather than time-dependent. 2) Some parameters are designable for the trade-off between the event interval and the performance of the controlled system. Besides, the optimization of some parameters is studied to reduce the trigger frequency. All the agents can achieve consensus with an exponential speed when communications among follower agents are intermittent, and Zeno behavior is excluded under the proposed method. 3) When applying this method to the cluster control problem, agents in the same cluster share the same form of triggering function. Cluster consensus can be achieved regardless of intra- and inter-cluster relative coupling strength under the event-triggered control framework.     

科学共同体中的民主策略

科学共同体中的研究活动符合民主所需要的条件和精神,科学共同体在科学知识生产中并不总是意见一致,而是往往充满了分歧,他们通过基于期刊论文、公共展示和资源压力等策略进行说服活动,根据科学知识共识程度的高低和利益共识程度的高低形成四种共识形式。在后学院科学中,科学共同体发生了新的变化,共识的形成和变化不仅受到利益的影响,而且受到外部压力的影响,民主不仅成为科学共同体中的事实存在,而且成为科学共同体的需要。     

Distributed optimal output feedback consensus control for nonlinear Euler-Lagrange systems under input saturation

In this paper, the distributed optimal consensus control of a group of Euler-Lagrange systems under input saturation is considered. The objective function is only known by each agent itself. Meanwhile it is assumed that the velocities of the systems are unknown. To solve this problem, the filters and observers are designed for each agent. The magnitudes of the control input could be guaranteed within the bounds which are given in advance. It is shown that global optimal consensus control could be achieved under the proposed bounded controllers. The states of all agents will reach a consensus which minimizes the sum of the objective functions of all agents. Simulation results illustrate the effectiveness of the control schemes.     

Fractional-order follower observer design for tracking consensus in second-order leader multi-agent systems: Periodic sampled-based event-triggered control

This paper investigates the tracking consensus problem for the second-order leader systems by designing fractional-order observer, where a periodic sampled-based data event-triggered control is employed. In order to track the position information of leader, observers for followers are designed by fractional-order system, where only the relative position information is available. Furthermore, in the process of observers design, a sampled-based event-triggered strategy is proposed so that observers use the event-triggered sampled-data, to reduce the overall load of the network. In our proposed event-triggered strategy, the event detection only works at every sampling time instant which determines whether the sampled-data should be discarded or used. Under this control strategy, the Zeno-behavior is absolutely excluded since the minimum of inter-event times is inherently lower bounded by one sampling period. It is found that the followers can track state of the leader if fractional-order observers are appropriately designed and relevant parameters are properly selected. By using the generalized Nyquist stability criterion, a necessary and sufficient condition for the observer tracking consensus of the second-order leader systems is derived. The results show that the real and imaginary parts of the eigenvalues of the augmented Laplacian matrix, and fractional-order α of observer play a vital role in reaching consensus.     

Scaled consensus problem for multi-agent systems with semi-Markov switching topologies: A view from the probability

This paper investigates the stochastic scaled consensus problem for multi-agent systems with semi-Markov switching topologies. Sufficient conditions are established to guarantee the addressed system to realize the scaled consensus with probability one, which means that all agents’ states almost surely reach a dictated proportion. Here, the semi-Markov process concerned is much more general than those utilized in the recent literature, which can be characterized by two important factors: (1) the transition probability matrix, and (2) the polytropical distribution functions of sojourn times. In addition, pinning scaled consensus protocol is designed by employing the pinning control technique, where only the root nodes of the union set of all the topologies are chosen to be pinned, and the final desired state value of the considered system can be realized with probability one. Finally, numerical simulations are provided to illustrate validity of the obtained main results.     

A fully distributed approach for consensus of multi-agent systems under multiple state-variables-dependent interaction topologies

In this paper, the consensus problem of multi-agent systems with general linear dynamics is studied. Motivated by the MIMO communication technique, a general framework is considered in which different state variables are exchanged in different independent interaction topologies. This novel framework could improve the control system design flexibility and potentially improve the system performance. Fully distributed consensus control laws are proposed and analyzed for the settings of fixed and switching multiple topologies. The control law can be applied using only local information. And the control gain can be designed depending on the dynamics of the individual agent. By transforming the overall multi-agent systems into cascade systems, necessary and sufficient conditions are provided to guarantee the consensus of the overall systems under fixed and switching state variable dependent topologies, respectively. Two simulation examples are provided to illustrate the effectiveness of the proposed theoretical results.     

Event-triggered consensus control for second-order multi-agent system subject to saturation and time delay

The event-triggered consensus control for second-order multi-agent systems subject to actuator saturation and input time delay, is investigated in this paper. Based on the designed triggering function, a distributed event-triggered control strategy is presented to drive the system to achieve consensus. Communication energy can be saved as the agents send their state information only at infrequent event instants, the continuous communication among agents is not necessary. Lyapunov-Krasovskii functional is used together with linear matrix inequality technique to analyze the stability of the closed-loop error system. The results show that agents achieve exponentially consensus under the proposed controller. Furthermore, the bounds of solution are obtained by establishing the differential equation associated with the first delay interval. The initial domain is estimated by optimizing the linear matrix inequalities. Finally, simulation examples are presented to illustrate the effectiveness of the proposed controller.     

Event-triggered consensus for second-order multi-agent systems with sampled position data via impulsive control

In this paper, the sampled-data-based event-triggered (SDBET) consensus problem of second-order multi-agent systems (MASs) with sampled position data is studied via impulsive control. Firstly, two kinds of SDBET impulsive control protocols are proposed, both of which employ sampled position data only. Secondly, a novel SDBET transmission scheme is designed to ensure the maximum length of triggering intervals exists, which can be regulated by the parameters in the triggering function. Also, the Zeno behavior is naturally excluded under the SDBET transmission scheme. And by using the designed SDBET impulsive control scheme, consensus of second-order MASs can be achieved with lower transmission and control updating frequency than using the periodical impulsive control scheme. Thirdly, sufficient conditions on the communication topology, the length of triggering intervals and control gains are derived to achieve SDBET consensus. It is also shown that to achieve consensus, both the maximum and minimum lengths of triggering intervals should be restricted. Also, a practical method for calculating the sampling period and other triggering parameters is given to ensure that the length of the triggering interval does not exceed the given range, and the SDBET transmission scheme is truly realized. Finally, some numerical examples are given to demonstrate the effectiveness of the theoretical results.     

Sliding-mode consensus algorithms for disturbed second-order multi-agent systems

In this paper, both leaderless and leader-follower consensus problems for a class of disturbed second-order multi-agent systems are studied. Based on integral sliding-mode control, sliding-mode consensus protocols are proposed for leaderless and leader-follower multi-agent systems with disturbances, respectively. Firstly, for leaderless second-order multi-agent systems, a sliding-mode consensus protocol is proposed to make the agents achieve asymptotic consensus. Secondly, for leader-follower second-order multi-agent systems, a finite-time sliding-mode consensus protocol is designed to make the agents achieve consensus in finite time. Both kinds of consensus protocols inherit the anti-disturbance performance and robustness of sliding-mode control and require less communication information. Finally, two numerical simulations are given for leaderless and leader-follower second-order multi-agent systems to validate the efficiency of the proposed consensus protocols.     

基于知识协调的知识异质性团队研发任务共识效率研究

成员对研发任务相关内容形成一致理解往往需要彼此间进行以团队学习为核心的知识协调活动。为揭示微观视角下协调活动对知识异质性团队任务共识效率的具体作用过程,提炼了知识协调的基本原理及学习策略;借鉴Deffuant有界自信模型假设,构建了成员知识水平变化影响下的任务共识模型;运用仿真方法,研究了成员学习能力、信任阈值水平、知识学习策略及学习对象搜索半径对知识异质性团队研发任务共识效率的影响。研究发现：成员学习能力及其信任阈值水平与团队任务共识效率正向相关;成员知识学习策略及学习对象搜索半径对团队研发任务共识效率具有显著影响。     

A continuous-time consensus algorithm using neurodynamic system for distributed time-varying optimization with inequality constraints

In this paper, a distributed time-varying convex optimization problem with inequality constraints is discussed based on neurodynamic system. The goal is to minimize the sum of agents’ local time-varying objective functions subject to some time-varying inequality constraints, each of which is known only to an individual agent. Here, the optimal solution is time-varying instead of constant. Under an undirected and connected graph, a distributed continuous-time consensus algorithm is designed by using neurodynamic system, signum functions and log-barrier penalty functions. The proposed algorithm can be understood through two parts: one part is used to reach consensus and the other is used to achieve gradient descent to track the optimal solution. Theoretical studies indicate that all agents will achieve consensus and the proposed algorithm can track the optimal solution of the time-varying convex problem. Two numerical examples are provided to validate the theoretical results.