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.     

Adaptive mean-square consensus of heterogeneous multiagent systems with stochastic switching topologies

The leader–following consensus of linear heterogeneous multiagent systems is investigated in this paper. To comply with the most practical scenario, the communicating topologies among agents are assumed to switch stochastically and driven by a continuous-time discrete-state Markov process, whose state space corresponds to all the possible topologies. A novel distributed adaptive compensator is designed for the followers to reconstruct the exogenous signals without knowing the Laplacian matrix who is regarded as a global information, and sufficient conditions are given to ensure the compensator converges to the dynamic of the leader asymptotically in the mean square sense. Then, based on the compensator, we solved the consensus problem both by distributed state and measurement output feedback control schemes under output regulation framework, which allow followers to have nonidentical state dimensions. Finally, the theoretical results are demonstrated by a numerical example.     

Stationary consensus of heterogeneous multi-agent systems with bounded communication delays

Consensus seeking is investigated for the discrete-time heterogeneous multi-agent systems composed of first-order agents and second-order agents, and two stationary consensus algorithms are constructed for the first-order agents and the second-order agents, respectively. Based on the properties of nonnegative matrices, sufficient consensus criteria are obtained for the agents with bounded communication delays under fixed topology and switching topologies, respectively. With some prerequisites on the coupling weights and the sampling interval, the asymptotic consensus achievement of the dynamic agents is independent of the communication delay, but strictly depends on the connectedness of the interconnection topology. Simulation results illustrate the correctness of the results.     

切换拓扑下多自主体系统的事件触发一致性控制

本文针对一阶非线性多自主体系统,考察了切换拓扑下的事件触发一致性控制问题.当切换拓扑子图的并图包含有向生成树时,基于一阶保持器提出了一种分布式事件触发一致性算法,用以降低网络的通信负载.运用迭代法和不等式法,得到了多自主体系统达到有界一致性的充分条件.此外,证明了所提事件触发机制不存在Zeno现象,并得到了触发间隔的正下界.最后,给出仿真实例,验证了所提事件触发一致性算法和理论分析结果的有效性.     

Cluster consensus of high-order multi-agent systems with switching topologies

This paper investigates the cluster consensus problems of generic linear multi-agent systems with switching topologies. Sufficient criteria for cluster consensus, which generalise the results in existing literatures, are derived for both state feedback and observer-based control schemes. By using an averaging method, it is shown that cluster consensus can be achieved when the union of the acyclic topologies contains a directed spanning tree within each cluster frequently enough. We also provide a principle to construct digraphs with inter-cluster cyclic couplings that promote cluster consensus regardless of the magnitude of inter-agent coupling weights. Finally, numerical examples are given to demonstrate the effectiveness of the proposed approaches.     

基于时变时滞动态拓扑的二阶Leader-Following多智能体一致性分析

针对具有时变时滞的二阶Leader-Following多智能体系统,研究了其一致性问题。假设其通信拓扑是时刻切换的,并且每个子时间段内系统拓扑不完全连通,采用Lyapunov-Krasovskii泛函和矛盾分析法,对系统进行了解耦分析,得出只需所有时间段内的拓扑并集连通,且系统的特征根满足一定条件,系统能达到一致,并进行了理论证明。以4个following智能体与1个leader智能体做成的网络为例进行具体说明,所得仿真结果验证了理论的有效性。     

Group consensus control for heterogeneous multi-agent systems with fixed and switching topologies

In this paper, the group consensus problems of heterogeneous multi-agent systems with fixed and switching topologies are investigated. First, a class of distributed group consensus protocol is proposed for achieving the group consensus of heterogeneous multi-agent systems by using the neighbours’ information. Then, some corresponding sufficient conditions are obtained to guarantee the achievement of group consensus. Rigorous proofs are given by using graph theory, matrix theory and Lyapunov theory. Finally, numerical simulations are also given to verify the theoretical analysis.     

时延多智能体系统领导跟随一致性研究

为符合实际情形,针对不确定与随机发生非线性的多智能体系统,研究了有时延且网络拓扑切换时系统的领导跟随一致性。传统协议通常保守的假设邻接个体间通信时延与个体和领导者间通信时延大小相同,新协议中上述时延可以大小不同。相比于传统方法,新颖的将复杂网络同步问题研究领域对时延的处理方法引入到多智能体系统一致性问题的研究中,利用一类推广的Halanay不等式,给出系统实现领导跟随一致性需满足的两个与时延无关的充分条件,即时延在相关参数满足定理条件的前提下不影响系统最终实现一致性。相比其他方法得到的含有时延的判定条件,本研究结果保守性更低,实例仿真验证了新协议的可行性。     

Distributed consensus of heterogeneous multi-agent systems with fixed and switching topologies

In this article, we study distributed consensus of heterogeneous multi-agent systems with fixed and switching topologies. The analysis is based on graph theory and nonnegative matrix theory. We propose two kinds of consensus protocols based on the consensus protocol of first-order and second-order multi-agent systems. Some necessary and sufficient conditions that the heterogeneous multi-agent system solves the consensus problems under different consensus protocols are presented with fixed topology. We also give some sufficient conditions for consensus of the heterogeneous multi-agent system with switching topology. Simulation examples are provided to demonstrate the effectiveness of the theoretical results.     

Controllability and observability of multi-agent systems with heterogeneous and switching topologies

ABSTRACT

This paper focuses on controllability and observability of multi-agent systems with heterogeneous and switching topologies, where the first- and the second-order information interaction topologies are different and switching. First, based on the controllable state set, a controllability criterion is obtained in terms of the controllability matrix corresponding to the switching sequence. Next, by virtue of the subspace sequence, two necessary and sufficient algebraic conditions are established for controllability in terms of the system matrices corresponding to all the possible topologies. Furthermore, controllability is considered from the graphic perspective. It is proved that the system is controllable if the union graph of all the possible topologies is controllable. With respect to observability, two sufficient and necessary conditions are derived by taking advantage of the system matrices and the corresponding invariant subspace, respectively. Finally, some simulation examples are worked out to illustrate the theoretical results.     

异构多智能体系统有限时间一致性分析

研究二阶智能体速度不可测情况下由一阶和二阶智能体构成的异构多智能体系统有限时间一致性问题。在固定拓扑结构下,给出了异构系统实现一致性的控制协议,通过LaSalle不变集原理和齐次控制方法得到了异构系统有限时间一致性的充分条件;在切换拓扑结构下,给出了异构系统一致性的控制协议,得到了异构系统有限时间一致性的充分条件。仿真结果验证了相关结果的有效性。     

Leader-following consensus of stochastic dynamical multi-agent systems with fixed and switching topologies under proportional-integral protocols

With the rapid development of swarm intelligence, consensus problem for multi-agent systems (MASs) has attracted substantial attention. To deal with the leader-following consensus problems in stochastic dynamical MASs with fixed and switching topologies, this article designed proportional-integral (PI) control protocols. On the basis of algebraic graph theory and stochastic analysis techniques, by selecting appropriate Lyapunov functions, it is theoretically shown that leader-following consensus of MASs with stochastic dynamics underlying fixed and switching topologies can be achieved in mean square, respectively. Sufficient criteria are derived for selecting the PI control gains. Finally, the theoretical results are illustrated through several numerical simulations.     

Stochastic consensus of double-integrator leader-following multi-agent systems with measurement noises and time delays

This paper studies a leader-following consensus problem of continuous-time double-integrator multi-agent systems with measurement noises and time-varying communication delays under directed topology. By utilising the neighbour position and velocity information, which are delayed and disturbed by measurement noises whose intensities are considered a function related to the neighbour position and velocity of agents, a distributed consensus protocol is presented, sufficient conditions of the tracking consensus in the sense of mean square are derived. Finally, the effectiveness of the proposed consensus protocol is proved by some simulations.     

Analysis of linear asynchronous hybrid stochastic systems and its application to multi-agent systems with Markovian switching topologies

This paper studies the stability and stabilisation of a class of asynchronous hybrid stochastic systems described by linear Markov jump systems with asynchronous parameters induced by hysteretic mode and input delay. By exploring the essential properties of the Markov chain and developing novel Lyapunov function/functional based approaches, we derive sufficient conditions in terms of sizes of the delays ensuring the mean square asymptotical stability of the systems. Interestingly, the Lyapunov functional based approach further leads to the mean square stability criteria that depend only on the drift part and allow an arbitrary large delay for the diffusion part, which is different from the Lyapunov-Razumikhin based results. The theoretical results are applied to solve the consensus problems of multi-agent systems with Markovian switching topologies and input delay. Numerical examples demonstrate the established results.     

Consensus problem of heterogeneous multi-agent systems with time delay under fixed and switching topologies

Consensus problem is investigated for heterogeneous multi-agent systems composed of first-order agents and second-order agents in this paper. Leader-following consensus protocol is adopted to solve consensus problem of heterogeneous multi-agent systems with time-varying communication and input delays. By constructing Lyapunov-Krasovkii functional, sufficient consensus conditions in linear matrix inequality(LMI) form are obtained for the system under fixed interconnection topology. Moreover, consensus conditions are also obtained for the heterogeneous systems under switching topologies with time delays. Simulation examples are given to illustrate effectiveness of the results.     

Event-triggered finite-time consensus of multiple Euler Lagrange systems under Markovian switching topologies

Finite-time consensus problem for multiple Euler Lagrange systems under Markovian switching topologies is investigated through an event-triggered control protocol. First, instead of the general stochastic topology, the graph of the entire system is governed by some Markov chains to the edge set, which can recover the traditional Markovian switching topologies in line with the practical communication environment. Then, by utilising an integral sliding-mode control strategy, rigorous analysis of finite-time consensus is performed through the graph theory and Lyapunov stability theory. An event-triggered communication law is delicately carried out for each agent, and Zeno behaviour of triggering time sequences is excluded absolutely. Finally, several simulation results on six two-link manipulators are given to verify the effectiveness of the designed control strategy.     

Controllability of multi-agent systems with periodically switching topologies and switching leaders

This paper considers controllability of multi-agent systems with periodically switching topologies and switching leaders. The concept of m-periodic controllability is proposed, and a criterion for m-periodic controllability is established. The effect of the duration of subsystems on controllability is analysed by utilising a property of analytic functions. In addition, the influence of switching periods on controllability is investigated, and an algorithm is proposed to search for the fewest periods to ensure controllability. A necessary condition for m-periodic controllability is obtained from the perspective of eigenvectors of the subsystems’ Laplacian matrices. For a system with switching leaders, it is proved that switching-leader controllability is equivalent to multiple-leader controllability. Furthermore, both the switching order and the tenure of agents being leaders have no effect on the controllability. Some examples are provided to illustrate the theoretical results.     

Sampled-data consensus of general linear multi-agent systems under switching topologies: averaging method

This paper investigates sampled-data consensus problems of general linear multi-agent systems under switching topologies. To perform the consensus analysis by the averaging method, the multi-agent system in the sampled-data setting is first converted into the continuous-time system with the input delay. Then, the approximate relationship between the states of this input delay system and the states of its averaged system is established by using the tool from non-standard analysis. Subsequently, a sufficient condition ensuring the sampled-data consensus is obtained by linear matrix inequalities. It is shown that the sampled-data consensus of general linear multi-agent systems, including exponential unstable agents, can be achieved, if the speed of topology switching is fast enough and the sampled-data consensus under the averaging topology can be achieved. Finally, numerical simulations are provided to demonstrate the effectiveness of theoretical analyses.     

Necessary and sufficient conditions for mean square consensus under Markov switching topologies

This article deals with the mean square consensus problem for second-order discrete-time multi-agent systems. Both cases of systems with and without time delays in Markov switching topologies are considered. With the introduced control protocols, necessary and sufficient conditions for mean square consensus of second-order multi-agent systems are derived. Under the given control protocols in Markov switching topologies, the second-order multi-agent systems can reach mean square consensus if and only if each union of the graphs corresponding to all the nodes in closed sets has a spanning tree. Finally, a simulation example is provided to illustrate the effectiveness of our theoretical results.     

Finite-time consensus for leader-following second-order multi-agent system

The finite-time consensus problems of second-order multi-agent system under fixed and switching network topologies are studied in this article. Based on the graph theory, LaSalle's invariance principle and the homogeneity with dilation, the finite-time consensus protocol of each agent using local information is designed. The leader-following finite-time consensus is analysed in detail. Moreover, some examples and simulation results are given to illustrate the effectiveness of the obtained theoretical results.