Robust pinning control of heterogeneous complex networks with jointly connected topologies and time-varying parametric uncertainty

The pinning/leader control problems provide the design of the leader or pinning controller in order to guide a complex network to a desired trajectory or target (synchronisation or consensus). Let a time-invariant complex network, pinning/leader control problems include the design of the leader or pinning controller gain and number of nodes to pin in order to guide a network to a desired trajectory (synchronization or consensus). Usually, lower is the number of pinned nodes larger is the pinning gain required to assess network synchronisation. On the other side, realistic application scenario of complex networks is characterised by switching topologies, time-varying node coupling strength and link weight that make hard to solve the pinning/leader control problem. Additionally, the system dynamics at nodes can be heterogeneous. In this paper, we derive robust stabilisation conditions of time-varying heterogeneous complex networks with jointly connected topologies when coupling strength and link weight interactions are affected by time-varying uncertainties. By employing Lyapunov stability theory and linear matrix inequality (LMI) technique, we formulate low computationally demanding stabilisability conditions to design a pinning/leader control gain for robust network synchronisation. The effectiveness of the proposed approach is shown by several design examples applied to a paradigmatic well-known complex network composed of heterogeneous Chua's circuits.     

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.     

Signed consensus problems on networks of agents with fixed and switching topologies

This paper deals with signed consensus problems for networks of agents in the presence of both fixed and switching topologies. By specifying signs for the agents, they are divided into two groups and are enabled to reach agreement on a consensus value which is the same in modulus for both groups but not in sign. Using nearest-neighbour interaction rules, we propose the distributed protocols and address their exponential convergence problem. It is shown that the quasi-strong connectivity of fixed networks or joint quasi-strong connectivity of switching networks can provide a necessary and sufficient guarantee for all agents to achieve signed consensus exponentially fast. In particular, the signed consensus results can include as special cases those of bipartite consensus in signed networks with fixed and switching topologies. Numerical simulations are also provided to illustrate the exponential convergence performance of the proposed signed consensus protocols.     

具有时滞的混合阶多智能体系统的组一致性

针对由离散时间一阶和二阶智能体组成的混合阶多智能体系统,研究其在固定和切换拓扑结构下受通信时滞影响时的组一致性问题。分别为两类智能体提出组一致性协议,引入模型变换,将闭环系统转化为等价系统。在一定假设条件下,以代数图论、矩阵理论为主要研究工具,分别在固定和切换拓扑结构下给出了混合阶多智能体系统实现渐近组一致性的条件。采用数值仿真对所得结果的有效性进行了验证。     

时延异构多自主体系统的群一致性分析

针对由一阶自主体和二阶自主体构成的异构多自主体系统的静态群一致性问题,分别提出了在固定连接拓扑和切换连接拓扑结构下的静态群一致性算法。通过构造Lyapunov-Krasovskii函数,得到了系统在具有相同时变通信时延的群一致性算法作用下渐近收敛群一致的充分条件,并以线性矩阵不等式表示。最后,仿真结果表明,所提算法在满足一定条件下能使时延异构多自主体系统渐近收敛群一致。     

Distributed algorithms for reaching consensus on general functions

This paper presents analysis and design results for distributed consensus algorithms in multi-agent networks. We consider continuous consensus functions of the initial state of the network agents. Under mild smoothness assumptions, we obtain necessary and sufficient conditions characterizing any algorithm that asymptotically achieves consensus. This characterization is the building block to obtain various design results for networks with weighted, directed interconnection topologies. We first identify a class of smooth functions for which one can synthesize in a systematic way distributed algorithms that achieve consensus. We apply this result to the family of weighted power mean functions, and characterize the exponential convergence properties of the resulting algorithms. We establish the validity of these results for scenarios with switching interconnection topologies. Finally, we conclude with two discontinuous distributed algorithms that achieve, respectively, max and min consensus in finite time.     

离散多智能体切换系统的二阶分组一致性研究

针对随机切换拓扑下离散多智能体系统的二阶分组一致性问题进行了研究。 设计了一种新颖的分组一致性协议,该协议不依赖于保守的假设条件,能全面反映系统中智能体在分组内与分组间的相互影响。引入马尔科夫链来模拟系统的随机拓扑变化, 基于矩阵理论和图论得到了在马尔科夫切换拓扑条件下,应用新协议使系统达到分组一致的充分条件。 在证明过程的结尾部分,使用线性不等式 (LMI) 工具给出了获取协议中控制参数的算法。最后,通过数字仿真实例证明了理论结果的有效性。     

Guaranteed‐cost consensus for multiagent networks with Lipschitz nonlinear dynamics and switching topologies

Guaranteed‐cost consensus for high‐order nonlinear multiagent networks with switching topologies is investigated. By constructing a time‐varying nonsingular matrix with a specific structure, the whole dynamics of multiagent networks is decomposed into the consensus and disagreement parts with nonlinear terms, which is the key challenge to be dealt with. An explicit expression of the consensus dynamics, which contains the nonlinear term, is given and its initial state is determined. Furthermore, by the structure property of the time‐varying nonsingular transformation matrix and the Lipschitz condition, the impacts of the nonlinear term on the disagreement dynamics are linearized, and the gain matrix of the consensus protocol is determined on the basis of the Riccati equation. Moreover, an approach to minimize the guaranteed cost is given in terms of linear matrix inequalities. Finally, the numerical simulation is shown to demonstrate the effectiveness of theoretical results.     

On local synchronisability of nonlinear networked systems with a unit inner-coupling matrix and switching topology

The local synchronisation of the nonlinear networked systems with switching topology is studied in this article for the special case in which the inner-coupling matrix is a unit matrix. The critical idea is to convert synchronisation problem to consensus problem such that the switching topology can be dealt with effectively without any extra assumption on the relationship among the involved topologies. A novel local synchronous criterion consisting of the maximum Lyapunov exponent of nodal self-dynamics and the consensus convergent rate of the switching topology is given. To illustrate the effectiveness of the analytical results, two numerical examples on chaos synchronisation are simulated, respectively, for the periodic switching case and randomly switching case.     

Cooperative output regulation of heterogeneous multiagent systems based on event‐triggered control with fixed and switching topologies

This paper addresses the cooperative output regulation problem of multiagent systems with fixed and switching topologies. Each agent is a heterogeneous linear system, and the output of the exosystem can be available to only a subset of agents. For the agents that can directly access the exosystem, a common observer based on an event‐triggered strategy is constructed to estimate the exogenous signal for feedback control design. For the rest of the agents, estimators based on an event‐triggered mechanism to acquire the estimation value of the exogenous signal are designed under some essential assumptions. A decentralized event‐triggered formulation is considered first by applying a Lyapunov function for a fixed topology. Furthermore, a topology‐dependent triggering condition and the average dwell‐time switching law are deduced simultaneously by using multiple Lyapunov functions for switching topologies. Under communication constraints, we propose observer‐based and estimator‐based feedback controllers to solve the cooperative output regulation problem using available local information among agents. Two examples are finally provided to verify the effectiveness of the proposed theoretical results.