Consensus of nonlinear multi-agent systems with observer-based protocols

This paper is concerned with distributed pinning consensus problem for a class of nonlinear multi-agent system with observer-based protocols. Two types of state observers including local observer and distributed pinning observer are proposed for the single nonlinear agent with the first one designed by the local output information and the second one designed via the relative output information of its neighboring agents. According to the state information observed, a distributed pinning observer-based protocol is proposed for the leader-following consensus of the multi-agent system. Furthermore, two multi-step algorithms are presented to construct the observer gains and the protocol parameters for the proposed protocols respectively. It is shown that under the condition that the pinning joint communication topology contains a directed spanning tree, the sufficient criteria established can not only ensure the observation error to be globally asymptotically stable, but also guarantee the consensus of the multi-agent system to be solved asymptotically. Finally, two numerical examples are provided to demonstrate the effectiveness of the observer-based protocols.     

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.     

Leader–follower consensus of linear multi-agent systems with unknown external disturbances

This paper addresses the leader–follower consensus tracking problem for multi-agent systems with identical general linear dynamics and unknown external disturbances. First, a distributed extended state observer is proposed, where both the local states and disturbance of each agent are estimated simultaneously by using the relative output information between neighbors. Then a consensus algorithm is proposed for each agent based on the relative estimated states between neighbors and its own disturbance estimate. It is shown that, with the proposed observer-based consensus algorithm, the leader–follower consensus problem can be solved. Finally, we present a simulation example to demonstrate the effectiveness of the proposed algorithm.     

多智能体系统自适应跟踪控制

基于带有非线性动态的二阶多智能体系统,研究了在有动态领导者条件下的跟踪一致性问题。假设跟随者只能获取邻居智能体的相对状态信息,只有一部分跟随者可以获得领导者的位置和速度信息,领导者的控制输入非零且不被任何一个跟随者可知。在通信拓扑为无向连通图的条件下,为了避免全局信息的不确定性,设计了分布式自适应控制协议。将系统的一致性问题转化为误差系统的一致性问题,通过Lyapunov稳定性理论和矩阵理论分析得到了该协议使系统达到一致的充分条件。最后用仿真例子证明了设计方法的有效性。     

Fully distributed bipartite output consensus of heterogeneous linear multiagent systems based on event‐triggered transmission mechanism

This study investigates the fully distributed bipartite output consensus issue of heterogeneous linear multiagent systems (HLMASs) based on event‐triggered transmission mechanism. Both the cooperative interaction and the antagonistic interaction between neighbor agents are considered. A fully distributed bipartite compensator consisting of time‐varying coupling gain and dynamic event‐triggered mechanism is first proposed to estimate the leader's states. Different from the existing schemes, the proposed compensator is independent of any global information of the network topology, is capable of achieving intermittent communication between neighbors, and is applicable for the signed communication topology. Then the distributed output feedback control protocol is developed such that the fully distributed bipartite event‐triggered output consensus problem can be achieved. Moreover, we extend the results in HLMASs without external disturbances to HLMASs with disturbances, which is more challenging in three cases (a) the disturbances are not available for measurement, (b) the disturbances suffered by each agent are heterogeneous, and (c) the disturbances are not required to be stable or bounded. It is proven that the proposed controllers fulfill the exclusion of Zeno behavior in two consensus problems. Finally, two examples are provided to illustrate the feasibility of the theoretical results.     

Global finite-time attitude consensus tracking control for a group of rigid spacecraft

The problem of finite-time attitude consensus for multiple rigid spacecraft with a leader–follower architecture is investigated in this paper. To achieve the finite-time attitude consensus, at the first step, a distributed finite-time convergent observer is proposed for each follower to estimate the leader's attitude in a finite time. Then based on the terminal sliding mode control method, a new finite-time attitude tracking controller is designed such that the leader's attitude can be tracked in a finite time. Finally, a finite-time observer-based distributed control strategy is proposed. It is shown that the attitude consensus can be achieved in a finite time under the proposed controller. Simulation results are given to show the effectiveness of the proposed method.     

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 for linear multi-agent system with intermittent information transmissions using the time-scale theory

This paper investigates the consensus problem for linear multi-agent system with fixed communication topology in the presence of intermittent communication using the time-scale theory. Since each agent can only obtain relative local information intermittently, the proposed consensus algorithm is based on a discontinuous local interaction rule. The interaction among agents happens at a disjoint set of continuous-time intervals. The closed-loop multi-agent system can be represented using mixed linear continuous-time and linear discrete-time models due to intermittent information transmissions. The time-scale theory provides a powerful tool to combine continuous-time and discrete-time cases and study the consensus protocol under a unified framework. Using this theory, some conditions are derived to achieve exponential consensus under intermittent information transmissions. Simulations are performed to validate the theoretical results.     

Admissible consensus for networked singular multi-agent systems with communication delays

This study concerns the admissible consensus problem for networked singular multi-agent systems with communication delays and agents described by general singular systems. Only the information of outputs is available through the network. An observer-based networked predictive control scheme (NPCS) is employed to compensate for the communication delays actively. Based on NPCS and dynamic compensator (dynamic output feedback), a novel protocol is proposed. Based on graph, algebra and singular system theory, the necessary and sufficient conditions are given to guarantee existence of the proposed protocol. The conditions depend on the topologies of singular multi-agent systems and the structure properties of each agent dynamics. Moreover, a consensus algorithm is provided to design the predictive protocol. A numerical example demonstrates the effectiveness of compensation for networked delays.     

Active fault‐tolerant consensus control of Lipschitz nonlinear multiagent systems

This article investigates the active fault‐tolerant consensus problem for Lipschitz nonlinear multiagent systems under detailed balanced directed graph and actuator faults. First, a fault detection filter for each agent is designed, and all agents can be divided into two categories: healthy agents and possibly faulty agents. Second, fully distributed adaptive fault‐tolerant consensus protocols for healthy and possibly faulty agents are proposed to achieve state consensus. Third, based on the fault detection method and fault‐tolerant consensus protocols, active fault‐tolerant consensus algorithms are given. Simulation examples are presented to verify the effectiveness of the proposed active fault‐tolerant algorithms.     

Observer-based event-triggered leader-following control of a class of linear multi-agent systems

This paper addresses an observer-based consensus problem for leader-following control of a class of linear multi-agent systems (MASs) under a directed communication topology via event-triggered approaches. State observers are employed to tackle the scenario wherein inner information of the follower agents are not available for measurement. And then, an observer-based distributed leader-following control scheme is developed on the basis of event-triggered mechanisms. Further, to avoid continuous measurement information monitor, we present a technical approach for generation of the combinational information from their own neighbouring agents only at triggered instants. In theory, the stability of the resulting closed-loop system is rigorously investigated, and it is proven that all signals in the closed-loop system are bounded and Zeno behaviour is also excluded. Finally, simulation examples are presented for illustration of the theoretical claims.     

Finite-time weighted average consensus with respect to a monotonic function and its application

The consensus state is an important and fundamental quantity for consensus problems of multi-agent systems, which indicates where all the dynamical agents reach. In this paper, weighted average consensus with respect to a monotonic function, which means that the trajectories of the monotonic function along the state of each agent reach the weighted average of their initial values, is studied for a group of kinematic agents with time-varying topology. By constructing a continuous nonlinear distributed protocol, such a consensus problem can be solved in finite time even though the time-varying topology involves unconnected graphs. Then the distributed protocol is employed to compute the maximum-likelihood estimation of unknown parameters over sensor networks. Compared with the existing results, the estimate scheme proposed here may reduce the costs of data communication, storage memory, book-keeping and computational overheads.     

Round-Robin协议下基于观测器的多智能体系统H∞一致性控制

针对一类具有非线性动态特性的多智能体系统,研究Round-Robin(RR)通信协议下基于观测器的H_∞一致性控制问题。在智能体与其邻居智能体之间的通信信道引入了Round-Robin通信协议,缓解信道拥堵带来的测量丢失、时延等问题。通过RR协议的调度,使得智能体在每一时刻确保能够接收到一个邻居智能体信息。首先,根据智能体的测量输出设计状态观测器,对每个智能体的状态进行估计,然后,根据估计状态设计一致性控制器,基于李雅普诺夫稳定性理论,给出多智能体系统满足H_∞一致性性能指标的充分条件,进而通过求解线性矩阵不等式(LMI)获得观测器及控制器参数。最后,将本文设计的控制算法应用于数值仿真和柔性连杆机器人的一致性控制,验证所设计算法的可行性和有效性。     

Cooperative control of multiple heterogeneous agents with unknown high-frequency-gain signs

In this paper, we investigate the cooperative control of networked agents with unknown high-frequency-gain signs. A Nussbaum-type adaptive controller is designed for each agent such that consensus of the network can be achieved while all signals in the overall system maintain bounded. The distributed controller for each agent has two parts: neighborhood error between itself and the neighbors and a Nussbaum-type item for seeking control direction adaptively. The argument of the Nussbaum-type function is tuned on line via an appropriately designed update law. It is proved that when the undirected graph is connected or the balanced digraph is weakly connected, consensus of the network can be realized. Furthermore, a distributed asymptotic regulator is proposed to regulate the overall system to the equilibrium. Simulation results are presented to verify the effectiveness of the proposed controllers.     

Event‐Based Consensus Controller for Linear Multi‐Agent Systems Over Directed Communication Topologies: A Co‐Design Approach

The paper addresses the distributed event‐triggered consensus problem in directed topologies for multi‐agent systems (MAS) with general linear dynamic agents. A co‐design approach is proposed to determine parameters of the consensus controller and its event‐triggered mechanism (ETM), simultaneously. This approach guarantees asymptotic stability along with decreasing data transmission among agents. In the proposed event‐based consensus controller, each agent broadcasts data to the neighbors only at its own triggering instants; this differs from previous studies in which continuous data streams among agents were required. Furthermore, the proposed control law is based on the piecewise constant functions of the measurement values, which are updated at triggering instants. In this case the control scheme decreases the communication network usage, energy consumption, and wear of the actuator. As a result, it facilitates distributed implementation of the proposed consensus controller for real‐world applications. A theorem is proved to outline sufficient conditions to guarantee the asymptotic stability of the closed‐loop system with the event‐based consensus controller. Another theorem is also proved to show the Zeno behavior exclusion. As a case study, the proposed event‐based controller is applied for a diving consensus problem to illustrate the effectiveness of the method.     

Distributed low-complexity output feedback tracking control for nonlinear multi-agent systems with unmodeled dynamics and prescribed performance

This paper investigates the prescribed performance distributed output consensus problem under directed graphs. With the utilisation of a filter, the original system of each follower can be converted into a strict-feedback system. Then, we design a prescribed performance output feedback distributed control protocol by applying the backstepping approach in the converted system. The proposed protocol can guarantee that the consensus tracking error of each agent evolves in predefined decaying bounds to achieve the prescribed performance, that is, the consensus tracking error of each agent converges to a predetermined residual set at a convergence rate no less than a prespecified value and exhibiting a maximum overshoot less than a preassigned constant. Moreover, during the process of consensus, all the signals in the closed-loop system are globally uniformly bounded. A simulation example is given to verify the effectiveness of the proposed control protocol.     

Robust finite-time consensus tracking for second-order multi-agent systems with input saturation under general directed communication graphs

In this paper, we study the global finite-time consensus tracking problem for uncertain second-order multi-agent systems subject to input saturation. The communication graphs are allowed to be general directed graphs. Sliding-mode observer-based distributed controllers are proposed such that global finite-time consensus tracking is achieved with bounded control inputs. Only relative state or output measurements are used in the proposed controller which reduces the communication requirement on the agents. Simulation examples are given to illustrate the effectiveness of the proposed control strategies.     

Second-order consensus of multi-agent systems with unknown but bounded disturbance

This paper addresses a consensus problem for second-order agents with unknown but bounded (UBB for short) disturbance which may affect the measure of neighbors’ velocities. In this study, the communication topology of the multi-agent system is supposed to be connected. In order to solve this consensus problem, a new velocity estimation called distributed lazy rule is firstly proposed, where each agent can estimate its neighbors’ velocities one by one. Then, a group of sufficient conditions for this second-order consensus problem are presented by adopting graph theory and the well-known Barbalat lemma, and the bounded consensus protocol is taken into account due to actuator saturation. Theoretically, the group of agents can reach consensus under the proposed control protocol, which is also validated by some numerical experiments.     

Consensus control of output‐constrained multiagent systems with unknown control directions under a directed graph

This paper presents a novel distributed adaptive control algorithm for uncertain higher‐order nonlinear multiagent systems subject to output constraints and unknown control directions. Regarding the latter, a generic class of cases is considered, allowing completely unknown and even nonidentical control directions. Furthermore, the communication topology is only required to contain a fixed directed spanning tree. To guarantee the output constraints and address the asymmetric directed communication topology, a new reference output using the transformation strategy is introduced for each agent, benefiting from which the consensus problem of the multiagent system is recast as local tracking control problems of single agents. Then, the distributed control algorithm is recursively established based on the backstepping technique and the Nussbaum‐type function. By leveraging the unique properties of the Laplacian matrix on directed graphs and matrix theory, it is shown that, under the proposed distributed algorithm, uniform boundedness of all closed‐loop signals can be ensured, and asymptotic consensus is achieved without violation of the output constraints. Finally, simulation studies on the angle control of single‐link robots are given to verify the effectiveness of the proposed algorithm.     

Distributed adaptive output feedback tracking control for a class of uncertain nonlinear multi-agent systems

This paper addresses the distributed output feedback tracking control problem for multi-agent systems with higher order nonlinear non-strict-feedback dynamics and directed communication graphs. The existing works usually design a distributed consensus controller using all the states of each agent, which are often immeasurable, especially in nonlinear systems. In this paper, based only on the relative output between itself and its neighbours, a distributed adaptive consensus control law is proposed for each agent using the backstepping technique and approximation technique of Fourier series (FS) to solve the output feedback tracking control problem of multi-agent systems. The FS structure is taken not only for tracking the unknown nonlinear dynamics but also the unknown derivatives of virtual controllers in the controller design procedure, which can therefore prevent virtual controllers from containing uncertain terms. The projection algorithm is applied to ensure that the estimated parameters remain in some known bounded sets. Lyapunov stability analysis shows that the proposed control law can guarantee that the output of each agent synchronises to the leader with bounded residual errors and that all the signals in the closed-loop system are uniformly ultimately bounded. Simulation results have verified the performance and feasibility of the proposed distributed adaptive control strategy.