Adaptive multi-agent containment control with multiple parametric uncertain leaders

In this paper, an adaptive containment control is considered for a class of multi-agent systems with multiple leaders containing parametric uncertainties. The agents are heterogeneous though their dynamics have the same relative degree and are minimum phase, while the interconnection topology is described by a general directed graph. A distributed containment control is proposed for the agents to enter the moving convex set spanned by the leaders, based on an adaptive internal model and a recursive stabilization control law.     

Distributed finite-time attitude containment control for multiple rigid bodies

Distributed finite-time attitude containment control for multiple rigid bodies is addressed in this paper. When there exist multiple stationary leaders, we propose a model-independent control law to guarantee that the attitudes of the followers converge to the stationary convex hull formed by those of the leaders in finite time by using both the one-hop and two-hop neighbors’ information. We also discuss the special case of a single stationary leader and propose a control law using only the one-hop neighbors’ information to guarantee cooperative attitude regulation in finite time. When there exist multiple dynamic leaders, a distributed sliding-mode estimator and a non-singular sliding surface were given to guarantee that the attitudes and angular velocities of the followers converge, respectively, to the dynamic convex hull formed by those of the leaders in finite time. We also explicitly show the finite settling time.     

带强连通分支的多智能体系统可控包含控制

研究有强连通子图拓扑结构的有向多智能体系统领导者选择及可控包含控制问题.根据网络拓扑结构,智能体被分为两类:单元智能体和一般智能体.首先设计强连通子图中个体组成的单元智能体的一致性协议实现各个单元的一致;后由单元智能体和一般智能体构成新的拓扑结构,结合复杂网络可控性理论与二分图最大匹配算法确定满足网络可控的最少领导者集合,并为所有智能个体设计相应的控制协议,驱使跟随者渐近收敛到多个领导者组成的动态凸包中,从而实现网络的可控包含控制.仿真结果验证了理论分析的正确性.     

Distributed Containment Control of Networked Nonlinear Second-order Systems With Unknown Parameters

In this paper, we study the containment control problem for nonlinear second-order systems with unknown parameters and multiple stationary/dynamic leaders. The topologies that characterize the interaction among the leaders and the followers are directed graphs. Necessary and sufficient criteria which guarantee the control objectives are established for both stationary leaders (regulation case) and dynamic leaders (dynamic tracking case) based protocols. The final states of all the followers are exclusively determined by the initial values of the leaders and the topology structures. In the regulation case, all the followers converge into the convex hull spanned by the leaders, while in the dynamic tracking case, not only the positions of the followers converge into the convex hull but also the velocities of the followers converge into the velocity convex hull of the leaders. Finally, all the theoretical results are illustrated by numerical simulations.      

Global target aggregation and state agreement of nonlinear multi-agent systems with switching topologies

In this paper, we discuss coordination problems of a group of autonomous agents, including the target aggregation to a convex set and the state agreement. The aggregation of the whole agent group, consisting of leaders (informed agents) and followers, to a given set is investigated with switching interconnection topologies described by the connectivity assumptions on the joint topology in the time interval [t,+∞) for any time t, and then the state agreement problem is studied in a similar way. An approach based on set stability and limit set analysis is given to study the multi-agent convergence problems. With the help of graph theory and convex analysis, coordination conditions are obtained in some important cases, and the results show that simple local rules can make the networked agents with first-order nonlinear individual dynamics achieve desired collective behaviors.     

Distributed containment control with multiple stationary or dynamic leaders in fixed and switching directed networks

In this paper, we study the problem of distributed containment control of a group of mobile autonomous agents with multiple stationary or dynamic leaders under both fixed and switching directed network topologies. First, when the leaders are stationary and all followers share an inertial coordinate frame, we present necessary and sufficient conditions on the fixed or switching directed network topology such that all followers will ultimately converge to the stationary convex hull formed by the stationary leaders for arbitrary initial states in a space of any finite dimension. When the directed network topology is fixed, we partition the (nonsymmetric) Laplacian matrix and explore its properties to derive the convergence results. When the directed network topology is switching, the commonly adopted decoupling technique based on the Kronecker product in a high-dimensional space can no longer be applied and we hence present an important coordinate transformation technique to derive the convergence results. The proposed coordinate transformation technique also has potential applications in other high-dimensional distributed control scenarios and might be used to simplify the analysis of a high-dimensional system to that of a one-dimensional system when the decoupling technique based on the Kronecker product cannot be applied. Second, when the leaders are dynamic and all followers share an inertial coordinate frame, we propose a distributed tracking control algorithm without velocity measurements. When the directed network topology is fixed, we derive conditions on the network topology and the control gain to guarantee that all followers will ultimately converge to the dynamic convex hull formed by the dynamic leaders for arbitrary initial states in a space of any finite dimension. When the directed network topology is switching, we derive conditions on the network topology and the control gain such that all followers will ultimately converge to the minimal hyperrectangle that contains the dynamic leaders and each of its hyperplanes is normal to one axis of the inertial coordinate frame in any high-dimensional space. We also show via some counterexamples that it is, in general, impossible to find distribute containment control algorithms without velocity measurements to guarantee that all followers will ultimately converge to the convex hull formed by the dynamic leaders under a switching network topology in a high-dimensional space. Simulation results are presented as a proof of concept.     

Theory and Experiments on Enclosing Control of Multi-Agent Systems

This paper proposes a control strategy called enclosing control. This strategy can be described as follows: the followers design their control inputs based on the state information of neighbor agents and move to specified positions. The convex hull formed by these followers contains the leaders. We use the single-integrator model to describe the dynamics of the agents and proposes a continuous-time control protocol and a sampled-data based protocol for multi-agent systems with stationary leaders with fixed network topology. Then the state differential equations are analyzed to obtain the parameter requirements for the system to achieve convergence. Moreover, the conditions achieving enclosing control are established for both protocols. A special enclosing control with no leader located on the convex hull boundary under the protocols is studied, which can effectively prevent enclosing control failures caused by errors in the system. Moreover, several simulations are proposed to validate theoretical results and compare the differences between the three control protocols. Finally, experimental results on the multi-robot platform are provided to verify the feasibility of the protocol in the physical system.      

Event-based broadcasting containment control for multi-agent systems under directed topology

The event-based broadcasting containment control problem for both first-order and second-order multi-agent systems under directed topology is investigated. Based on certain event, each agent decides when to transmit its current states to its neighbours and the agents’ distributed control algorithms are based on these sampled state measurements, which can significantly decrease the number of the controllers’ updates. All the agents are divided into two groups, namely, the leaders and the followers. The formation control is introduced. The leaders exchange their information to converge to a formation. The followers utilise the information from both their leader neighbours and their follower neighbours and are driven to the convex hull of the leaders using the proposed control algorithms. Numerical simulations are provided to illustrate the effectiveness of the obtained theoretical results.     

具有通信时延的跟随者–多领导者聚集控制

本文考虑了一个连续时间多智能体系统跟随者–多领导者聚集控制问题. 假设智能体之间的通信频道是有向的且存在时延. 基于邻居原理, 提出了一个新的跟踪协议. 应用线性矩阵不等式技术和Lyapunov方法得到所有的跟随者都能够群集于由多个领导者组成的凸多边形区域的充分条件. 此外, 并将文中结果推广到通信频道含有时延和噪声情形. 最后, 数值仿真验证了文中理论结果的有效性和正确性.     

Distributed containment control for first‐order and second‐order multiagent systems with arbitrarily bounded delays

This paper studies containment control with communication delays and switching topologies. Firstly, a containment control algorithm for first‐order discrete‐time followers is proposed. Then, it is extended to handle double‐integrator dynamics. The main approach is to use the convexity of the convex hull spanned by multiple stationary leaders to verify the nonincreasing monotonicity of the largest distance from the followers to the convex hull. It is shown that both algorithms are robust to arbitrarily bounded communication delays as long as each follower jointly has a path from some leaders to itself. Finally, a numerical example is implemented to illustrate the effectiveness of the theoretical results.     

Consensus analysis for leader‐following multi‐agent systems with second‐order individual dynamics and arbitrary sampling

This paper performs a consensus analysis of leader‐following multi‐agent systems with multiple double integrators in the framework of sampled‐data control. Both single‐leader and multiple‐leader scenarios are considered under the assumption of networks with detectable position‐like state information. The coordination tasks are accomplished by a given protocol with the robustness against the change of sampling periods. The sampling periods can be chosen to be of an arbitrary fixed length or large time‐varying length. Under the proposed protocol, we achieve two objectives: (i) in the single leader‐subgroup case, all followers reach an agreement with leaders on states asymptotically and (ii) in the multiple leader‐subgroup case, each follower converges to some convex combination of the final states of all leaders. It is shown that the final state configuration of the convex combination is uniquely determined by the underlying interaction topology, which can be any weakly connected graph. Compared with the existing results on leader‐following networks, the consensus problem and the containment problem are solved in a unified framework with large sampling periods. Some numerical experiments are conducted to illustrate the dynamic behavior of all agents with this protocol. Copyright © 2017 John Wiley & Sons, Ltd.     

Adaptive task-space synchronisation of networked robotic agents without task-space velocity measurements

In this paper, we investigate the problem of task-space synchronisation of multiple robotic agents in the presence of uncertain kinematics and dynamics. Our control objective is to realise synchronisation without the measurements of task-space velocity. The communication topology is assumed to be directed graphs containing a spanning tree. A decentralised task-space observer with kinematic parameter updating is proposed to avoid the reliance of task-space velocity. Based on the observer, we propose the distributed adaptive synchronisation controller for two cases: (1) the leaderless consensus case and (2) the leader-follower case, where all the followers track the convex hull spanned by the virtual leaders and for each follower, it is required that there exists at least one leader that has a directed path to the follower. The asymptotic synchronisation is proved with Lyapunov analysis and input–output stability analysis tools. Simulations with multiple robotic agents are performed to show the effectiveness of the proposed schemes.     

Adaptive containment control of nonlinear multi-agent systems with non-identical agents

This paper addresses the containment control problem for a group of non-identical agents, where the dynamics of agents are supposed to be nonlinear with unknown parameters and parameterised by some functions. In controller design approach for each follower, adaptive control and Lyapunov theory are utilised as the main control strategies to guarantee the convergence of all non-identical followers to the dynamic convex hull formed by the leaders. The design of distributed adaptive controllers is based on the exchange of neighbourhood errors among the agents. For analysis of containment control problem, a new formulation has been developed using M-matrices. The validity of theoretical results are demonstrated through an example.     

Necessary and sufficient conditions for containment control of networked multi-agent systems

In this paper, containment control problems for networked multi-agent systems with multiple stationary or dynamic leaders are investigated. The topologies that characterize the interaction among the leaders and the followers are directed graphs. Necessary and sufficient criteria which guarantee the achievement of containment control are established for both continuous-time and sampled-data based protocols. When the leaders are stationary, the convergence for continuous-time protocol (sampled-data based protocol) is completely dependent on the topology structure (both the topology structure and the size of sampling period). When the leaders are dynamic, the convergence for continuous-time protocol (sampled-data based protocol) is completely dependent on the topology structure and the gain parameters (the topology structure, the gain parameters, and the size of sampling period). Moreover, the final states of all the followers are exclusively determined by the initial values of the leaders and the topology structure. In the stationary leaders case, all the followers will move into the convex hull spanned by the leaders, while in the dynamic leaders case, the followers will not only move into the convex hull but also move with the leaders with the same velocity. Finally, all the theoretical results are illustrated by numerical simulations.     

Distributed adaptive containment control of networked flexible-joint robots using neural networks

This study presents a distributed adaptive containment control approach for a group of uncertain flexible-joint (FJ) robots with multiple dynamic leaders under a directed communication graph. The leaders are neighbors of only a subset of the followers. The derivatives of the leaders are unknown, namely, the position information of the leaders is only available for implementing the proposed control approach. The local adaptive dynamic surface containment controller for each follower is designed using only neighbors’ information to guarantee that all followers converge to the dynamic convex hull spanned by the dynamic leaders. The function approximation technique using neural networks is employed to estimate the model uncertainties of each follower. It is proved that the containment control errors converge to an adjustable neighborhood of the origin regardless of model uncertainties and the lack of shared communication information. Simulation results for FJ manipulators are provided to illustrate the effectiveness of the proposed adaptive containment control scheme.     

Distributed containment control for Lagrangian networks with parametric uncertainties under a directed graph

In this paper, we study the distributed containment control problem for networked Lagrangian systems with multiple dynamic leaders in the presence of parametric uncertainties under a directed graph that characterizes the interaction among the leaders and the followers. We propose a distributed adaptive control algorithm combined with distributed sliding-mode estimators. A necessary and sufficient condition on the directed graph is presented such that all followers converge to the dynamic convex hull spanned by the dynamic leaders asymptotically. As a byproduct, we show a necessary and sufficient condition on leaderless consensus for networked Lagrangian systems under a directed graph. Numerical simulation results are given to show the effectiveness of the proposed control algorithms.     

Containment control of multi‐agent systems by exploiting the control inputs of neighbors

This paper studies the containment control problem for multi‐agent systems consisting of multiple leaders and followers connected as a network. The objective is to design control protocols so that the leaders will converge to a certain desired formation while the followers converge to the convex hull of the leaders. A novel protocol is proposed by exploiting the control input information of neighbors. Both continuous‐time and discrete‐time systems are considered. For continuous‐time systems, it is proved that the protocol is robust to any constant delays of the neighbors' control inputs. For discrete‐time systems, a sufficient condition on the feedback gain for the containment control is given in terms of the time delay and graph information. Some numerical examples are given to demonstrate the results. Copyright © 2013 John Wiley & Sons, Ltd.     

Event-triggered containment control for multi-agent systems under hybrid cyber attacks

This paper studies event-triggered containment control problem of multi-agent systems (MASs) under deception attacks and denial-of-service (DoS) attacks. First, to save limited network resources, an event-triggered mechanism is proposed for MASs under hybrid cyber attacks. Different from the existing event-triggered mechanisms, the negative influences of deception attacks and DoS attacks are considered in the proposed triggering function. The communication frequencies between agents are reduced. Then, based on the proposed event-triggered mechanism, a corresponding control protocol is proposed to ensure that the followers will converge to the convex hull formed by the leaders under deception attacks and DoS attacks. Compared with the previous researches about containment control, in addition to hybrid cyber attacks being considered, the nonlinear functions related to the states of the agents are applied to describe the deception attack signals in the MAS. By orthogonal transformation of deception attack signals, the containment control problem under deception attacks and DoS attacks is reformulated as a stability problem. Then, the sufficient conditions on containment control can be obtained. Finally, a set of simulation example is used to verify the effectiveness of the proposed method.     

高阶有向积分器网络的包含控制

研究高阶固定有向积分器网络的包含控制问题。针对静止和运动的领导者,分别为跟随者提出了不同的控制协议。领导者是静止的情况下,应用拉普拉斯变换终值定理提出线性控制协议,驱使跟随者渐近进入由多个领导者所构成的静态凸包中;领导者是移动的情况下,提出非线性控制协议,以保证跟随者能够渐近进入由多个领导者所构成的动态凸包中,并使跟随者一直保持在该凸包中,同时提出了能够达到这一目标的充分条件。仿真结果验证了该理论分析的正确性。     

Event-triggered distributed containment control of heterogeneous linear multi-agent systems by an output regulation approach

In this paper, the event-triggered distributed containment control of heterogeneous linear multi-agent systems in the output regulation framework is studied. The leaders are treated as exosystems and the containment control problem will be converted into an output regulation problem. An event-triggered protocol is then designed for each follower by the output information of neighbours. It is proved that the followers can asymptotically converge to the dynamic convex hull spanned by multiple leaders under the designed protocol and triggered strategy. Furthermore, it is shown that the proposed protocol and triggered condition can exclude Zeno behaviour, so the feasibility of the control strategy is verified. Finally, a numerical simulation is given to illustrate the effectiveness of the proposed protocol.