Containment Control of Second-order Multi-agent Systems Under Directed Graphs and Communication Constraints

The distributed coordination problem of multi-agent systems is addressed in this paper under the assumption of intermittent communication between agents in the presence of time-varying communication delays. Specifically, we consider the containment control problem of second-order multi-agent systems with multiple dynamic leaders under a directed interconnection graph topology. Also, communication between agents is performed only at some discrete instants of time in the presence of irregular communication delays and packet dropout. First, we present distributed control algorithms for double integrator dynamics in the full and partial state feedback cases. Then, we propose a method to extend our results to second-order systems with locally Lipschitz nonlinear dynamics. In both cases, we show that the proposed approach leads to our control objectives under sufficient conditions relating the characteristics of the communication process and the control gains. We also show that our approach can be applied to solve various similar coordination problems in multi-agent systems under the same communication constraints. The effectiveness of the proposed control schemes is illustrated through some examples and numerical simulations.Comment: Modified version. Paper submitted for publicatio

Distributed Adaptive Consensus Protocols for Linear Multi-agent Systems with Directed Graphs and External Disturbances

This paper addresses the distributed consensus design problem for linear multi-agent systems with directed communication graphs and external disturbances. Both the cases with strongly connected communication graphs and leader-follower graphs containing a directed spanning tree with the leader as the root are discussed. Distributed adaptive consensus protocols based on the relative states of neighboring agents are designed, which can ensure the ultimate boundedness of the consensus error and adaptive gains in the presence of external disturbances. The upper bounds of the consensus error are further explicitly given. Compared to the existing consensus protocols, the merit of the adaptive protocols proposed in this paper is that they can be computed and implemented in a fully distributed fashion and meanwhile are robust with respect to external disturbances.Comment: 17 pages, 3 figure

On the Synchronization of Second-Order Nonlinear Systems with Communication Constraints

This paper studies the synchronization problem of second-order nonlinear multi-agent systems with intermittent communication in the presence of irregular communication delays and possible information loss. The control objective is to steer all systems' positions to a common position with a prescribed desired velocity available to only some leaders. Based on the small-gain framework, we propose a synchronization scheme relying on an intermittent information exchange protocol in the presence of time delays and possible packet dropout. We show that our control objectives are achieved with a simple selection of the control gains provided that the directed graph, describing the interconnection between all systems (or agents), contains a spanning tree. The example of Euler-Lagrange systems is considered to illustrate the application and effectiveness of the proposed approach.Comment: 21 pages, 8 figures. Submitted for journal publicatio

Fully Distributed Adaptive Output Feedback Protocols for Linear Multi-Agent Systems with Directed Graphs: A Sequential Observer Design Approach

This paper studies output feedback consensus protocol design problems for linear multi-agent systems with directed graphs. We consider both leaderless and leader-follower consensus with a leader whose control input is nonzero and bounded. We propose a novel sequential observer design approach, which makes it possible to design fully distributed adaptive output feedback protocols that the existing methods fail to accomplish. With the sequential observer architecture, we show that leaderless consensus can be achieved for any strongly connected directed graph in a fully distributed manner, whenever the agents are stabilizable and detectable. For the case with a leader of bounded control input, we further present novel distributed adaptive output feedback protocols, which include nonlinear functions to deal with the effect of the leaders's nonzero control input and are able to achieve leader-follower consensus for any directed graph containing a directed spanning tree with the leader as the root.Comment: 14 pages, 8 figures, submitted for publicatio

Distributed Average Tracking for Second-order Agents with Nonlinear Dynamics

This paper addresses distributed average tracking of physical second-order agents with nonlinear dynamics, where the interaction among the agents is described by an undirected graph. In both agents' and reference inputs' dynamics, there is a nonlinear term that satisfying the Lipschitz-type condition. To achieve the distributed average tracking problem in the presence of nonlinear term, a non-smooth filter and a control input are designed for each agent. The idea is that each filter outputs converge to the average of the reference inputs and the reference velocities asymptotically and in parallel each agent's position and velocity are driven to track its filter outputs. To overcome the nonlinear term unboundedness effect, novel state-dependent time varying gains are employed in each agent's filter and control input. In the proposed algorithm, each agent needs its neighbors' filters outputs besides its own filter outputs, absolute position and absolute velocity and its neighbors' reference inputs and reference velocities. Finally, the algorithm is simplified to achieve the distributed average tracking of physical second-order agents in the presence of an unknown bounded term in both agents' and reference inputs' dynamics.Comment: 6 pages, conferenc

Distributed average tracking for multiple reference signals with general linear dynamics

This technical note studies the distributed average tracking problem for multiple time-varying signals with general linear dynamics, whose reference inputs are nonzero and not available to any agent in the network. In distributed fashion, a pair of continuous algorithms with, respectively, static and adaptive coupling strengths are designed. Based on the boundary layer concept, the proposed continuous algorithm with static coupling strengths can asymptotically track the average of the multiple reference signals without chattering phenomenon. Furthermore, for the case of algorithms with adaptive coupling strengths, the average tracking errors are uniformly ultimately bounded and exponentially converge to a small adjustable bounded set. Finally, a simulation example is presented to show the validity of the theoretical results

Containment Control of Linear Multi-Agent Systems with Multiple Leaders of Bounded Inputs Using Distributed Continuous Controllers

This paper considers the containment control problem for multi-agent systems with general linear dynamics and multiple leaders whose control inputs are possibly nonzero and time varying. Based on the relative states of neighboring agents, a distributed static continuous controller is designed, under which the containment error is uniformly ultimately bounded and the upper bound of the containment error can be made arbitrarily small, if the subgraph associated with the followers is undirected and for each follower there exists at least one leader that has a directed path to that follower. It is noted that the design of the static controller requires the knowledge of the eigenvalues of the Laplacian matrix and the upper bounds of the leaders' control inputs. In order to remove these requirements, a distributed adaptive continuous controller is further proposed, which can be designed and implemented by each follower in a fully distributed fashion. Extensions to the case where only local output information is available are discussed.Comment: 16 pages, 4 figures. arXiv admin note: text overlap with arXiv:1312.737

Novel Distributed Robust Adaptive Consensus Protocols for Linear Multi-agent Systems with Directed Graphs and External Disturbances

This paper addresses the distributed consensus protocol design problem for linear multi-agent systems with directed graphs and external unmatched disturbances. A novel distributed adaptive consensus protocol is proposed to achieve leader-follower consensus for any directed graph containing a directed spanning tree with the leader as the root node. It is noted that the adaptive protocol might suffer from a problem of undesirable parameter drift phenomenon when bounded external disturbances exist. To deal with this issue, a distributed robust adaptive consensus protocol is designed to guarantee the ultimate boundedness of both the consensus error and the adaptive coupling weights in the presence of external disturbances. Both adaptive protocols are fully distributed, relying on only the agent dynamics and the relative states of neighboring agents.Comment: 9 pages, 5 figures. submitted for publication. arXiv admin note: text overlap with arXiv:1312.737

Distributed Average Tracking for Multiple Signals Generated by Linear Dynamical Systems: An Edge-based Framework

This paper studies the distributed average tracking problem for multiple time-varying signals generated by linear dynamics, whose reference inputs are nonzero and not available to any agent in the network. In the edge-based framework, a pair of continuous algorithms with, respectively, static and adaptive coupling strengths are designed. Based on the boundary layer concept, the proposed continuous algorithm with static coupling strengths can asymptotically track the average of multiple reference signals without the chattering phenomenon. Furthermore, for the case of algorithms with adaptive coupling strengths, average tracking errors are uniformly ultimately bounded and exponentially converge to a small adjustable bounded set. Finally, a simulation example is presented to show the validity of theoretical results.Comment: accepted in press, Automatica 2016. arXiv admin note: substantial text overlap with arXiv:1312.744

Connectivity-Preserving Coordination Control of Multi-Agent Systems with Time-Varying Delays

This paper presents a distributed position synchronization strategy that also preserves the initial communication links for single-integrator multi-agent systems with time-varying delays. The strategy employs a coordinating proportional control derived from a specific type of potential energy, augmented with damping injected through a dynamic filter. The injected damping maintains all agents within the communication distances of their neighbours, and asymptotically stabilizes the multi-agent system, in the presence of time delays. Regarding the closed-loop single-integrator multi-agent system as a double-integrator system suggests an extension of the proposed strategy to connectivity-preserving coordination of Euler-Lagrange networks with time-varying delays. Lyapunov stability analysis and simulation results validate the two designs