Fully Distributed Flocking with a Moving Leader for Lagrange Networks with Parametric Uncertainties

This paper addresses the leader-follower flocking problem with a moving leader for networked Lagrange systems with parametric uncertainties under a proximity graph. Here a group of followers move cohesively with the moving leader to maintain connectivity and avoid collisions for all time and also eventually achieve velocity matching. In the proximity graph, the neighbor relationship is defined according to the relative distance between each pair of agents. Each follower is able to obtain information from only the neighbors in its proximity, involving only local interaction. We consider two cases: i) the leader moves with a constant velocity, and ii) the leader moves with a varying velocity. In the first case, a distributed continuous adaptive control algorithm accounting for unknown parameters is proposed in combination with a distributed continuous estimator for each follower. In the second case, a distributed discontinuous adaptive control algorithm and estimator are proposed. Then the algorithm is extended to be fully distributed with the introduction of gain adaptation laws. In all proposed algorithms, only one-hop neighbors' information (e.g., the relative position and velocity measurements between the neighbors and the absolute position and velocity measurements) is required, and flocking is achieved as long as the connectivity and collision avoidance are ensured at the initial time and the control gains are designed properly. Numerical simulations are presented to illustrate the theoretical results

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

Fixed-time consensus of multiple double-integrator systems under directed topologies: A motion-planning approach

This paper investigates the fixed-time consensus problem under directed topologies. By using a motion-planning approach, a class of distributed fixed-time algorithms are developed for a multi-agent system with double-integrator dynamics. In the context of the fixed-time consensus, we focus on both directed fixed and switching topologies. Under the directed fixed topology, a novel class of distributed algorithms are designed, which guarantee the consensus of the multi-agent system with a fixed settling time if the topology has a directed spanning tree. Under the directed periodically switching topologies, the fixedtime consensus is solved via the proposed algorithms if the topologies jointly have a directed spanning tree. In particular, the fixed settling time can be off-line pre-assigned according to task requirements. Compared with the existing results, to our best knowledge, it is the first time to solve the fixed-time consensus problem for double-integrator systems under directed topologies. Finally, a numerical example is given to illustrate the effectiveness of the analytical results

Multi-Agent Distributed Coordination Control: Developments and Directions

In this paper, the recent developments on distributed coordination control, especially the consensus and formation control, are summarized with the graph theory playing a central role, in order to present a cohesive overview of the multi-agent distributed coordination control, together with brief reviews of some closely related issues including rendezvous/alignment, swarming/flocking and containment control.In terms of the consensus problem, the recent results on consensus for the agents with different dynamics from first-order, second-order to high-order linear and nonlinear dynamics, under different communication conditions, such as cases with/without switching communication topology and varying time-delays, are reviewed, in which the algebraic graph theory is very useful in the protocol designs, stability proofs and converging analysis. In terms of the formation control problem, after reviewing the results of the algebraic graph theory employed in the formation control, we mainly pay attention to the developments of the rigid and persistent graphs. With the notions of rigidity and persistence, the formation transformation, splitting and reconstruction can be completed, and consequently the range-based formation control laws are designed with the least required information in order to maintain a formation rigid/persistent. Afterwards, the recent results on rendezvous/alignment, swarming/flocking and containment control, which are very closely related to consensus and formation control, are briefly introduced, in order to present an integrated view of the graph theory used in the coordination control problem. Finally, towards the practical applications, some directions possibly deserving investigation in coordination control are raised as well.Comment: 28 pages, 8 figure

Time-varying formation tracking of multiple manipulators via distributed finite-time control

Comparing with traditional fixed formation for a group of dynamical systems, time-varying formation can produce the following benefits: i) covering the greater part of complex environments; ii) collision avoidance. This paper studies the time-varying formation tracking for multiple manipulator systems (MMSs) under fixed and switching directed graphs with a dynamic leader, whose acceleration cannot change too fast. An explicit mathematical formulation of time-varying formation is developed based on the related practical applications. A class of extended inverse dynamics control algorithms combining with distributed sliding-mode estimators are developed to address the aforementioned problem. By invoking finite-time stability arguments, several novel criteria (including sufficient criteria, necessary and sufficient criteria) for global finite-time stability of MMSs are established. Finally, numerical experiments are presented to verify the effectiveness of the theoretical results

Consensus tracking in multi agent system with nonlinear and non identical dynamics via event driven sliding modes

In this work, leader follower consensus objective has been addressed with the synthesis of an event based controller utilizing sliding mode robust control. The schema has been partitioned into two parts viz. finite time consensus problem and event triggered control mechanism. A nonlinear multi agent system with non identical dynamics has been put forward to illustrate the robust capabilities of the proposed control. The first part incorporates matching of states of the followers with those of the leader via consensus tracking algorithm. In the subsequent part, an event triggered rule is devised to save computational power and restrict periodic updating of the controller involved while ensuring desired closed loop performance of the system. Switching of the event based controller is achieved via sliding mode control. Advantage of using switched controller like sliding mode is that it retains its inherent robustness as well as event triggering approach aids in saving energy expenditure. Efficacy of the proposed scheme is confirmed via numerical simulations.Comment: preprint, "IEEE Transactions on Automatic Control

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

Dynamic Feedback for Consensus of Networked Lagrangian Systems

This paper investigates the consensus problem of multiple uncertain Lagrangian systems. Due to the discontinuity resulted from the switching topology, achieving consensus in the context of uncertain Lagrangian systems is challenging. We propose a new adaptive controller based on dynamic feedback to resolve this problem and additionally propose a new analysis tool for rigorously demonstrating the stability and convergence of the networked systems. The new introduced analysis tool is referred to as uniform integral-L_p stability, which is motivated for addressing integral-input-output properties of linear time-varying systems. It is then shown that the consensus errors between the systems converge to zero so long as the union of the graphs contains a directed spanning tree. It is also shown that the proposed controller enjoys the robustness with respect to constant communication delays. The performance of the proposed adaptive controllers is shown by numerical simulations.Comment: 7 pages, 8 figures, submitted to IEEE Transactions on Automatic Contro

A New Encounter Between Leader-Follower Tracking and Observer-Based Control: Towards Enhancing Robustness against Disturbances

This paper studies robust tracking control for a leader-follower multi-agent system (MAS) subject to disturbances. A challenging problem is considered here, which differs from those in the literature in two aspects. First, we consider the case when all the leader and follower agents are affected by disturbances, while the existing studies assume only the followers to suffer disturbances. Second, we assume the disturbances to be bounded only in rates of change rather than magnitude as in the literature. To address this new problem, we propose a novel observer-based distributed tracking control design. As a distinguishing feature, the followers can cooperatively estimate the disturbance affecting the leader to adjust their maneuvers accordingly, which is enabled by the design of the first-of-its-kind distributed disturbance observers. We build specific tracking control approaches for both first- and second-order MASs and prove that they can lead to bounded-error tracking, despite the challenges due to the relaxed assumptions about disturbances. We further perform simulation to validate the proposed approaches

Distributed Consensus for Multiple Lagrangian Systems with Parametric Uncertainties and External Disturbances Under Directed Graphs

In this paper, we study the leaderless consensus problem for multiple Lagrangian systems in the presence of parametric uncertainties and external disturbances under directed graphs. For achieving asymptotic behavior, a robust continuous term with adaptive varying gains is added to alleviate the effects of the external disturbances with unknown bounds. In the case of a fixed directed graph, by introducing an integrate term in the auxiliary variable design, the final consensus equilibrium can be explicitly derived. We show that the agents achieve weighted average consensus, where the final equilibrium is dependent on three factors, namely, the interactive topology, the initial positions of the agents, and the control gains of the proposed control algorithm. In the case of switching directed graphs, a model reference adaptive consensus based algorithm is proposed such that the agents achieve leaderless consensus if the infinite sequence of switching graphs is uniformly jointly connected. Motivated by the fact that the relative velocity information is difficult to obtain accurately, we further propose a leaderless consensus algorithm with gain adaptation for multiple Lagrangian systems without using neighbors' velocity information. We also propose a model reference adaptive consensus based algorithm without using neighbors' velocity information for switching directed graphs. The proposed algorithms are distributed in the sense of using local information from its neighbors and using no comment control gains. Numerical simulations are performed to show the effectiveness of the proposed algorithms.Comment: 15 pages, 5 figure