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

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

On finite-time and fixed-time consensus algorithms for dynamic networks switching among disconnected digraphs

The aim of this paper is to analyze a class of consensus algorithms with finite-time or fixed-time convergence for dynamic networks formed by agents with first-order dynamics. In particular, in the analyzed class a single evaluation of a nonlinear function of the consensus error is performed per each node. The classical assumption of switching among connected graphs is dropped here, allowing to represent failures and intermittent communications between agents. Thus, conditions to guarantee finite and fixed-time convergence, even while switching among disconnected graphs, are provided. Moreover, the algorithms of the considered class are shown to be computationally simpler than previously proposed finite-time consensus algorithms for dynamic networks, which is an important feature in scenarios with computationally limited nodes and energy efficiency requirements such as in sensor networks. The performance of the considered consensus algorithms is illustrated through simulations, comparing it to existing approaches for dynamic networks with finite-time and fixed-time convergence. It is shown that the settling time of the considered algorithms grows slower when the number of nodes increases than with other consensus algorithms for dynamic networks

Nonlinear Consensus Strategies for Multi-Agent Networks in Presence of Communication Delays and Switching Topologies: Real-Time Receding Horizon Approach

This paper presents a novel framework which combines a non-iterative solution of Real-Time Nonlinear Receding Horizon Control (NRHC) methodology to achieve consensus within complex network topologies with existing time-delays and in presence of switching topologies. In this formulation, we solve the distributed nonlinear optimization problem for multi-agent network systems directly, \emph{in real-time}, without any dependency on iterative processes, where the stability and convergence guarantees are provided for the solution. Three benchmark examples on non-linear chaotic systems provide validated results which demonstrate the significant outcomes of such methodology.Comment: 26 pages, 8 figures (under review). arXiv admin note: substantial text overlap with arXiv:1510.0779

Designing Distributed Fixed-Time Consensus Protocols for Linear Multi-Agent Systems Over Directed Graphs

This technical note addresses the distributed fixed-time consensus protocol design problem for multi-agent systems with general linear dynamics over directed communication graphs. By using motion planning approaches, a class of distributed fixed-time consensus algorithms are developed, which rely only on the sampling information at some sampling instants. For linear multi-agent systems, the proposed algorithms solve the fixed-time consensus problem for any directed graph containing a directed spanning tree. In particular, the settling time can be off-line pre-assigned according to task requirements. Compared with the existing results for multi-agent systems, to our best knowledge, it is the first-time to solve fixed-time consensus problems for general linear multi-agent systems over directed graphs having a directed spanning tree. Extensions to the fixed-time formation flying are further studied for multiple satellites described by Hill equations

Distributed Real-Time Non-Linear Receding Horizon Control Methodology for Multi-Agent Consensus Problems

This work investigates the consensus problem for multi-agent nonlinear systems through the distributed real-time nonlinear receding horizon control methodology. With this work, we develop a scheme to reach the consensus for nonlinear multi agent systems under fixed directed/undirected graph(s) without the need of any linearization techniques. For this purpose, the problem of consensus is converted into an optimization problem and is directly solved by the backwards sweep Riccati method to generate the control protocol which results in a non-iterative algorithm. Stability analysis is conducted to provide convergence guarantees of proposed scheme. In addition, an extension to the leader-following consensus of nonlinear multi-agent systems is presented. Several examples are provided to validate and demonstrate the effectiveness of the presented scheme and the corresponding theoretical results.Comment: (submitted and under review in Applied Mathematics and Computation

Adaptive Leader-Following Consensus for a Class of Higher-Order Nonlinear Multi-Agent Systems with Directed Switching Networks

In this paper, we study the leader-following consensus problem for a class of uncertain nonlinear multi-agent systems under jointly connected directed switching networks. The uncertainty includes constant unbounded parameters and external disturbances. We first extend the recent result on the adaptive distributed observer from global asymptotical convergence to global exponential convergence. Then, by integrating the conventional adaptive control technique with the adaptive distributed observer, we present our solution by a distributed adaptive state feedback control law. Our result is illustrated by the leader-following consensus problem for a group of van der Pol oscillators.Comment: 21 pages, 5 figures. In this replacement version, the higher-order case is considered instead of the second-order case. Also, the main difference of this version from the reference [16] is that Appendix B is added to show the existence of the limit of the function V(t) defined in the equation (33) as t tends to infinit

Convergence Analysis using the Edge Laplacian: Robust Consensus of Nonlinear Multi-agent Systems via ISS Method

This study develops an original and innovative matrix representation with respect to the information flow for networked multi-agent system. To begin with, the general concepts of the edge Laplacian of digraph are proposed with its algebraic properties. Benefit from this novel graph-theoretic tool, we can build a bridge between the consensus problem and the edge agreement problem; we also show that the edge Laplacian sheds a new light on solving the leaderless consensus problem. Based on the edge agreement framework, the technical challenges caused by unknown but bounded disturbances and inherently nonlinear dynamics can be well handled. In particular, we design an integrated procedure for a new robust consensus protocol that is based on a blend of algebraic graph theory and the newly developed cyclic-small-gain theorem. Besides, to highlight the intricate relationship between the original graph and cyclic-small-gain theorem, the concept of edge-interconnection graph is introduced for the first time. Finally, simulation results are provided to verify the theoretical analysis.Comment: 22 pages, 10 figures; Submitted to International Journal of Robust and Nonlinear Contro

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

A class of robust consensus algorithms with predefined-time convergence under switching topologies

This paper addresses the robust consensus problem under switching topologies. Contrary to existing methods, the proposed approach provides decentralized protocols that achieve consensus for networked multi-agent systems in a predefined time. Namely, the protocol design provides a tuning parameter that allows setting the convergence time of the agents to a consensus state. An appropriate Lyapunov analysis exposes the capability of the current proposal to achieve predefined-time consensus over switching topologies despite the presence of bounded perturbations. Finally, the paper presents a comparison showing that the suggested approach subsumes existing fixed-time consensus algorithms and provides extra degrees of freedom to obtain predefined-time consensus protocols that are less over-engineered, i.e., the difference between the estimated convergence time and its actual value is lower in our approach. Numerical results are given to illustrate the effectiveness and advantages of the proposed approach.Comment: International Journal of Robust and Nonlinear Control, 201