Brief paper: Finite-time consensus algorithm for multi-agent systems with double-integrator dynamics
TL;DR: This paper discusses the finite-time consensus problem for leaderless and leader-follower multi-agent systems with external disturbances, and proposes continuous distributed control algorithms designed for these agents described by double integrators.
About: This article is published in Automatica.The article was published on 2011-08-01. It has received 816 citations till now. The article focuses on the topics: Double integrator & Consensus.
Citations
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TL;DR: This paper investigates the fixed-time consensus tracking problem for second-order multi-agent systems in networks with directed topology with a proposed framework that eliminates the singularity and the settling time is assignable for any initial conditions.
716 citations
TL;DR: A global nonsingular terminal sliding-mode control strategy for nonlinear systems is developed and it is shown that the proposed control strategy can eliminate the singularity, while guaranteeing the finite-time reachability of the systems to the terminal slide-mode surface.
441 citations
TL;DR: This approach employs a scaling of the state by a function of time that grows unbounded towards the terminal time and is followed by a design of a controller that stabilizes the system in the scaled state representation, yielding regulation in prescribed finite time for the original state.
436 citations
TL;DR: An overview of recent advances in fixed-time cooperative control of multiagent systems is presented and several challenging issues that need to be addressed in the near future are raised.
Abstract: Fixed-time cooperative control is currently a hot research topic in multiagent systems since it can provide a guaranteed settling time, which does not depend on initial conditions. Compared with asymptotic cooperative control algorithms, fixed-time cooperative control algorithms can achieve better closed-loop performance and disturbance rejection properties. Different from finite-time control, fixed-time cooperative control produces the faster rate of convergence and provides an explicit estimation of the settling time independent of initial conditions, which is desirable for multiagent systems. This paper aims at presenting an overview of recent advances in fixed-time cooperative control of multiagent systems. Some fundamental concepts about finite- and fixed-time stability and stabilization are first recalled with insight understanding. Then, recent results in finite- and fixed-time cooperative control are reviewed in detail and categorized according to different agent dynamics. Finally, this paper raises several challenging issues that need to be addressed in the near future.
409 citations
Cites methods from "Brief paper: Finite-time consensus ..."
...From the Lyapunov stability analysis provided in [51], it can be seen that the construction and manipulation of...
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...Based on Lyapunov functions, in [51], a leaderless consensus protocol is constructed for double-integrator networks under undirected and connected topology...
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TL;DR: The discontinuous and continuous super-twisting protocols upon integral sliding mode (ISM) algorithm are respectively developed to achieve finite-time tracking consensus ofMAS with one leader and finite- time containment consensus of MAS with multiple leaders in spite of the disturbances.
344 citations
References
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TL;DR: A distinctive feature of this work is to address consensus problems for networks with directed information flow by establishing a direct connection between the algebraic connectivity of the network and the performance of a linear consensus protocol.
Abstract: In this paper, we discuss consensus problems for networks of dynamic agents with fixed and switching topologies. We analyze three cases: 1) directed networks with fixed topology; 2) directed networks with switching topology; and 3) undirected networks with communication time-delays and fixed topology. We introduce two consensus protocols for networks with and without time-delays and provide a convergence analysis in all three cases. We establish a direct connection between the algebraic connectivity (or Fiedler eigenvalue) of the network and the performance (or negotiation speed) of a linear consensus protocol. This required the generalization of the notion of algebraic connectivity of undirected graphs to digraphs. It turns out that balanced digraphs play a key role in addressing average-consensus problems. We introduce disagreement functions for convergence analysis of consensus protocols. A disagreement function is a Lyapunov function for the disagreement network dynamics. We proposed a simple disagreement function that is a common Lyapunov function for the disagreement dynamics of a directed network with switching topology. A distinctive feature of this work is to address consensus problems for networks with directed information flow. We provide analytical tools that rely on algebraic graph theory, matrix theory, and control theory. Simulations are provided that demonstrate the effectiveness of our theoretical results.
11,658 citations
TL;DR: A theoretical framework for design and analysis of distributed flocking algorithms, and shows that migration of flocks can be performed using a peer-to-peer network of agents, i.e., "flocks need no leaders."
Abstract: In this paper, we present a theoretical framework for design and analysis of distributed flocking algorithms. Two cases of flocking in free-space and presence of multiple obstacles are considered. We present three flocking algorithms: two for free-flocking and one for constrained flocking. A comprehensive analysis of the first two algorithms is provided. We demonstrate the first algorithm embodies all three rules of Reynolds. This is a formal approach to extraction of interaction rules that lead to the emergence of collective behavior. We show that the first algorithm generically leads to regular fragmentation, whereas the second and third algorithms both lead to flocking. A systematic method is provided for construction of cost functions (or collective potentials) for flocking. These collective potentials penalize deviation from a class of lattice-shape objects called /spl alpha/-lattices. We use a multi-species framework for construction of collective potentials that consist of flock-members, or /spl alpha/-agents, and virtual agents associated with /spl alpha/-agents called /spl beta/- and /spl gamma/-agents. We show that migration of flocks can be performed using a peer-to-peer network of agents, i.e., "flocks need no leaders." A "universal" definition of flocking for particle systems with similarities to Lyapunov stability is given. Several simulation results are provided that demonstrate performing 2-D and 3-D flocking, split/rejoin maneuver, and squeezing maneuver for hundreds of agents using the proposed algorithms.
4,693 citations
TL;DR: A Nyquist criterion is proved that uses the eigenvalues of the graph Laplacian matrix to determine the effect of the communication topology on formation stability, and a method for decentralized information exchange between vehicles is proposed.
Abstract: We consider the problem of cooperation among a collection of vehicles performing a shared task using intervehicle communication to coordinate their actions. Tools from algebraic graph theory prove useful in modeling the communication network and relating its topology to formation stability. We prove a Nyquist criterion that uses the eigenvalues of the graph Laplacian matrix to determine the effect of the communication topology on formation stability. We also propose a method for decentralized information exchange between vehicles. This approach realizes a dynamical system that supplies each vehicle with a common reference to be used for cooperative motion. We prove a separation principle that decomposes formation stability into two components: Stability of this is achieved information flow for the given graph and stability of an individual vehicle for the given controller. The information flow can thus be rendered highly robust to changes in the graph, enabling tight formation control despite limitations in intervehicle communication capability.
4,377 citations
TL;DR: It is shown that the regularity properties of the Lyapunov function and those of the settling-time function are related and converse Lyap Unov results can only assure the existence of continuous Lyap unov functions.
Abstract: Finite-time stability is defined for equilibria of continuous but non-Lipschitzian autonomous systems. Continuity, Lipschitz continuity, and Holder continuity of the settling-time function are studied and illustrated with several examples. Lyapunov and converse Lyapunov results involving scalar differential inequalities are given for finite-time stability. It is shown that the regularity properties of the Lyapunov function and those of the settling-time function are related. Consequently, converse Lyapunov results can only assure the existence of continuous Lyapunov functions. Finally, the sensitivity of finite-time-stable systems to perturbations is investigated.
3,894 citations
TL;DR: This work addresses the problem of performing Kalman filtering with intermittent observations by showing the existence of a critical value for the arrival rate of the observations, beyond which a transition to an unbounded state error covariance occurs.
Abstract: Motivated by navigation and tracking applications within sensor networks, we consider the problem of performing Kalman filtering with intermittent observations. When data travel along unreliable communication channels in a large, wireless, multihop sensor network, the effect of communication delays and loss of information in the control loop cannot be neglected. We address this problem starting from the discrete Kalman filtering formulation, and modeling the arrival of the observation as a random process. We study the statistical convergence properties of the estimation error covariance, showing the existence of a critical value for the arrival rate of the observations, beyond which a transition to an unbounded state error covariance occurs. We also give upper and lower bounds on this expected state error covariance.
2,343 citations