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Proceedings ArticleDOI

Distributed Consensus of Euler-Lagrange Systems Under Switching Directed Graphs

27 Jun 2018-pp 56-61
TL;DR: An adaptive distributed control algorithm is presented that solves the leaderless consensus problem without conservative assumptions on the directed and switching interaction between agents and is based on an additional dynamical system that ensures the control objective without the need of relative velocity signals.
Abstract: The consensus problem of Euler-Lagrange networks with parametric uncertainties is addressed in this paper. In particular, we present an adaptive distributed control algorithm that solves the leaderless consensus problem without conservative assumptions on the directed and switching interaction between agents. The proposed algorithm is based on an additional dynamical system that ensures the control objective without the need of relative velocity signals. We further show that the proposed protocol can be extended to take into account the discontinuity of the input torque that results from the switching interaction between agents. Simulation results are given to illustrate the effectiveness of the proposed control schemes.
Citations
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Journal ArticleDOI
TL;DR: It is shown that the proposed consensus protocol achieves consensus without using neighbor's velocity information and accounts for the discontinuity of the input torque that results from the switching interaction between agents.
Abstract: This paper studies the consensus problem of nonidentical Euler–Lagrange systems with parametric uncertainties, under switching directed graphs. We present an adaptive distributed control algorithm that solves this problem in the leaderless scenario, under weak assumptions on the switching interconnection between agents. It is shown that the proposed consensus protocol achieves consensus without using neighbor's velocity information and accounts for the discontinuity of the input torque that results from the switching interaction between agents. Simulation results are given to illustrate the effectiveness of the proposed control schemes.

25 citations


Cites background or methods from "Distributed Consensus of Euler-Lagr..."

  • ...As mentioned in Section I, we presented in [28] a consensus algorithm for Euler–Lagrange systems that ensures a similar result under a switching topology....

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  • ...approach has been exploited in our preliminary result [28] to solve the same problem using a discontinuous input torque for the Euler–...

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  • ...The case of k = 2 was also highlighted in [28] without proof....

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Journal ArticleDOI
TL;DR: In this article, a leaderless consensus problem for multiple Lagrangian systems in the presence of parametric uncertainties and external disturbances under directed graphs is studied, and a robust continuous term with adaptive varying gains is added to alleviate the effects of the external disturbances with unknown bounds.
Abstract: 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. To achieve 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 common control gains. Numerical simulations are performed to show the effectiveness of the proposed algorithms.

21 citations

Posted Content
25 Jul 2019
TL;DR: This paper studies the leaderless consensus problem for multiple Lagrangian systems in the presence of parametric uncertainties and external disturbances under directed graphs, and proposes a model-reference-adaptive-consensus-based algorithm without using neighbors’ velocity information for switching directed graphs.
Abstract: 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.

13 citations


Cites background or methods from "Distributed Consensus of Euler-Lagr..."

  • ...As a result, the novel integral-input-output property of linear time-varying systems is introduced in [24] for the consensus convergence analysis, while the results in [25] and this current paper only need the standard setting of input-output properties of dynamical systems....

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  • ...A common method is to introduce distributed sliding variables [17]–[25], inspired by the classical work of [43], where the control algorithms are firstly designed for the agents such that the agents’ states converge to the designed sliding surfaces....

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  • ...The other concern is the associated topology representing the information interaction among the agents, including undirected graphs [15], [16], directed graphs [17]–[28], and even time-varying graphs [24], [25], [32]....

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  • ...In [17]–[25], adaptive controllers are proposed for the parameter uncertainties....

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  • ...The difference lies in the vanishing term, which is the derivative of the sliding variable in [24], the sliding variable in [25], and the relative tracking error in the current paper....

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Proceedings ArticleDOI
01 Jul 2019
TL;DR: A class of dynamic feedback is proposed by adding differentiators to accommodate the discontinuity and uncertainty resulting from time-varying delay and switching topologies, yielding arbitrary times differentiable reference velocities.
Abstract: In this paper, we mainly focus on developing a new paradigm motivated by investigating the consensus problem of networked Lagrangian systems with unknown time-varying delay and switching topologies. We propose a class of dynamic feedback by adding differentiators to accommodate the discontinuity and uncertainty resulting from time-varying delay and switching topologies, yielding arbitrary times differentiable reference velocities. Using these reference velocities, we develop delay/topology-independent adaptive controllers with arbitrary times differentiable control torques for networked Lagrangian systems. This specific practice motivates the formulation of a new paradigm, referred to as forwardstepping, for handling discontinuity, time-varying uncertainty, and unavailable state measurement in control systems.

7 citations


Cites background or methods from "Distributed Consensus of Euler-Lagr..."

  • ...This generalizes the specific design and analysis in [12], [13] in the context of consensus of multiple Lagrangian systems with switching topologies, which basically introduces a reference velocity whose derivative or high-order derivative exists to realize consensus in the case of switching topologies....

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  • ...considers both the time-varying delay and switching topologies (with or without relative velocity measurement), in contrast with the one in [13] that only handles the case with switching topologies and without relative velocity measurement....

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  • ..., [12], [11], [13]), and we formally propose a new paradigm that is referred to as forwardstepping, which can be considered as a constructive approach....

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  • ...The most attractive feature of the high-order solution, in our opinion, may lie in the design freedom that it provides, beyond the smoother control input as emphasized in [13]....

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  • ...In the context involving only switching topologies, a specific solution in [13] extends the first-order solution in [12] to yield a reference velocity that is arbitrary times differentiable using an arbitrary-order dynamic system without involving relative velocity measurement, by combining the basic framework in [12] with the results for linear integrator systems (see, e....

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Journal ArticleDOI
TL;DR: The paper investigates the weighted containment control problem of Lagrangian systems with cooperative– competitive weighted interactions with cooperative-competitive weighted interactions.
Abstract: The paper investigates the weighted containment control problem of Lagrangian systems with cooperative–competitive weighted interactions. Networked systems consist of multiple leaders and followers...

5 citations


Cites background from "Distributed Consensus of Euler-Lagr..."

  • ...Remark 3.2: An augmented digraph G̃ constructed in this way inherits all the connectivity properties of digraph G (Abdessameud, 2018a)....

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  • ...In fact, following the procedure in Abdessameud (2018a, 2018b) and K. Liu et al. (2016), we can construct a digraph G̃ = (Ṽ , Ẽ , Ã, ̃) as: Ṽ = V ∪ V ′, where V ′ = {1′, 2′, . . . ,N′} is associated with the vector z̄....

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References
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BookDOI
01 Jan 2008
TL;DR: In this article, the authors present a survey of the use of consensus algorithms in multi-vehicle cooperative control, including single-and double-integrator dynamical systems, rigid-body attitude dynamics, rendezvous and axial alignment, formation control, deep-space formation flying, fire monitoring and surveillance.
Abstract: The coordinated use of autonomous vehicles has an abundance of potential applications from the domestic to the hazardously toxic. Frequently the communications necessary for the productive interplay of such vehicles may be subject to limitations in range, bandwidth, noise and other causes of unreliability. Information consensus guarantees that vehicles sharing information over a network topology have a consistent view of information critical to the coordination task. Assuming only neighbor-neighbor interaction between vehicles, Distributed Consensus in Multi-vehicle Cooperative Control develops distributed consensus strategies designed to ensure that the information states of all vehicles in a network converge to a common value. This approach strengthens the team, minimizing power consumption and the deleterious effects of range and other restrictions. The monograph is divided into six parts covering introductory, theoretical and experimental material and featuring: an overview of the use of consensus algorithms in cooperative control; consensus algorithms in single- and double-integrator dynamical systems; consensus algorithms for rigid-body attitude dynamics; rendezvous and axial alignment, formation control, deep-space formation flying, fire monitoring and surveillance. Notation drawn from graph and matrix theory and background material on linear and nonlinear system theory are enumerated in six appendices. The authors maintain a website at which can be found a sample simulation and experimental video material associated with experiments in several chapters of this book. Academic control systems researchers and their counterparts in government laboratories and robotics- and aerospace-related industries will find the ideas presented in Distributed Consensus in Multi-vehicle Cooperative Control of great interest. This text will also serve as a valuable support and reference for graduate courses in robotics, and linear and nonlinear control systems.

2,720 citations

Book
26 Oct 2007
TL;DR: Academic control systems researchers and their counterparts in government laboratories and robotics- and aerospace-related industries will find the ideas presented in Distributed Consensus in Multi-vehicle Cooperative Control of great interest.
Abstract: The coordinated use of autonomous vehicles has an abundance of potential applications from the domestic to the hazardously toxic. Frequently the communications necessary for the productive interplay of such vehicles may be subject to limitations in range, bandwidth, noise and other causes of unreliability. Information consensus guarantees that vehicles sharing information over a network topology have a consistent view of information critical to the coordination task. Assuming only neighbor-neighbor interaction between vehicles, Distributed Consensus in Multi-vehicle Cooperative Control develops distributed consensus strategies designed to ensure that the information states of all vehicles in a network converge to a common value. This approach strengthens the team, minimizing power consumption and the deleterious effects of range and other restrictions. The monograph is divided into six parts covering introductory, theoretical and experimental material and featuring: an overview of the use of consensus algorithms in cooperative control; consensus algorithms in single- and double-integrator dynamical systems; consensus algorithms for rigid-body attitude dynamics; rendezvous and axial alignment, formation control, deep-space formation flying, fire monitoring and surveillance. Notation drawn from graph and matrix theory and background material on linear and nonlinear system theory are enumerated in six appendices. The authors maintain a website at which can be found a sample simulation and experimental video material associated with experiments in several chapters of this book. Academic control systems researchers and their counterparts in government laboratories and robotics- and aerospace-related industries will find the ideas presented in Distributed Consensus in Multi-vehicle Cooperative Control of great interest. This text will also serve as a valuable support and reference for graduate courses in robotics, and linear and nonlinear control systems.

755 citations

Journal ArticleDOI
TL;DR: A distributed adaptive control algorithm combined with distributed sliding-mode estimators is proposed 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.

518 citations

Journal ArticleDOI
TL;DR: This work studies global exponential synchronization and concurrent synchronization in the context of Lagrangian systems control and proposes a decentralized tracking control law that globally exponentially synchronizes an arbitrary number of robots.
Abstract: Concurrent synchronization is a regime where diverse groups of fully synchronized dynamic systems stably coexist. We study global exponential synchronization and concurrent synchronization in the context of Lagrangian systems control. In a network constructed by adding diffusive couplings to robot manipulators or mobile robots, a decentralized tracking control law globally exponentially synchronizes an arbitrary number of robots, and represents a generalization of the average consensus problem. Exact nonlinear stability guarantees and synchronization conditions are derived by contraction analysis. The proposed decentralized strategy is further extended to adaptive synchronization and partial-state coupling.

488 citations


"Distributed Consensus of Euler-Lagr..." refers background in this paper

  • ...For example, the authors in [1]–[3] studied the leaderless consensus problem for EulerLagrange systems under undirected graphs, and the case of directed graphs has been studied in [4]....

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Posted Content
TL;DR: In this article, a decentralized tracking control law globally exponentially synchronizes an arbitrary number of robots, and represents a generalization of the average consensus problem, and exact nonlinear stability guarantees and synchronization conditions are derived by contraction analysis.
Abstract: Concurrent synchronization is a regime where diverse groups of fully synchronized dynamic systems stably coexist. We study global exponential synchronization and concurrent synchronization in the context of Lagrangian systems control. In a network constructed by adding diffusive couplings to robot manipulators or mobile robots, a decentralized tracking control law globally exponentially synchronizes an arbitrary number of robots, and represents a generalization of the average consensus problem. Exact nonlinear stability guarantees and synchronization conditions are derived by contraction analysis. The proposed decentralized strategy is further extended to adaptive synchronization and partial-state coupling.

475 citations