Distributed robust leaderless consensus of Lipschitz nonlinear multi-agent systems with matching uncertainties
14 Jul 2014-pp 858-863
TL;DR: In this article, the authors considered the distributed robust consensus problem of multi-agent systems with Lipschitz nonlinear dynamics and subject to different matching uncertainties, and designed distributed continuous static and adaptive consensus protocols under which the consensus error is uniformly ultimately bounded and exponentially converges to a small adjustable residual set.
Abstract: This paper considers the distributed robust consensus problem of multi-agent systems with Lipschitz nonlinear dynamics and subject to different matching uncertainties. Due to the existence of nonidentical uncertainties, the multi-agent systems discussed in this paper are essentially heterogeneous. For the case where the communication graph is undirected and connected, based on the local state information of neighboring agents, distributed continuous static and adaptive consensus protocols are designed, under which the consensus error is uniformly ultimately bounded and exponentially converges to a small adjustable residual set.
Citations
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TL;DR: A consensus protocol for high-order multiagent systems with general linear models is proposed, introducing a common Lyapunov candidate for the set of switching topologies and based on the Cauchy convergence criterion, which guarantees achieving consensus in networks of agents with jointly connected topologies.
Abstract: The leaderless consensus problem in a class of high-order multiagent systems with Lipschitz nonlinearities is studied in this paper. Despite existing leaderless consensus protocols devoted to high-order multiagent systems with Lipschitz nonlinearities, the proposed protocol in this paper guarantees achieving consensus in networks of agents with jointly connected topologies. To achieve this goal, first a consensus protocol for high-order multiagent systems with general linear models is proposed. By introducing a common Lyapunov candidate for the set of switching topologies and based on the Cauchy convergence criterion, achieving consensus under the proposed protocol is studied. Then, sufficient conditions are derived under which the results are extended to the case of Lipschitz nonlinearities in agents models. Numerical examples validate the proposed consensus protocol.
60 citations
Cites background from "Distributed robust leaderless conse..."
...In [30], achieving consensus in networks of agents with nonlinear matching uncertainties was addressed....
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01 Jun 2019
TL;DR: It is proven that the boundedness of all closed-loop signals and the practical consensus for all the subsystems are ensured and the adaptive control approach based on backstepping technique is proposed.
Abstract: In this paper, we investigate the leaderless consensus problem for MAS consisting of second-order nonlinear subsystems with a class of unknown parameters. The communication topology among subsystems is directed and fixed. An adaptive control approach based on backstepping technique is proposed. The estimations of the unknown parameters of the neighbors' systems are no longer required in constructing the local adaptive controller. Moreover, the additional local estimates to compensate for the uncertainties involved in its neighbors as well as extra transmissions of online parameter estimates required among linked subsystems can be avoided. It is proven that the boundedness of all closed-loop signals and the practical consensus for all the subsystems are ensured. Simulation results show the effectiveness of the proposed control scheme.
2 citations
01 Aug 2019
TL;DR: This paper investigates leaderless consensus problem for multi-agent systems consisting of second-order nonlinear subsystems with a class of uncertainties and designs adaptive output feedback distributed nonlinear controllers to guarantee that the consensus errors converge to a small neighborhood around the origin.
Abstract: In this paper, we investigate leaderless consensus problem for multi-agent systems consisting of second-order nonlinear subsystems with a class of uncertainties. The communication topology among subsystems is directed and fixed. In the system, only the output signals of the subsystems can be measured. First, a linear observer is designed to estimate the unmeasured states. Then, by the backstepping method, adaptive output feedback distributed nonlinear controllers are designed. Consequently, the designed controllers guarantee that the consensus errors converge to a small neighborhood around the origin and all the signals in the closed-loop dynamics are uniformly ultimately bounded, while the additional local estimates for the uncertainties involved in the neighbors can be avoided as well as extra transmissions of online parameter estimates required among linked subsystems. Simulation results show the effectiveness of the proposed control scheme.
01 Jan 2023
TL;DR: In this article , the dynamic saturation reconstruction approach was explored to deal with the robust coordinated tracking of saturated multi-agent systems, and the adaptive control input that restrict and influence each other can achieve consensus tracking, and resolve the contradiction between high performance and saturation limits.
Abstract: This paper explores the dynamic saturation reconstruction approach to deal with the robust coordinated tracking of saturated multi-agent systems. The first-order differential equation of the dynamic saturation function is constructed and given in quadratic form with the unrestricted control input affected by bounded input disturbance. It is shown that the dynamic saturation reconstruction function and the adaptive control input that restrict and influence each other can achieve consensus tracking, and resolve the contradiction between high performance and saturation limits. Finally, simulation results show that the actual engineering situation can be perfect by adjusting the coefficients of dynamic saturation function.
08 May 2018
TL;DR: Two consensus protocols are proposed based on a future state predictor and a finite time estimator that ensure achieving consensus in a group of agents in the presence of input delay and external disturbances in Lipschitz multiagent systems.
Abstract: This paper investigates the consensus problem in Lipschitz multiagent systems in the presence of input delay and external disturbances. For this purpose, two consensus protocols are proposed based on a future state predictor and a finite time estimator that ensure achieving consensus in a group of agents in the presence of input delay and external disturbances. Finally, the effectiveness of the suggested algorithms is demonstrated by simulation results.
Cites background or methods from "Distributed robust leaderless conse..."
...In [19], consensus problem has been studied for LMSs subject to external disturbances....
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...Furthermore, the proposed algorithms in [17-19] has been designed based on a complicated method and cannot be used for other types of multiagent systems....
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...There are few CPs which have solved the consensus problem of LMSs with external disturbances and input delay [16-20]....
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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
"Distributed robust leaderless conse..." refers background in this paper
...Since the two pioneering works [1] and [2], the consensus problem has been extensively studied by many researchers from different perspectives; see [3, 4, 5, 6, 7] and references therein....
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TL;DR: A theoretical explanation for the observed behavior of the Vicsek model, which proves to be a graphic example of a switched linear system which is stable, but for which there does not exist a common quadratic Lyapunov function.
Abstract: In a recent Physical Review Letters article, Vicsek et al. propose a simple but compelling discrete-time model of n autonomous agents (i.e., points or particles) all moving in the plane with the same speed but with different headings. Each agent's heading is updated using a local rule based on the average of its own heading plus the headings of its "neighbors." In their paper, Vicsek et al. provide simulation results which demonstrate that the nearest neighbor rule they are studying can cause all agents to eventually move in the same direction despite the absence of centralized coordination and despite the fact that each agent's set of nearest neighbors change with time as the system evolves. This paper provides a theoretical explanation for this observed behavior. In addition, convergence results are derived for several other similarly inspired models. The Vicsek model proves to be a graphic example of a switched linear system which is stable, but for which there does not exist a common quadratic Lyapunov function.
8,233 citations
"Distributed robust leaderless conse..." refers background in this paper
...Since the two pioneering works [1] and [2], the consensus problem has been extensively studied by many researchers from different perspectives; see [3, 4, 5, 6, 7] and references therein....
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TL;DR: It is shown that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves.
Abstract: This note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies. Both discrete and continuous update schemes are proposed for information consensus. This note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves.
6,135 citations
TL;DR: Theoretical results regarding consensus-seeking under both time invariant and dynamically changing communication topologies are summarized in this paper, where several specific applications of consensus algorithms to multivehicle coordination are described.
Abstract: The purpose of this article is to provide a tutorial overview of information consensus in multivehicle cooperative control. Theoretical results regarding consensus-seeking under both time invariant and dynamically changing communication topologies are summarized. Several specific applications of consensus algorithms to multivehicle coordination are described
3,028 citations
"Distributed robust leaderless conse..." refers background in this paper
...Since the two pioneering works [1] and [2], the consensus problem has been extensively studied by many researchers from different perspectives; see [3, 4, 5, 6, 7] and references therein....
[...]
TL;DR: In this article, a distributed observer-type consensus protocol based on relative output measurements is proposed to solve the consensus problem of multi-agent systems with a time-invariant communication topology consisting of general linear node dynamics.
Abstract: This paper addresses the consensus problem of multiagent systems with a time-invariant communication topology consisting of general linear node dynamics. A distributed observer-type consensus protocol based on relative output measurements is proposed. A new framework is introduced to address in a unified way the consensus of multiagent systems and the synchronization of complex networks. Under this framework, the consensus of multiagent systems with a communication topology having a spanning tree can be cast into the stability of a set of matrices of the same low dimension. The notion of consensus region is then introduced and analyzed. It is shown that there exists an observer-type protocol solving the consensus problem and meanwhile yielding an unbounded consensus region if and only if each agent is both stabilizable and detectable. A multistep consensus protocol design procedure is further presented. The consensus with respect to a time-varying state and the robustness of the consensus protocol to external disturbances are finally discussed. The effectiveness of the theoretical results is demonstrated through numerical simulations, with an application to low-Earth-orbit satellite formation flying.
2,096 citations