Distributed model‐independent consensus of Euler–Lagrange agents on directed networks

This paper proposes three different distributed event-triggered control algorithms to achieve leader-follower consensus for a network of Euler-Lagrange agents. We firstly propose two model-independent algorithms for a subclass of Euler-Lagrange agents without the vector of gravitational potential forces. By model-independent, we mean that each agent can execute its algorithm with no knowledge of the agent selfdynamics. A variable-gain algorithm is employed when the sensing graph is undirected; algorithm parameters are selected in a fully distributed manner with much greater flexibility compared to all previous work concerning event-triggered consensus problems. When the sensing graph is directed, a constant-gain algorithm is employed. The control gains must be centrally designed to exceed several lower bounding inequalities which require limited knowledge of bounds on the matrices describing the agent dynamics, bounds on network topology information and bounds on the initial conditions. When the Euler-Lagrange agents have dynamics which include the vector of gravitational potential forces, an adaptive algorithm is proposed which requires more information about the agent dynamics but can estimate uncertain agent parameters.For each algorithm, a trigger function is proposed to govern the event update times. At each event, the controller is updated, which ensures that the control input is piecewise constant and saves energy resources. We analyse each controllers and trigger function and exclude Zeno behaviour. Extensive simulations show 1) the advantages of our proposed trigger function as compared to those in existing literature, and 2) the effectiveness of our proposed controllers.

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“…Since V is bounded, according to (47), both s i andΘ i (t), for all i ∈ {1, ..., n}, are bounded. Now we return to (40) and obtain that…”

Section: A Main Resultsmentioning

confidence: 99%

Event-Triggered Algorithms for Leader–Follower Consensus of Networked Euler–Lagrange Agents

Liu

Qin

et al. 2019

IEEE Trans. Syst. Man Cybern, Syst.

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“…First, one may select β to satisfy (36). Then, µ should be set to satisfy (24). The quantities X and Y discussed in Section III-C are then computed with η 1; we noted below (33) that X and Y are independent of η as η increases.…”

Section: Stability Proofmentioning

confidence: 99%

Leader Tracking of Euler–Lagrange Agents on Directed Switching Networks Using a Model-Independent Algorithm

Anderson

2019

IEEE Trans. Control Netw. Syst.

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In this paper, we propose a discontinuous distributed model-independent algorithm for a directed network of Euler-Lagrange agents to track the trajectory of a leader with nonconstant velocity. We initially study a fixed network and show that the leader tracking objective is achieved semi-globally exponentially fast if the graph contains a directed spanning tree. By model-independent, we mean that each agent executes its algorithm with no knowledge of the parameter values of any agent's dynamics. Certain bounds on the agent dynamics (including any disturbances) and network topology information are used to design the control gain. This fact, combined with the algorithm's model-independence, results in robustness to disturbances and modelling uncertainties. Next, a continuous approximation of the algorithm is proposed, which achieves practical tracking with an adjustable tracking error. Last, we show that the algorithm is stable for networks that switch with an explicitly computable dwell time. Numerical simulations are given to show the algorithm's effectiveness.

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“…In [17]- [25], adaptive controllers are proposed for the parameter uncertainties. Recently, in [26], for Lagrangian systems without gravity, a distributed model-independent algorithm using only relative position and absolute velocity information is proposed to achieve leaderless consensus under a directed graph. Additional requirements on the control gains are needed.…”

Section: Introductionmentioning

confidence: 99%

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

Mei

2020

IEEE Trans. Control Netw. Syst.

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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. where he is currently an Associate Professor. His current research interests include coordination of distributed multi-agent systems and its applications on formation of unmanned vehicles and robots.

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Distributed model‐independent consensus of Euler–Lagrange agents on directed networks

Cited by 24 publications

References 40 publications

Event-Triggered Algorithms for Leader–Follower Consensus of Networked Euler–Lagrange Agents

Event-Triggered Algorithms for Leader–Follower Consensus of Networked Euler–Lagrange Agents

Leader Tracking of Euler–Lagrange Agents on Directed Switching Networks Using a Model-Independent Algorithm

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

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