Distributed average tracking for multiple signals generated by linear dynamical systems: An edge-based framework

Zhao, Yu; Liu, Yongfang; Li, Zhongkui; Duan, Zhisheng

doi:10.1016/j.automatica.2016.09.005

Cited by 144 publications

(45 citation statements)

References 34 publications

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“…The containment errors are bounded and the error variables in satisfy the requirement of error constraints.Remark For algorithms and , sign function is used to ensure that the related variables could reach the sliding surface in finite time. In order to eliminate the chattering phenomenon that the discontinuous functions may introduce, inspired by the works of Zhao et al and Zhao et al, we can use the following function h i (·) to replace sign function for follower i so that the chattering phenomenon can be avoided:

h_{i} ((),, ω, t_{i}) = \frac{ω}{true‖ ω true‖ + ϵ e^{- η t_{i}}},

where

\frac{normald t_{i}}{normald t} = 1 + \sum_{j \in ν_{F}} a_{ij} {sig}^{\frac{1}{2}} ((), t_{i} - t_{j})

is a finite‐time clock synchronization device, ϵ and η are positive constants, and t i is a local time of the local clock in the follower i . The related theoretical analysis can refer to the works of Zhao et alRemark This study achieves distributed finite‐time containment control for multiple EL systems with communication delays.…”

Section: Distributed Finite‐time Error Constrained Containment Contromentioning

confidence: 99%

“…For algorithms (14) and (44), sign function is used to ensure that the related variables could reach the sliding surface in finite time. In order to eliminate the chattering phenomenon that the discontinuous functions may introduce, inspired by the works of Zhao et al 52 and Zhao et al, 53 we can use the following function h i (·) to replace sign function for follower i so that the chattering phenomenon can be avoided:…”

Section: Theorem 2 For Multiple El Systems (1) With Model Uncertaintmentioning

confidence: 99%

“…is a finite-time clock synchronization device, and are positive constants, and t i is a local time of the local clock in the follower i. The related theoretical analysis can refer to the works of Zhao et al 52,53 Remark 8. This study achieves distributed finite-time containment control for multiple EL systems with communication delays.…”

Section: Theorem 2 For Multiple El Systems (1) With Model Uncertaintmentioning

confidence: 99%

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Distributed finite‐time containment control for multiple Euler‐Lagrange systems with communication delays

Chen

Sun

et al. 2018

Intl J Robust & Nonlinear

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Summary In this paper, distributed finite‐time containment control for multiple Euler‐Lagrange systems with communication delays and general disturbances is investigated under directed topology by using sliding‐mode control technique. We consider that the information of dynamic leaders can be obtained by only a portion of the followers. Firstly, a nonsingular fast terminal sliding surface is selected to achieve the finite‐time convergence for the error variables. Then, a distributed finite‐time containment control algorithm is proposed where the neural network is utilized to approximate the model uncertainties and external disturbances of the systems. Furthermore, considering that error constraint method can improve the performance of the systems, a distributed finite‐time containment control algorithm is developed by transforming the error variable into another form. It is demonstrated that the containment errors are bounded in finite time by using Lyapunov theory, graph theory, and finite‐time stability theory. Numerical simulations are provided to show the effectiveness of the proposed methods.

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h_{i} ((),, ω, t_{i}) = \frac{ω}{true‖ ω true‖ + ϵ e^{- η t_{i}}},

where

\frac{normald t_{i}}{normald t} = 1 + \sum_{j \in ν_{F}} a_{ij} {sig}^{\frac{1}{2}} ((), t_{i} - t_{j})

Section: Distributed Finite‐time Error Constrained Containment Contromentioning

confidence: 99%

Section: Theorem 2 For Multiple El Systems (1) With Model Uncertaintmentioning

confidence: 99%

Section: Theorem 2 For Multiple El Systems (1) With Model Uncertaintmentioning

confidence: 99%

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Distributed finite‐time containment control for multiple Euler‐Lagrange systems with communication delays

Chen

Sun

et al. 2018

Intl J Robust & Nonlinear

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“…Numerous multi-agent coordination and cooperation problems have been the subject of considerable attention from researchers over the past several years: aggregation, consensus, formation, social foraging, synchronization, containment, distributed averaging/optimization, etc. [11,[18][19][20]22,29,34,39,40]. In this paper, we are primarily concerned with the formation problem, which regards the situation where a desired geometric shape in space is assumed and maintained by a team of agents.…”

Section: Introductionmentioning

confidence: 99%

3D Multi‐Agent Formation Control with Rigid Body Maneuvers

Zhang

Queiroz

2018

Asian Journal of Control

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In this paper, we propose a control scheme for the formation maneuvering problem of multi-agent systems where the team of agents can translate and rotate as a virtual rigid body in 3D. Using the single-integrator model, we formulate the basic control law which is comprised of a formation acquisition term, function of the graph rigidity matrix, and a rigid body maneuvering term. The control is dependent on the relative position of agents that are connected in an infinitesimally and minimally rigid framework in addition to the desired rigid body motion of the formation. To facilitate the design of the rigid body maneuver, one agent in the convex hull of the formation serves as the reference point for the rotation component. A simulation study demonstrates the formation controller.

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“…According to the number of leaders in the network, existing explorations about the consensus problem are classified into three subareas, i.e., leaderless consensus without leaders, consensus tracking with a single leader, and containment control with multiple leaders. For leaderless consensus, control strategies are proposed for first-order [5], second-order [6], fractional-order [7], linear [8,9] multi-agent systems, and for synchronization [10]. For consensus tracking, the aim is to drive the states of followers to reach the state of the leader.…”

Section: Introductionmentioning

confidence: 99%

Distributed Fixed‐Time Coordinated Tracking for Nonlinear Multi‐Agent Systems Under Directed Graphs

Ning

Jin

Zheng

2017

Asian Journal of Control

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This paper is concerned with the fixed‐time coordinated tracking problem for a class of nonlinear multi‐agent systems under detail‐balanced directed communication graphs. Different from conventional finite‐time coordinated tracking strategies, the fixed‐time approach developed in this paper guarantees that a settling time bound is prescribed without dependence on initial states of agents. First, for the case of a single leader, a distributed protocol based on fixed‐time stability techniques is proposed for each follower to accomplish the consensus tracking in a fixed time. Second, in the presence of multiple leaders, a new distributed protocol is proposed such that states of followers converge to the dynamic convex hull spanned by those of leaders in a fixed time. In addition, for a class of linear multi‐agent systems, sufficient conditions that guarantee the fixed‐time coordinated tracking are provided. Finally, numerical simulations are given to demonstrate the effectiveness of the theoretical results.

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Distributed average tracking for multiple signals generated by linear dynamical systems: An edge-based framework

Cited by 144 publications

References 34 publications

Distributed finite‐time containment control for multiple Euler‐Lagrange systems with communication delays

Distributed finite‐time containment control for multiple Euler‐Lagrange systems with communication delays

3D Multi‐Agent Formation Control with Rigid Body Maneuvers

Distributed Fixed‐Time Coordinated Tracking for Nonlinear Multi‐Agent Systems Under Directed Graphs

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