Consensus of Multiagent Systems With Distance-Dependent Communication Networks

Jing, Gangshan; Zheng, Yufan; Wang, Long

doi:10.1109/tnnls.2016.2598355

Cited by 69 publications

(37 citation statements)

References 37 publications

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“…1(b), the resulting framework is non-rigid. Nevertheless, the geometric shape can still be uniquely determined up to rigid transformations by ||e 12 ||, ||e 13 || and e T 12 e 13 . This is due to the fact that ||e 23 || 2 = || − e 12 + e 13 || 2 = ||e 12 || 2 + ||e 13 || 2 − 2e T 12 e 13 .…”

Section: Center Manifold Theorymentioning

confidence: 99%

“…Let δ(p) = (· · · , δ (i,j,k) , · · · ) T = r G f (p) − r G f (p * ), then V (p) = 1 2 ||δ(p)|| 2 . By the chain rule, the dynamic equation of multi-agent system (9) with control law (11) can be written in the following compact form (13)…”

Section: Control Objectivementioning

confidence: 99%

“…Let z = (p T ,z T ) T = Qp, wherez ∈ R nd−d , Q ∈ R nd×nd is an orthogonal matrix with its first d rows being 1 n 1 T n ⊗I d . Using the centroid invariance property, i.e.,ṗ = 0, shown in Lemma 4.2,(13) can also be equivalently transformed into a reduced-order systemż =f (z) with a compact manifold of equilibriaĒ . Since the target formation E = r −1 K (r K (p * )) has been shown to be a d(d+1)/2−dimensional manifold in the proof of Theorem 3.14,Ē is a d(d − 1)/2−dimensional manifold characterized by rotations around the centroidp(0).…”

Section: Stability Analysismentioning

confidence: 99%

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Weak Rigidity Theory and Its Application to Formation Stabilization

Jing¹,

Lee²,

Wang

2018

SIAM J. Control Optim.

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This paper introduces the notion of weak rigidity to characterize a framework by pairwise inner products of inter-agent displacements. Compared to distance-based rigidity, weak rigidity requires fewer constrained edges in the graph to determine a geometric shape in an arbitrarily dimensional space. A necessary and sufficient graphical condition for infinitesimal weak rigidity of planar frameworks is derived. As an application of the proposed weak rigidity theory, a gradient based control law and a non-gradient based control law are designed for a group of single-integrator modeled agents to stabilize a desired formation shape, respectively. Using the gradient control law, we prove that an infinitesimally weakly rigid formation is locally exponentially stable. In particular, if the number of agents is one greater than the dimension of the space, a minimally infinitesimally weakly rigid formation is almost globally asymptotically stable. In the literature of rigid formation, the sensing graph is always required to be rigid. Using the non-gradient control law based on weak rigidity theory, the sensing graph is unnecessary to be rigid for local exponential stability of the formation. A numerical simulation is performed for illustrating effectiveness of our main results.

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Section: Center Manifold Theorymentioning

confidence: 99%

Section: Control Objectivementioning

confidence: 99%

Section: Stability Analysismentioning

confidence: 99%

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Weak Rigidity Theory and Its Application to Formation Stabilization

Jing¹,

Lee²,

Wang

2018

SIAM J. Control Optim.

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“…Email addresses: nameisjing@gmail.com (Gangshan Jing), Guofeng.Zhang@polyu.edu.hk (Guofeng Zhang), Joseph.Lee@polyu.edu.hk (Heung Wing Joseph Lee), longwang@pku.edu.cn (Long Wang ). change and improvement of robustness of the control strategy, a displacement-constrained formation method, which determines the target formation shape by relative positions between agents, has been extensively studied [12,25,32,8,15]. This method is also called consensusbased formation since the formation problem can often be transformed into a consensus problem, which is a hot topic being widely studied [24,31,30,15].…”

Section: Introductionmentioning

confidence: 99%

Angle-based shape determination theory of planar graphs with application to formation stabilization

et al. 2019

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This paper presents an angle-based approach for distributed formation shape stabilization of multi-agent systems in the plane. We develop an angle rigidity theory to study whether a planar framework can be determined by angles between segments uniquely up to translations, rotations, scalings and reflections. The proposed angle rigidity theory is applied to the formation stabilization problem, where multiple single-integrator modeled agents cooperatively achieve an angle-constrained formation. During the formation process, the global coordinate system is unknown for each agent and wireless communications between agents are not required. Moreover, by utilizing the advantage of high degrees of freedom, we propose a distributed control law for agents to stabilize a target formation shape with desired orientation and scale. Simulation examples are performed for illustrating effectiveness of the proposed control strategies.

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“…Distributed coordination control of multi-agent systems (MASs) has been intensively investigated in various areas including engineering, natural science, and social science [1]- [3]. As a fundamental coordination problem, the consensus which requires that a group of autonomous agents achieve a common state has attracted much attention, see [4]- [11]. This is due to its Comparing with computing the intersection and solving linear equations, a more general problem is solving CFPs, which usually needs to solve linear equations and convex inequalities simultaneously, and ensure the solution to be in the intersection of some simple convex sets.…”

Section: Introductionmentioning

confidence: 99%

Distributed algorithms for solving the convex feasibility problems

Jing

Wang

2020

Sci. China Inf. Sci.

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In this paper, a class of convex feasibility problems (CFPs) are studied for multi-agent systems through local interactions. The objective is to search a feasible solution to the convex inequalities with some set constraints in a distributed manner. The distributed control algorithms, involving subgradient and projection, are proposed for both continuous-and discrete-time systems, respectively. Conditions associated with connectivity of the directed communication graph are given to ensure convergence of the algorithms. It is shown that under mild conditions, the states of all agents reach consensus asymptotically and the consensus state is located in the solution set of the CFP. Simulation examples are presented to demonstrate the effectiveness of the theoretical results. DRAFT 2 wide applications in distributed control and estimation [12], distributed optimization [13]-[15] and distributed methods for solving linear equations [16], [17]. Researches on consensus can be roughly categorized depending on whether the agents have continuous-or discrete-time dynamics. Noticeable works focusing on the multi-agent systems include [6], [9], [18], [19] for the continuous-time case and [5], [19]-[21] for the discrete-time case. In the aforementioned works, the agents interact with each other through a network and each agent adjusts its own state by using only local information from its neighbors. Within this framework, connectivity of the communication graph plays a key role in achieving consensus, and consequently several conditions of the connectivity have been established. For example, the communication graph must have a spanning tree when the topology is fixed [6], while the union of the communication graphs should have a spanning tree frequently enough as the system evolves when the topology is switching [9], [21]. In addition, infinitely-joint connectedness, i.e., the infinitely occurring communication graphs are jointly connected, is necessary to make the agents reach consensus when the topology is time-varying [18], [19].In recent years, the constrained consensus problem that seeks to reach state agreement in the intersection of a number of convex sets has been widely investigated. In [22], a projection-based consensus algorithm was proposed when the communication graph is balanced. This algorithm with time delays was studied in [24], where the union of the communication graphs within a period was assumed to be strongly connected. The problem was extended to the continuous-time case in [25], where each set serves as an optimal solution set of a local objective function, and the global optimal solution is achieved as long as the intersection of the constrained sets is computed. By taking the advantages of the property that the solution set of linear equations is an affine set, the projection-based consensus algorithm in [25] was successfully applied to solving linear equations in [26], where the projection operator in [25] was replaced with a special affine projection operator. Unlike the distributed algorithm for so...

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Consensus of Multiagent Systems With Distance-Dependent Communication Networks

Cited by 69 publications

References 37 publications

Weak Rigidity Theory and Its Application to Formation Stabilization

Weak Rigidity Theory and Its Application to Formation Stabilization

Angle-based shape determination theory of planar graphs with application to formation stabilization

Distributed algorithms for solving the convex feasibility problems

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