Eigenstructure assignment with application to consensus of linear heterogeneous agents

Wu, Andy; Iwasaki, Tetsuya

doi:10.1109/cdc.2015.7402511

Cited by 3 publications

(4 citation statements)

References 18 publications

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“…An earlier version of our result, assigning a single pair of eigenvalue/eigenvector, appeared in [29] without proof. This paper generalizes the result in [29] to include the assignment of an arbitrary number of eigenvalues/eigenvectors and extends the multi-agent result to reflect the added complexity.…”

Section: Introductionmentioning

confidence: 92%

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Pattern Formation Via Eigenstructure Assignment: General Theory and Multi-Agent Application

Iwasaki

2018

IEEE Trans. Automat. Contr.

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Complex dynamical systems often exhibit formation of a pattern in observed variables in the steady state. An important special case is when the system consists of multiple subsystems (or "agents") subjected to local interactions to reach consensus or an arbitrary pattern specified by their relative positioning in the state space. This paper formulates a general pattern formation problem as the design of a feedback controller such that selected outputs of a linear plant exponentially converge to Re Λt ρo for some vector ρo, with prescribed matrices R and Λ. We show that the problem reduces equivalently to an eigenstructure assignment problem, and provide a necessary and sufficient condition for existence of a feasible controller as well as a parameterization of all such controllers. This general theory is further specialized to give a complete solution to a heterogeneous multi-agent synchronization problem. Two numerical examples are provided to demonstrate the efficacy of the proposed design method: one illustrates the importance of adaptive pattern formation through sensory feedback and another suggests an extension for achieving stable limit cycles by additional nonlinearities.

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Section: Introductionmentioning

confidence: 92%

“…We show (i) first. Let the controller in Theorem 5 be described by (29) and u k =K kxk , whereK k contains (30) and (31). Suppose C k = I and define e k =x k − x k .…”

Section: Structured Eigenstructure Assignment For Multi-agent Sysmentioning

confidence: 99%

Pattern Formation Via Eigenstructure Assignment: General Theory and Multi-Agent Application

Iwasaki

2018

IEEE Trans. Automat. Contr.

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“…(i) For each group k ∈ [1, l] and its dynamics (22), compute F k by (5) such that A k + B k F k has a simple eigenvalue 0 with the corresponding eigenvector g k , and other eigenvalues have negative real parts; moreover the topology defined by F k has a unique root node y k1 (e.g. star or line by the method given in Section III.A).…”

Section: Hierarchical Eigenstructure Assignmentmentioning

confidence: 99%

“…We note that [22] also proposed an eigenstructure assignment method and applied it to the multi-agent consensus problem. Their approach is bottom-up: first a communication topology is imposed among the agents, then local control strategies are designed based on eigenstructure assignment respecting the topology, and finally the correctness of the proposed strategies is verified at the global level.…”

Section: Introductionmentioning

confidence: 99%

Top-down synthesis of multi-agent formation control: An eigenstructure assignment based approach

Motoyama

Cai

2017

2017 American Control Conference (ACC)

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We propose a top-down approach for formation control of heterogeneous multi-agent systems, based on the method of eigenstructure assignment. Given the problem of achieving scalable formations on the plane, our approach globally computes a state feedback control that assigns desired closed-loop eigenvalues/eigenvectors. We characterize the relation between the eigenvalues/eigenvectors and the resulting inter-agent communication topology, and design special (sparse) topologies such that the synthesized control may be implemented locally by the individual agents. Moreover, we present a hierarchical synthesis procedure that significantly improves computational efficiency. Finally, we extend the proposed approach to achieve rigid formation and circular motion, and illustrate these results by simulation examples.

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Top-Down Synthesis of Multiagent Formation Control: An Eigenstructure Assignment Based Approach

Motoyama

Cai

2019

IEEE Trans. Control Netw. Syst.

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Eigenstructure assignment with application to consensus of linear heterogeneous agents

Cited by 3 publications

References 18 publications

Pattern Formation Via Eigenstructure Assignment: General Theory and Multi-Agent Application

Pattern Formation Via Eigenstructure Assignment: General Theory and Multi-Agent Application

Top-down synthesis of multi-agent formation control: An eigenstructure assignment based approach

Top-Down Synthesis of Multiagent Formation Control: An Eigenstructure Assignment Based Approach

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