Geometric Control of Patterned Linear Systems

Hamilton, Sarah C.; Broucke, Mireille E.

doi:10.1007/978-3-642-28804-3

Cited by 15 publications

(7 citation statements)

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“…This is not the first attempt to introduce a hierarchy to network structures for multi-agent systems. For example, Smith et al [6] proposed a hierarchical cyclic pursuit scheme and Hamilton and Broucke [7,8] introduced a framework named patterned linear system which is capable of dealing with a class of hierarchy. This paper is related to [6], where agents, which are modeled as the integrator, are divided into some groups and the hierarchy means that cyclic pursuit is achieved both on a micro and a macro levels.…”

Section: Introductionmentioning

confidence: 99%

Eigenvector-based intergroup connection of low rank for hierarchical multi-agent dynamical systems

Tsubakino

Hara

2012

Systems & Control Letters

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This paper proposes an eigenvector-based method for analysis and design of hierarchical networks for multi-agent systems. We first define the concept of eigen-connection by characterizing low rank information flow between layers based on the eigenvector of lower level interconnection structures. It is shown that the resulting intergroup interconnections affect only a few eigenvalues of interconnection structures in the lower layer, and we derive explicit expressions for shifted eigenvalues. Then a procedure for designing hierarchical networks that result in desirable eigenvalue distributions is proposed, where the eigen-connection is used for a key to move undesirable eigenvalues selectively. The effectiveness of the procedure is demonstrated by a numerical example.

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Section: Introductionmentioning

confidence: 99%

Eigenvector-based intergroup connection of low rank for hierarchical multi-agent dynamical systems

Tsubakino

Hara

2012

Systems & Control Letters

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“…More recently, [8] discussed the properties of fault tolerance of symmetric systems. Other relevant works are those related to patterned systems ( [11]) and block circulant systems ( [12]). …”

Section: A G Equivariant Controlled Linear Systemsmentioning

confidence: 99%

On the distributed stabilization and consensus of symmetrically interconnected agents

Consolini

Tosques

2015

2015 European Control Conference (ECC)

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One general principle of the theory of symmetric linear system is that a control problem can be solved by means of a generic controller if and only if it can be solved with a controller that preserves the symmetry properties of the system. In this paper, we specialize this general principle to the case of the distributed control of interconnected systems. Namely, we show that this class of systems admits a decentralized output feedback stabilizer if and only if it admits a controller of the same type that respects the symmetry of the graph automorphism group. We also show that a similar result holds for the consensus problem.

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“…More recently, [8] discussed the properties of fault tolerance of symmetric systems. Other relevant works are those related to patterned systems ( [9]) and block circulant systems ( [10]). …”

Section: Introductionmentioning

confidence: 99%

Static output feedback of equivariant linear systems with applications to the control of interconnected agents

Consolini

Tosques

2014

53rd IEEE Conference on Decision and Control

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We focus on controlled linear systems which are invariant with respect to a set of linear transformations associated to a general multiplicative finite group G. We investigate their control theoretical properties of stability, stabilizability, detectability and output feedback stabilizability. We apply the obtained results to systems obtained by the interconnection of identical subsystems, exploiting their invariance with respect to the group of the automorphisms of the connection graph.

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Geometric Control of Patterned Linear Systems

Cited by 15 publications

References 0 publications

Eigenvector-based intergroup connection of low rank for hierarchical multi-agent dynamical systems

Eigenvector-based intergroup connection of low rank for hierarchical multi-agent dynamical systems

On the distributed stabilization and consensus of symmetrically interconnected agents

Static output feedback of equivariant linear systems with applications to the control of interconnected agents

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