Random matrices and controllability of dynamical systems

Leventides, John; Poulios, N.; Poulios, Costas

doi:10.48550/arxiv.2011.11147

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2021

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“…A class of optimal control problems defined on certain kinds of symmetric spaces is discussed by Bloch et al [6,7]. Similarly a lot of progress has been made to study control of complex networks [5,28] and control of ensembles through structural controllability [12,13] and by other authors [2,3,26,27,39], but to our knowledge nobody has discussed about these in the context of random matrix ensembles like GOE, GSE, GUE which actually correspond to Riemannian symmetric spaces classified by Cartan [10]. Taking these view points into consideration we were motivated to extend the study of control theory on Lie groups (Lie algebras) to symmetric spaces(Lie triple systems).…”

Section: Introductionmentioning

confidence: 99%

On Controllability of Driftless Control System on Symmetric Spaces

Tiwari¹,

Padhan²,

Pati³

2021

Preprint

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Symmetric spaces arise in wide variety of problems in Mathematics and Physics. They are mostly studied in Representation theory, Harmonic analysis and Differential geometry. As many physical systems have symmetric spaces as their configuration spaces, the study of controllability on symmetric space is quite interesting. In this paper, a driftless control system of type ẋ = m i=1 u i f i (x) is considered on a symmetric space. For this we have established global controllability condition which is illustrated by few examples of exponential submanifolds of SE(3) and random matrix ensembles.

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