Cascade Linearization of Invariant Control Systems

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dc.contributor.authorVassiliou, Peter
dc.date.accessioned2020-06-15T03:59:50Z
dc.date.issued2018
dc.date.updated2019-12-22T07:33:22Z
dc.description.abstractLet Pfaffian system ω define an intrinsically nonlinear control system on manifold M that is invariant under the free, regular action of a Lie group G. The problem of identifying and constructing static feedback linearizable G-quotients of ω was solved in De Dona et al. (2016). Building on these results, the present paper proves that the trajectories of ω can often be expressed as the composition of the trajectories of a static feedback linearizable quotient control system, ω/G, on quotient manifold M/G, and those of a separate control system, γ G , evolving on a principal G-bundle over a jet space. Furthermore, we point out that ω may not only have a static feedback linearizable quotient, ω/G but additionally, γ G itself may possess a static feedback linearizable reduction as well. This enables one to express the trajectories of an intrinsically nonlinear control system as the composition of the trajectories of static feedback linearizable control systems, thereby providing a geometric criterion for the explicit integrability of intrinsically nonlinear systems. Moreover, special integrability properties arise when G is solvable. Examples are presented in which the above phenomena are explicitly demonstrated. An important aspect of the examples is that they gather evidence for the conjecture that our sufficient conditions for explicit integrability are also necessary.en_AU
dc.format.extent31 pagesen_AU
dc.format.mimetypeapplication/pdfen_AU
dc.identifier.issn1079-2724en_AU
dc.identifier.urihttp://hdl.handle.net/1885/205085
dc.language.isoen_AUen_AU
dc.publisherSpringeren_AU
dc.rights© Springer Science+Business Media, LLC, part of Springer Nature 2017en_AU
dc.sourceJournal of Dynamical and Control Systemsen_AU
dc.subjectLie symmetry, Contact geometry, Static feedback linearization, Dynamic feedback linearization, Trajectory decomposition, Integrabilityen_AU
dc.titleCascade Linearization of Invariant Control Systemsen_AU
dc.typeJournal articleen_AU
local.bibliographicCitation.lastpage623en_AU
local.bibliographicCitation.startpage593en_AU
local.contributor.affiliationVassiliou, Peter, College of Science, The Australian National Universityen_AU
local.contributor.authoremailPeter.Vassiliou@anu.edu.auen_AU
local.contributor.authoruidVassiliou, Peter, u5151422en_AU
local.description.embargo2037-12-31
local.description.notesImported from ARIESen_AU
local.identifier.absfor010203 - Calculus of Variations, Systems Theory and Control Theoryen_AU
local.identifier.absseo970101 - Expanding Knowledge in the Mathematical Sciencesen_AU
local.identifier.ariespublicationu4485658xPUB1601en_AU
local.identifier.citationvolume24en_AU
local.identifier.doi10.1007/s10883-017-9389-0en_AU
local.identifier.essn1573-8698en_AU
local.identifier.scopusID2-s2.0-85037102944
local.identifier.thomsonID000441233100005
local.identifier.uidSubmittedByu4485658en_AU
local.publisher.urlhttps://www.springer.com/gpen_AU
local.type.statusPublished Versionen_AU

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