Cascade Linearization of Invariant Control Systems
Date
2018
Authors
Vassiliou, Peter
Journal Title
Journal ISSN
Volume Title
Publisher
Springer
Abstract
Let 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.
Description
Keywords
Lie symmetry, Contact geometry, Static feedback linearization, Dynamic feedback linearization, Trajectory decomposition, Integrability
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Source
Journal of Dynamical and Control Systems
Type
Journal article
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DOI
10.1007/s10883-017-9389-0
Restricted until
2037-12-31