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Involutive flows and discretization errors for nonlinear driftless control systems
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0003-4142-6502
2017 (English)In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 110, p. 29-37Article in journal (Refereed) Published
Abstract [en]

In a continuous-time nonlinear driftless control system, an involutive flow is a composition of input profiles that does not excite any Lie bracket. Such flow composition is trivial, as it corresponds to a "forth and back" cyclic motion obtained rewinding the system along the same path. The aim of this paper is to show that, on the contrary, when a (nonexact) discretization of the nonlinear driftless control system is steered along the same trivial input path, it produces a net motion, which is related to the gap between the discretization used and the exact discretization given by a Taylor expansion. These violations of involutivity can be used to provide an estimate of the local truncation error of numerical integration schemes. In the special case in which the state of the driftless control system admits a splitting into shape and phase variables, our result corresponds to saying that the geometric phases of the discretization need not obey an area rule, i.e., even zero-area cycles in shape space can lead to nontrivial geometric phases. (C) 2017 Elsevier B.V. All rights reserved.

Place, publisher, year, edition, pages
ELSEVIER SCIENCE BV , 2017. Vol. 110, p. 29-37
Keywords [en]
Discrete-time nonlinear control systems; Nonintegrability condition; Discretization; Lie brackets; Geometric phase; Geometric numerical integration; Local error computation
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-144147DOI: 10.1016/j.sysconle.2017.08.009ISI: 000418628700005OAI: oai:DiVA.org:liu-144147DiVA, id: diva2:1172314
Note

Funding Agencies|Swedish Research Council [2015-04390]

Available from: 2018-01-09 Created: 2018-01-09 Last updated: 2018-02-01

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CiteExportLink to record
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Citation style
  • apa
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  • de-DE
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