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Involutive flows and discretization errors for nonlinear driftless control systems
Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten.ORCID-id: 0000-0003-4142-6502
2017 (engelsk)Inngår i: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 110, s. 29-37Artikkel i tidsskrift (Fagfellevurdert) 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.

sted, utgiver, år, opplag, sider
ELSEVIER SCIENCE BV , 2017. Vol. 110, s. 29-37
Emneord [en]
Discrete-time nonlinear control systems; Nonintegrability condition; Discretization; Lie brackets; Geometric phase; Geometric numerical integration; Local error computation
HSV kategori
Identifikatorer
URN: urn:nbn:se:liu:diva-144147DOI: 10.1016/j.sysconle.2017.08.009ISI: 000418628700005OAI: oai:DiVA.org:liu-144147DiVA, id: diva2:1172314
Merknad

Funding Agencies|Swedish Research Council [2015-04390]

Tilgjengelig fra: 2018-01-09 Laget: 2018-01-09 Sist oppdatert: 2018-02-01

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