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Nonintegrable discrete-time driftless control systems: geometric phases beyond the area rule
Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska fakulteten. (Automatic Control)ORCID-id: 0000-0003-4142-6502
2016 (engelsk)Inngår i: 2016 IEEE 55th Conference on Decision and Control (CDC), IEEE Press, 2016, s. 4692-4697Konferansepaper, Publicerat paper (Fagfellevurdert)
Abstract [en]

In a continuous-time nonlinear driftless control system, a geometric phase is a consequence of nonintegrability of the vector fields, and it describes how cyclic trajectories in shape space induce non-periodic motion in phase space, according to an area rule. The aim of this paper is to shown that geometric phases exist also for discrete-time driftless nonlinear control systems, but that unlike their continuous-time counterpart, they need not obey any area rule, i.e., even zero-area cycles in shape space can lead to nontrivial geometric phases. When the discrete-time system is obtained through Euler discretization of a continuous-time system, it is shown that the zero-area geometric phase corresponds to the gap between the Euler discretization and an exact discretization of the continuous-time system.

sted, utgiver, år, opplag, sider
IEEE Press, 2016. s. 4692-4697
Serie
IEEE Conference on Decision and Control, ISSN 0743-1546
HSV kategori
Identifikatorer
URN: urn:nbn:se:liu:diva-135542DOI: 10.1109/CDC.2016.7798984ISI: 000400048104142ISBN: 9781509018376 (digital)ISBN: 9781509018444 (digital)ISBN: 9781509018383 (digital)OAI: oai:DiVA.org:liu-135542DiVA, id: diva2:1082499
Konferanse
2016 IEEE 55th Conference on Decision and Control (CDC), 12-14 December, Las Vegas, USA
Tilgjengelig fra: 2017-03-16 Laget: 2017-03-16 Sist oppdatert: 2017-06-13bibliografisk kontrollert

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Nonintegrable discrete-time driftless control systems: geometric phases beyond the area rule(361 kB)111 nedlastinger
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