Limits of highly oscillatory controls and the approximation of general paths by admissible trajectories

Hector J. Sussmann, Wensheng Liu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

84 Scopus citations

Abstract

The authors describe sufficient conditions, extending earlier work by J. Kurzweil and J. Jarnik (Reults in Mathematics, vol. 14, pp. 125-137, 1988), for a sequence of inputs to be such that, for every m-tuple of smooth vector fields, the trajectories of the time derivative of x(t) converge to those of an extended system, where the new vector fields are Lie brackets of the original m-tuples. Using these conditions, the inverse problem is solved, wherein given a trajectory γ of the extended system, one must find trajectories of the original system that converge to γ. This is done by means of a universal construction that only involves knowledge of the coefficients of the extended system. These results can be applied to solve the problem of approximate tracking for a controllable system without drift.

Original languageEnglish (US)
Title of host publicationProceedings of the IEEE Conference on Decision and Control
PublisherPubl by IEEE
Pages437-442
Number of pages6
ISBN (Print)0780304500
StatePublished - Jan 1 1992
EventProceedings of the 30th IEEE Conference on Decision and Control Part 1 (of 3) - Brighton, Engl
Duration: Dec 11 1991Dec 13 1991

Other

OtherProceedings of the 30th IEEE Conference on Decision and Control Part 1 (of 3)
CityBrighton, Engl
Period12/11/9112/13/91

All Science Journal Classification (ASJC) codes

  • Chemical Health and Safety
  • Control and Systems Engineering
  • Safety, Risk, Reliability and Quality

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