GENERIC LOCAL TIME-OPTIMAL STABILIZING CONTROLS IN DIMENSION 3.

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

This paper studies the control system dx(t)/dt equals X(x(t)) plus Y(x(t))u(t), X(p//0) equals 0, vertical u(t) vertical less than equivalent to 1, where X and Y are C** infinity vector fields on a 3-dimensional manifold M. Under generic assumptions on X, Y, the structure of the time-optimal stabilizing controls is completely determined in a neighborhood of p//0. The proofs rely on a systematic use of a local asymptotic approximation of X and Y by means of vector fields which generate a nilpotent Lie algebra.

Original languageEnglish (US)
Pages (from-to)177-190
Number of pages14
JournalSIAM Journal on Control and Optimization
Volume24
Issue number2
DOIs
StatePublished - Jan 1 1986

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Local Time
Vector Field
Vertical
Nilpotent Lie Algebra
Local Approximation
Asymptotic Approximation
Algebra
Control System
Infinity
Control systems

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Applied Mathematics

Cite this

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abstract = "This paper studies the control system dx(t)/dt equals X(x(t)) plus Y(x(t))u(t), X(p//0) equals 0, vertical u(t) vertical less than equivalent to 1, where X and Y are C** infinity vector fields on a 3-dimensional manifold M. Under generic assumptions on X, Y, the structure of the time-optimal stabilizing controls is completely determined in a neighborhood of p//0. The proofs rely on a systematic use of a local asymptotic approximation of X and Y by means of vector fields which generate a nilpotent Lie algebra.",
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GENERIC LOCAL TIME-OPTIMAL STABILIZING CONTROLS IN DIMENSION 3. / Bressan, Alberto.

In: SIAM Journal on Control and Optimization, Vol. 24, No. 2, 01.01.1986, p. 177-190.

Research output: Contribution to journalArticle

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