### 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 language | English (US) |
---|---|

Pages (from-to) | 177-190 |

Number of pages | 14 |

Journal | SIAM Journal on Control and Optimization |

Volume | 24 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1986 |

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### All Science Journal Classification (ASJC) codes

- Control and Optimization
- Applied Mathematics

### Cite this

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*SIAM Journal on Control and Optimization*, vol. 24, no. 2, pp. 177-190. https://doi.org/10.1137/0324010

**GENERIC LOCAL TIME-OPTIMAL STABILIZING CONTROLS IN DIMENSION 3.** / Bressan, Alberto.

Research output: Contribution to journal › Article

TY - JOUR

T1 - GENERIC LOCAL TIME-OPTIMAL STABILIZING CONTROLS IN DIMENSION 3.

AU - Bressan, Alberto

PY - 1986/1/1

Y1 - 1986/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0022674191&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0022674191&partnerID=8YFLogxK

U2 - 10.1137/0324010

DO - 10.1137/0324010

M3 - Article

AN - SCOPUS:0022674191

VL - 24

SP - 177

EP - 190

JO - SIAM Journal on Control and Optimization

JF - SIAM Journal on Control and Optimization

SN - 0363-0129

IS - 2

ER -