### Abstract

Consider the problem of reaching the origin in minimum time, for the control system ẋ = F(x) + G(x)u, |u(t)| ≤ 1, assuming F(0) = 0, x ∈ ℝ^{2}. For a generic family of C^{3} vector fields F,G, we introduce an equivalence relation on the corresponding time-optimal feedback. We describe an algorithm to construct an optimal synthesis and give generic conditions in order to obtain the structural stability of feedbacks.

Original language | English (US) |
---|---|

Pages (from-to) | 335-371 |

Number of pages | 37 |

Journal | Dynamics of Continuous, Discrete and Impulsive Systems Series B: Application and Algorithm |

Volume | 3 |

Issue number | 3 |

State | Published - Sep 1 1997 |

Externally published | Yes |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Cite this

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*Dynamics of Continuous, Discrete and Impulsive Systems Series B: Application and Algorithm*, vol. 3, no. 3, pp. 335-371.

**Structural stability for time-optimal planar syntheses.** / Bressan, Alberto; Piccoli, Benedetto.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Structural stability for time-optimal planar syntheses

AU - Bressan, Alberto

AU - Piccoli, Benedetto

PY - 1997/9/1

Y1 - 1997/9/1

N2 - Consider the problem of reaching the origin in minimum time, for the control system ẋ = F(x) + G(x)u, |u(t)| ≤ 1, assuming F(0) = 0, x ∈ ℝ2. For a generic family of C3 vector fields F,G, we introduce an equivalence relation on the corresponding time-optimal feedback. We describe an algorithm to construct an optimal synthesis and give generic conditions in order to obtain the structural stability of feedbacks.

AB - Consider the problem of reaching the origin in minimum time, for the control system ẋ = F(x) + G(x)u, |u(t)| ≤ 1, assuming F(0) = 0, x ∈ ℝ2. For a generic family of C3 vector fields F,G, we introduce an equivalence relation on the corresponding time-optimal feedback. We describe an algorithm to construct an optimal synthesis and give generic conditions in order to obtain the structural stability of feedbacks.

UR - http://www.scopus.com/inward/record.url?scp=0000947809&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000947809&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0000947809

VL - 3

SP - 335

EP - 371

JO - Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms

JF - Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms

SN - 1492-8760

IS - 3

ER -