On a class of nonlinear time optimal control problems

Piermarco Cannarsa; Carlo Sinestrari

doi:10.3934/dcds.1995.1.285

Article Contents

1995, Volume 1, Issue 2: 285-300. Doi: 10.3934/dcds.1995.1.285

This issue Previous Article Periodic solutions to unbounded Hamiltonian system Next Article

On a class of nonlinear time optimal control problems

Piermarco Cannarsa^1, and
Carlo Sinestrari^2,

1.
Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata", Via della Ricerca Scientifica, 00133 Roma
2.
Dipartimento di Matematica, Università di Roma, Via della Ricerca Scientifica 1, 00133 Roma

Received: January 31, 1995

Published: March 1995

Abstract Related Papers Cited by

Abstract

We consider the minimum time optimal control problem for systems of the form

$ y'(t)=f(y(t),u(t))\,\quad y(t) \in \mathbb{R}^n,\ u(t)\in U \subset \mathbb{R}^d. $

We assume $f(x,U)$ to be a convex set with $C^1$ boundary for all $x\in\mathbb{R}^n$ and the target $\kappa$ to satisfy an interior sphere condition. For such problems we prove necessary and sufficient optimality conditions using the properties of the minimum time function $T(x)$. Moreover, we give a local description of the singular set of $T$.

Keywords:

Mathematics Subject Classification: 49L20, 49L25, 93C10.

Citation:

Article Metrics

HTML views() PDF downloads(112) Cited by(0)

On a class of nonlinear time optimal control problems

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

On a class of nonlinear time optimal control problems

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content