On a class of nonlinear time optimal control problems

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April 1995, 1(2): 285-300. doi: 10.3934/dcds.1995.1.285

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 February 1995 Published February 1995

Abstract
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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: optimal control problem, calculus of variations, interior sphere condition..

Mathematics Subject Classification: 49L20, 49L25, 93C1.

Citation: Piermarco Cannarsa, Carlo Sinestrari. On a class of nonlinear time optimal control problems. Discrete & Continuous Dynamical Systems - A, 1995, 1 (2) : 285-300. doi: 10.3934/dcds.1995.1.285

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