# American Institute of Mathematical Sciences

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

## On a class of nonlinear time optimal control problems

 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

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 $T$.

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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