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Article Contents

# On a class of nonlinear time optimal control problems

• 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 $T$.

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

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