Nearly Time Optimal Stabilizing Patchy Feedbacks

Details Nearly Time Optimal Stabilizing Patchy Feedbacks Nearly Time Optimal Stabilizing Patchy Feedbacks

2005-12-22

arxiv.org/abs/math/0512531v1

Mathematics

Classical Analysis and ODEs

42 pages, 8 figures

Scientific paper

We consider the time optimal stabilization problem for a nonlinear control system $\dot x=f(x,u)$. Let $\tau(y)$ be the minimum time needed to steer the system from the state $y\in\R^n$ to the origin, and call $\A(T)$ the set of initial states that can be steered to the origin in time $\tau(y)\leq T$. Given any $\ve>0$, in this paper we construct a patchy feedback $u=U(x)$ such that every solution of $\dot x=f(x, U(x))$, $x(0)=y\in \A(T)$ reaches an $\ve$-neighborhood of the origin within time $\tau(y)+\ve$.

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