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Nearly time optimal stabilizing patchy feedbacks

TitleNearly time optimal stabilizing patchy feedbacks
Publication TypeJournal Article
Year of Publication2007
AuthorsAncona, F, Bressan, A
JournalAnn. Inst. H. Poincare Anal. Non Lineaire 24 (2007) 279-310

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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