ABSTRACT. We consider the time optimal stabilization problem for a nonlinear control system $dot x=f(x,u)$. Let $T(y)$ be the minimum time needed to steer the system from the state $yin R^n$ to the origin, and call $A(tau)$ the set of initial states that can be steered to the origin in time $T(y)leq tau$. Given any $epsilon>0$, in this paper we construct a patchy feedback $u=U(x)$ such that every solution of $dot x=f(x, U(x))$, $x(0)=yin A(tau)$ reaches an $ve$-neighborhood of the origin within time $T(y)+epsilon$.
Nearly time optimal stabilizing patchy feedbacks
ANCONA, FABIO;
2007
Abstract
ABSTRACT. We consider the time optimal stabilization problem for a nonlinear control system $dot x=f(x,u)$. Let $T(y)$ be the minimum time needed to steer the system from the state $yin R^n$ to the origin, and call $A(tau)$ the set of initial states that can be steered to the origin in time $T(y)leq tau$. Given any $epsilon>0$, in this paper we construct a patchy feedback $u=U(x)$ such that every solution of $dot x=f(x, U(x))$, $x(0)=yin A(tau)$ reaches an $ve$-neighborhood of the origin within time $T(y)+epsilon$.File in questo prodotto:
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