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 $T(y)+epsilon$.
F. Ancona, A. Bressan (2007). Nearly time optimal stabilizing patchy feedbacks. ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE, 24, 390-422 [10.1016/j.anihpc.2006.03.010].
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 $T(y)+epsilon$.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
