TY - JOUR
T1 - Nearly time optimal stabilizing patchy feedbacks
AU - Ancona, Fabio
AU - Bressan, Alberto
PY - 2007
Y1 - 2007
N2 - We consider the time optimal stabilization problem for a nonlinear control system over(x, ̇) = f (x, u). Let T (y) be the minimum time needed to steer the system from the state y ∈ Rn to the origin, and call A (τ) the set of initial states that can be steered to the origin in time T (y) ≤ τ. Given any ε > 0, in this paper we construct a patchy feedback u = U (x) such that every solution of over(x, ̇) = f (x, U (x)), x (0) = y ∈ A (τ) reaches an ε-neighborhood of the origin within time T (y) + ε.
AB - We consider the time optimal stabilization problem for a nonlinear control system over(x, ̇) = f (x, u). Let T (y) be the minimum time needed to steer the system from the state y ∈ Rn to the origin, and call A (τ) the set of initial states that can be steered to the origin in time T (y) ≤ τ. Given any ε > 0, in this paper we construct a patchy feedback u = U (x) such that every solution of over(x, ̇) = f (x, U (x)), x (0) = y ∈ A (τ) reaches an ε-neighborhood of the origin within time T (y) + ε.
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U2 - 10.1016/j.anihpc.2006.03.010
DO - 10.1016/j.anihpc.2006.03.010
M3 - Article
AN - SCOPUS:33947143353
VL - 24
SP - 279
EP - 310
JO - Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis
JF - Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis
SN - 0294-1449
IS - 2
ER -