@article {2007,
title = {Nearly time optimal stabilizing patchy feedbacks},
journal = {Ann. Inst. H. Poincare Anal. Non Lineaire 24 (2007) 279-310},
number = {arXiv.org;math/0512531v1},
year = {2007},
abstract = {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 $\\\\tau(y)+\\\\ve$.},
doi = {10.1016/j.anihpc.2006.03.010},
url = {http://hdl.handle.net/1963/2185},
author = {Fabio Ancona and Alberto Bressan}
}
@article {2005,
title = {On the attainable set for Temple class systems with boundary controls},
journal = {SIAM J. Control Optim. 43 (2005) 2166-2190},
number = {SISSA;10/2002/M},
year = {2005},
publisher = {SISSA Library},
abstract = {Consider the initial-boundary value problem for a strictly hyperbolic, genuinely nonlinear, Temple class system of conservation laws \% $$ u_t+f(u)_x=0, \\\\qquad u(0,x)=\\\\ov u(x), \\\\qquad {{array}{ll} \&u(t,a)=\\\\widetilde u_a(t), \\\\noalign{\\\\smallskip} \&u(t,b)=\\\\widetilde u_b(t), {array}. \\\\eqno(1) $$ on the domain $\\\\Omega =\\\\{(t,x)\\\\in\\\\R^2 : t\\\\geq 0, a \\\\le x\\\\leq b\\\\}.$ We study the mixed problem (1) from the point of view of control theory, taking the initial data $\\\\bar u$ fixed, and regarding the boundary data $\\\\widetilde u_a, \\\\widetilde u_b$ as control functions that vary in prescribed sets $\\\\U_a, \\\\U_b$, of $\\\\li$ boundary controls. In particular, we consider the family of configurations $$ \\\\A(T) \\\\doteq \\\\big\\\\{u(T,\\\\cdot); ~ u {\\\\rm is a sol. to} (1), \\\\quad \\\\widetilde u_a\\\\in \\\\U_a, \\\\widetilde u_b \\\\in \\\\U_b \\\\big\\\\} $$ that can be attained by the system at a given time $T>0$, and we give a description of the attainable set $\\\\A(T)$ in terms of suitable Oleinik-type conditions. We also establish closure and compactness of the set $\\\\A(T)$ in the $lu$ topology.},
doi = {10.1137/S0363012902407776},
url = {http://hdl.handle.net/1963/1581},
author = {Fabio Ancona and Giuseppe Maria Coclite}
}
@article {2004,
title = {Stability rates for patchy vector fields},
journal = {ESAIM COCV 10 (2004) 168-200},
number = {arXiv.org;math/0111109v1},
year = {2004},
publisher = {EDP Sciences},
abstract = {This paper is concerned with the stability of the set of trajectories of a patchy vector field, in the presence of impulsive perturbations. Patchy vector fields are discontinuous, piecewise smooth vector fields that were introduced in Ancona and Bressan (1999) to study feedback stabilization problems. For patchy vector fields in the plane, with polygonal patches in generic position, we show that the distance between a perturbed trajectory and an unperturbed one is of the same order of magnitude as the impulsive forcing term.},
doi = {10.1051/cocv:2004003},
url = {http://hdl.handle.net/1963/2959},
author = {Fabio Ancona and Alberto Bressan}
}
@article {2004,
title = {Well-posedness for general 2x2 systems of conservation laws},
journal = {Mem. Amer. Math. Soc. 169 (2004), no. 801, x+170 pp.},
number = {SISSA;27/99/M},
year = {2004},
publisher = {SISSA Library},
url = {http://hdl.handle.net/1963/1241},
author = {Fabio Ancona and Andrea Marson}
}
@article {2003,
title = {Some results on the boundary control of systems of conservation laws},
journal = {SIAM J.Control Optim. 41 (2003),no.2, 607},
number = {SISSA;44/2002/M},
year = {2003},
publisher = {SISSA Library},
doi = {10.1137/S0363012901392529},
url = {http://hdl.handle.net/1963/1615},
author = {Alberto Bressan and Fabio Ancona and Giuseppe Maria Coclite}
}
@article {2002,
title = {Flow Stability of Patchy Vector Fields and Robust Feedback Stabilization},
journal = {SIAM J. Control Optim. 41 (2002) 1455-1476},
number = {SISSA;71/2001/M},
year = {2002},
publisher = {SIAM},
abstract = {The paper is concerned with patchy vector fields, a class of discontinuous, piecewise smooth vector fields that were introduced in AB to study feedback stabilization problems. We prove the stability of the corresponding solution set w.r.t. a wide class of impulsive perturbations. These results yield the robusteness of patchy feedback controls in the presence of measurement errors and external disturbances.},
doi = {10.1137/S0363012901391676},
url = {http://hdl.handle.net/1963/3073},
author = {Fabio Ancona and Alberto Bressan}
}
@article {1997,
title = {Homogeneous tangent vectors and high order necessary conditions for optimal controls},
journal = {J. Dynam. Control Systems 3 (1997), no. 2, 205--240},
number = {SISSA;113/95/M},
year = {1997},
publisher = {SISSA Library},
url = {http://hdl.handle.net/1963/1015},
author = {Fabio Ancona}
}
@article {1990,
title = {Existence of solutions for a class of non-convex differential inclusions},
journal = {Rend.Sem.Mat.Univ. Padova, 83 (1990), 71-76},
number = {SISSA;31/89/M},
year = {1990},
publisher = {SISSA Library},
url = {http://hdl.handle.net/1963/792},
author = {Fabio Ancona and Giovanni Colombo}
}