TY - JOUR
T1 - Nearly time optimal stabilizing patchy feedbacks
JF - Ann. Inst. H. Poincare Anal. Non Lineaire 24 (2007) 279-310
Y1 - 2007
A1 - Fabio Ancona
A1 - Alberto Bressan
AB - 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 $\\\\tau(y)+\\\\ve$.
UR - http://hdl.handle.net/1963/2185
U1 - 2059
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - On the attainable set for Temple class systems with boundary controls
JF - SIAM J. Control Optim. 43 (2005) 2166-2190
Y1 - 2005
A1 - Fabio Ancona
A1 - Giuseppe Maria Coclite
AB - 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.
PB - SISSA Library
UR - http://hdl.handle.net/1963/1581
U1 - 2537
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Stability rates for patchy vector fields
JF - ESAIM COCV 10 (2004) 168-200
Y1 - 2004
A1 - Fabio Ancona
A1 - Alberto Bressan
AB - 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.
PB - EDP Sciences
UR - http://hdl.handle.net/1963/2959
U1 - 1741
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Well-posedness for general 2x2 systems of conservation laws
JF - Mem. Amer. Math. Soc. 169 (2004), no. 801, x+170 pp.
Y1 - 2004
A1 - Fabio Ancona
A1 - Andrea Marson
PB - SISSA Library
UR - http://hdl.handle.net/1963/1241
U1 - 2702
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Some results on the boundary control of systems of conservation laws
JF - SIAM J.Control Optim. 41 (2003),no.2, 607
Y1 - 2003
A1 - Alberto Bressan
A1 - Fabio Ancona
A1 - Giuseppe Maria Coclite
PB - SISSA Library
UR - http://hdl.handle.net/1963/1615
U1 - 2503
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Flow Stability of Patchy Vector Fields and Robust Feedback Stabilization
JF - SIAM J. Control Optim. 41 (2002) 1455-1476
Y1 - 2002
A1 - Fabio Ancona
A1 - Alberto Bressan
AB - 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.
PB - SIAM
UR - http://hdl.handle.net/1963/3073
U1 - 1260
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Homogeneous tangent vectors and high order necessary conditions for optimal controls
JF - J. Dynam. Control Systems 3 (1997), no. 2, 205--240
Y1 - 1997
A1 - Fabio Ancona
PB - SISSA Library
UR - http://hdl.handle.net/1963/1015
U1 - 2841
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Existence of solutions for a class of non-convex differential inclusions
JF - Rend.Sem.Mat.Univ. Padova, 83 (1990), 71-76
Y1 - 1990
A1 - Fabio Ancona
A1 - Giovanni Colombo
PB - SISSA Library
UR - http://hdl.handle.net/1963/792
U1 - 2999
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -