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We consider the Cauchy problem for a strictly hyperbolic 2 2 system of conservation laws in one space dimension u t + F (u)] x = 0; u(0; x) = u(x); (1) which is neither linearly degenerate nor genuinely non-linear. We make the following assumption on the characteristic elds. If r i (u); i = 1; 2; denotes the i-th right eigenvector of DF (u) and i (u) the… (More)

Consider a general strictly hyperbolic, quasilinear system, in one space dimension ut +A(u)ux = 0, (1) where u 7→ A(u), u ∈ Ω ⊂ R , is a smooth matrix-valued map. Given an initial datum u(0, ·) with small total variation, let u(t, ·) be the corresponding (unique) vanishing viscosity solution of (1) obtained as limit of solutions to the viscous parabolic… (More)

- Fabio Ancona, Giuseppe Maria Coclite
- SIAM J. Control and Optimization
- 2005

Consider the initial-boundary value problem for a strictly hyperbolic, genuinely nonlinear, Temple class system of conservation laws ut + f(u)x = 0, u(0, x) = u(x), u(t, a) = ũa(t), u(t, b) = ũb(t), (1) on the domain Ω = {(t, x) ∈ R : t ≥ 0, a ≤ x ≤ b}. We study the mixed problem (1) from the point of view of control theory, taking the initial data u… (More)

We analize the structure of the general solution of the Riemann problem for a striclty hyperbolic system of conservation laws whose characteristic elds are neither genuinely non-linear nor linearly degenerate in the sense of Lax.

- Fabio Ancona, Anna Maria Colla, Stefano Rovetta, Rodolfo Zunino
- Neural Computing & Applications
- 1997

A modified PNN training algorithm is proposed. The standard PNN, though requiring a very short training time, when implemented in hardware exhibits the drawbacks of being costly in terms of classification time and of requiring an unlimited number of units. The proposed modification overcomes the latter drawback by introducing an elimination criterion to… (More)

Consider the Cauchy problem for a strictly hyperbolic, N×N quasilinear system in one space dimension ut + A(u)ux = 0, u(0, x) = ū(x), (1) where u 7→ A(u) is a smooth matrix-valued map, and the initial data u is assumed to have small total variation. We investigate the rate of convergence of approximate solutions of (1) constructed by the Glimm scheme, under… (More)

- Fabio Ancona, Alberto Bressan
- SIAM J. Control and Optimization
- 2002

The paper is concerned with patchy vector fields, a class of discontinuous, piecewise smooth vector fields that were introduced in [A-B] 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… (More)

We consider the initial-boundary value problem for a scalar non-linear conservation law u t + f(u)] x = 0; u(0; x) = u(x); u(; 0) = ~ u(t); () on the domain = f(t; x) 2 R 2 : t 0; x 0g. Here u = u(t; x) is the state variable, u; ~ u are integrable (possibly unbounded) initial and boundary data, and f is assumed to be strictly convex and superlinear. We rst… (More)

We consider the time optimal stabilization problem for a nonlinear control system ẋ = f(x, u). Let τ(y) be the minimum time needed to steer the system from the state y ∈ R to the origin, and call A(T ) the set of initial states that can be steered to the origin in time τ(y) ≤ T . Given any ε > 0, in this paper we construct a patchy feedback u = U(x) such… (More)

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… (More)