17 citations · 20 across the 7 of their papers we have counts for
9 papers
Generic uniqueness and conjugate points for optimal control problems
Alberto Bressan, Marco Mazzola, Khai T. Nguyen
The paper is concerned with an optimal control problem on , where the dynamics is linear w.r.t.~the control functions. For a terminal cost in a set…
On the structure of the value function of optimal exit time problems
Piermarco Cannarsa, Marco Mazzola, Khai T. Nguyen
In this paper, we study an optimal exit time problem with general running and terminal costs and a target having an inner ball property for a nonli…
Generic Properties of Conjugate Points in Optimal Control Problems
Alberto Bressan, Marco Mazzola, Khai T. Nguyen
The first part of the paper studies a class of optimal control problems in Bolza form, where the dynamics is linear w.r.t.~the control function. A necessary condition is derived, f…
Diffusion Approximations of Markovian Solutions to Discontinuous ODEs
Alberto Bressan, Marco Mazzola, Khai T. Nguyen
In a companion paper, the authors have characterized all deterministic semigroups, and all Markov semigroups, whose trajectories are Carathe'odory solutions to a given ODE x'=f(x),…
Markovian Solutions to Discontinuous ODEs
Alberto Bressan, Marco Mazzola, Khai T. Nguyen
Given a possibly discontinuous, bounded function , we consider the set of generalized flows, obtained by assigning a probability measure on the set o…
Approximation of Sweeping Processes and Controllability for a Set Valued Evolution
Alberto Bressan, Marco Mazzola, Khai T. Nguyen
We consider a controlled evolution problem for a set , originally motivated by a model where a dog controls a flock of sheep. Necessary conditions and sufficie…
Lyapunov's theorem via Baire category
Marco Mazzola, Khai T. Nguyen
Lyapunov's theorem is a classical result in convex analysis, concerning the convexity of the range of nonatomic measures. Given a family of integrable vector functions on a compact…
Global generalized characteristics for the Dirichlet problem for Hamilton-Jacobi equations at a supercritical energy level
Piermarco Cannarsa, Wei Cheng, Marco Mazzola +1
We study the nonhomogeneous Dirichlet problem for first order Hamilton-Jacobi equations associated with Tonelli Hamiltonians on a bounded domain of assuming the energy l…
Global Propagation of Singularities for Time Dependent Hamilton-Jacobi Equations
Piermarco Cannarsa, Marco Mazzola, Carlo Sinestrari
We investigate the properties of the set of singularities of semiconcave solutions of Hamilton-Jacobi equations of the form \begin{equation*} u_t(t,x)+H(\nabla u(t,x))=0, \qquad\te…