6 papers
On the rate of convergence in superquadratic Hamilton--Jacobi equations with state constraints
Prerona Dutta, Khai T. Nguyen, Son N. T. Tu
In this paper, we investigate the convergence rate in the vanishing viscosity limit for solutions to superquadratic Hamilton--Jacobi equations with state constraints. For every $p>…
Two-point boundary value problems for quasi-monotone dynamical systems
Lorena Bociu, Madhumita Roy, Khai T. Nguyen
This paper studies the existence of minimal solutions to two-point boundary value problems for quasi-monotone dynamical systems. Specifically, the pointwise infimum of all supersol…
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…
Generic Solutions to Controlled Balance Laws
Alberto Bressan, Khai T. Nguyen
The paper is concerned with a scalar balance law, where the source term depends on a control function . Given a control , it is prove…
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…