Caterina Sartori

Minimum Time with Bounded Energy, Minimum Energy with Bounded Time

Necessary and sufficient conditions for the regularity of the minimum time function and minimum energy function for a control system with controls in

Finite Fuel Problem in Nonlinear Singular Stochastic Control

L^p([0,+\infty[,{\Bbb R^m})

Discontinuous Solutions to Unbounded Differential Inclusions under State Constraints. Applications to Optimal Control Problems

and

Asymptotic analysis of delay differential equations

p\ge 1

The value function of an asymptotic exit-time optimal control problem

are given in terms of topological properties of the reachable sets. In particular, standard local controllability assumptions are sufficient to yield the continuity of both value functions for linear systems and

Approximation and regular perturbation of optimal control problems via Hamilton-Jacobi theory

p\ge1

Weakly Coercive Problems in Nonlinear Stochastic Control: Existence of Optimal Controls

and the Holder continuity of the minimum time function for nonlinear systems and p>1.

The value function of a finite fuel problem for a new class of singular stochastic controls

We investigate, via the dynamic programming approach, a finite fuel nonlinear singular stochastic control problem of Bolza type. We prove that the associated value function is continuous and that its continuous extension to the closure of the domain coincides with the value function of a nonsingular control problem, for which we prove the existence of an optimal control. Moreover, such a continuous extension is characterized as the unique viscosity solution of a quasi-variational inequality with suitable boundary conditions of mixed type.

Hamilton-Jacobi-Bellman equations with fast gradient-dependence

We consider a nonconvex and unbounded differential inclusion derived from a control system whose control sets are time and space-dependent. We extend the inclusion in order to allow discontinuous trajectories. We prove that the set of solutions of the original inclusion is dense in the set of solutions of the extended inclusion and, moreover, these last solutions are stable with respect to the initial data. Both of these results are also proven in the presence of state and integral constraints (assuming suitable conditions at the boundary of the constraining set). As an application, the value function of a Mayer problem is shown to be continuous and the unique viscosity solution of a Hamilton–Jacobi equation with suitable boundary conditions.

On asymptotic exit-time control problems lacking coercivity

AbstractWe present an asymptotic analysis for the solution of period 4 of