Optimal control and semicontinuous viscosity solutions

Viscosity Solutions of Hamilton-Jacobi Equations and Optimal Control Problems

Optimal Control Problems with Upper Semicontinuous Hamiltonians

In this paper we give examples of value functions in Bolza problem that are not bilateral or viscosity solutions and an example of a smooth value function that is even not a classic solution (in particular, it can be neither the viscosity nor the bilateral solution) of Hamilton-Jacobi-Bellman equation with upper semicontinuous Hamiltonian. Good properties of value functions motivate us to intro...

Nonconvex Duality and Semicontinuous Proximal Solutions of HJB Equation in Optimal Control

In this work, we study an optimal control problem dealing with differential inclusion. Without requiring Lipschitz condition of the set valued map, it is very hard to look for a solution of the control problem. Our aim is to find estimations of the minimal value, (α), of the cost function of the control problem. For this, we construct an intermediary dual problem leading to a weak duality resul...

Hybrid Control Systems and Viscosity Solutions

We investigate a model of hybrid control system in which both discrete and continuous controls are involved. In this general model, discrete controls act on the system at a given set interface. The state of the system is changed discontinuously when the trajectory hits predefined sets, namely, an autonomous jump set A or a controlled jump set C where the controller can choose to jump or not. At...

Uniqueness of Lower Semicontinuous Viscosity Solutions for the Minimum Time Problem

We obtain the uniqueness of lower semicontinuous (lsc for short) viscosity solutions of the transformed minimum time problem assuming that they converge to zero on a \reachable" part of the target in appropriate directions. We present a counterexample which shows that the uniqueness does not hold without this convergence assumption. It was shown by Soravia that the uniqueness of lsc viscosity s...