### Discontinuous Mayer control problem under state-constraints

DOI: http://dx.doi.org/10.12775/TMNA.2000.007

#### Abstract

This paper deals with Mayer's problem for control systems with

state constraints and, possibly, discontinuous terminal cost.

The main result of this paper consists in the characterization of

the value function as the unique solution to an Hamilton-Jacobi

equation. The above characterization extends results already

obtained in the case of regular cost functions and under some

controlability assumptions on the boundary of the set of

constraints.

state constraints and, possibly, discontinuous terminal cost.

The main result of this paper consists in the characterization of

the value function as the unique solution to an Hamilton-Jacobi

equation. The above characterization extends results already

obtained in the case of regular cost functions and under some

controlability assumptions on the boundary of the set of

constraints.

#### Keywords

Mayer control problem; state constraints; discontinuous terminal cost; Hamilton-Jacobi equations

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