# Convergence of Numerical Methods for Optimal Control Using Viscosity Solutions and Differential Inclusions

**Mattias Sandberg
**

Numerical Analysis Group

Computer Science and Communication

KTH

Stockholm

### Abstract:

Optimal control problems are ill-posed; no optimizer may exist, and if it exists it may depend discontinuously on data. This complicates the analysis of numerical methods for optimal control. In this talk, we will look at two ways how to perform such an analysis:

1) By rewriting the problem as a differential inclusion.

2) By using the fact that the value function associated with an optimal control problem is a viscosity solution to a Hamilton-Jacobi equation. For such equations there is a well-developed theoretical machinery.