# Interpolation-Based Operator in Dynamic Programming Procedures for Solving Conflict Control Problems

Nikolai Botkin^{*} and Varvara Turova

Nonlinear conflict control problems with state constraints and non-fixed termination time are considered. Using the fact that the value functions of such problems can be interpreted as viscosity solutions to appropriate Hamilton-Jacobi equations, a dynamic programming solution procedure which is associated with an operator based on grid interpolation is proposed. An accurate proof of important properties of this operator such as monotonicity and consistency is given. This allows us to design effective numerical methods for the computation of viscosity solutions. Various applications of this method are discussed.

Mathematics Subject Classification: 49N70 49L25 65M06 41A10

Keywords: Hamilton-Jacobi equations; viscosity solutions; grid methods

Minisymposion: Dynamic Programming Approach to Optimal Control Methods and Applications