An Algorithm for Construction of varepsilon-Value Functions for the Bolza Control Problem
Edyta Jacewicz · International Journal of Applied Mathematics and Computer Science · 2001
The problem considered is that of approximate numerical minimisation of the non-linear control problem of Bolza. Starting from the classical dynamic programming method of Bellman, an e-value function is defined as an approximation for the value function being a solution to the Hamilton-Jacobi equation. The paper shows how an e-value function which maintains suitable properties analogous to the original Hamilton-Jacobi value function can be constructed using a stable numerical algorithm. The paper shows the numerical closeness of the approximate minimum to the infimum of the Bolza functional.