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Paper details
Number 2 - June 2001
Volume 11 - 2001
An algorithm for construction of ε-value functions for the Bolza control problem
Edyta Jacewicz
Abstract
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 ε-value function is defined as an approximation for the value function being a solution to the Hamilton-Jacobi equation. The paper shows how an ε-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.
Keywords
non-linear optimisation, Bolza problem, optimal control, Hamilton-Jacobi equation, dynamic programming, ε-value function, approximate minimum