An Iterative Method for Final Time Optimization in Nonlinear Optimal Control

Abstract

This paper discusses a bilevel optimization approach for free finite final time optimal control problems and addresses a numerical method for their approximate solution. The core idea is to decouple the final time optimization from the optimal control and state trajectory. This is rigorously formulated as an equivalent bilevel problem seeking, at the upper level, the optimal final time and optimal control and corresponding state at the lower level. Standard solvers for nonlinear optimal control can deal with the latter, while the former is a box-constrained optimization problem with one scalar decision variable. The interface between the two levels is based on the Hamilton function associated to the problem and its relationship with the cost function. A method for solving the upper level problem is developed, that combines a tailored fast first-order method with a robust and guaranteed root-finding algorithm. Finally, numerical results demonstrate the robustness of the method and show