Extension of Switch Point Algorithm to Boundary-Value Problems
Abstract
In an earlier paper (https://doi.org/10.1137/21M1393315), the Switch Point Algorithm was developed for solving optimal control problems whose solutions are either singular or bang-bang or both singular and bang-bang, and which possess a finite number of jump discontinuities in an optimal control at the points in time where the solution structure changes. The class of control problems that were considered had a given initial condition, but no terminal constraint. The theory is now extended to include problems with both initial and terminal constraints, a structure that often arises in boundary-value problems. Substantial changes to the theory are needed to handle this more general setting. Nonetheless, the derivative of the cost with respect to a switch point is again the jump in the Hamiltonian at the switch point.
Cite
@article{arxiv.2307.09722,
title = {Extension of Switch Point Algorithm to Boundary-Value Problems},
author = {William W. Hager},
journal= {arXiv preprint arXiv:2307.09722},
year = {2025}
}