We present a trust-region steepest descent method for dynamic optimal control problems with binary-valued integrable control functions. Our method interprets the control function as an indicator function of a measurable set and makes set-valued adjustments derived from the sublevel sets of a topological gradient function. By combining this type of update with a trust-region framework, we are able to show by theoretical argument that our method achieves asymptotic stationarity despite possible discretization errors and truncation errors during step determination. To demonstrate the practical applicability of our method, we solve two simple optimal control problems constrained by ordinary and partial differential equations, respectively, as well as a more complex topological optimization problem.
Hahn, M., Leyffer, S. & Sager, S. Binary optimal control by trust-region steepest descent. Math. Program. (2022). https://doi.org/10.1007/s10107-021-01733-z | (Licensed under Creative Commons Attribution 4.0 International License, http://creativecommons.org/licenses/by/4.0/)