Abstract An adaptive treatment strategy is a set of rules for choosing effective medical treatments for individual patients. In the statistical literature, methods for optimal dynamic treatment (ODT) include Q-learning and A-learning methods, which are linked to machine learning in engineering and computer science. The research project behind this article aims to develop new methodology for both ODT and engineering control, through the integration of techniques and approaches that have been developed in both fields, with a particular focus on the problem of robustness. The methodological framework is based on a regret-regression approach from the statistical literature and non-minimal state-space methods from control. This article provides an introduction to some of these concepts and presents preliminary novel contributions based on the application of robust H∞ methods to ODT problems.