eXplainable AI for data driven control: an inverse optimal control approach

Understanding the behavior of black-box data-driven controllers is a key challenge in modern control design. In this work, we propose an eXplainable AI (XAI) methodology based on Inverse Optimal Control (IOC) to obtain local explanations for the behavior of a controller operating around a given region. Specifically, we extract the weights assigned to tracking errors and control effort in the implicit cost function that a black-box controller is optimizing, offering a more transparent and interpretable representation of the controller's underlying objectives. This approach presents connections with well-established XAI techniques, such as Local Interpretable Model-agnostic Explanations (LIME) since it is still based on a local approximation of the control policy. However, rather being limited to a standard sensitivity analysis, the explanation provided by our method relies on the solution of an inverse Linear Quadratic (LQ) problem, offering a structured and more control-relevant perspective. Numerical examples demonstrate that the inferred cost function consistently provides a deeper understanding of the controller's decision-making process, shedding light on otherwise counterintuitive or unexpected phenomena.