Data-Driven Distributionally Robust Optimal Control with State-Dependent Noise

Distributionally Robust Optimal Control (DROC) is a framework that enables robust control in a stochastic setting where the true disturbance distribution is unknown. Traditional DROC approaches require given ambiguity sets and KL divergence bounds to represent the distributional uncertainty; however, these quantities are often unavailable a priori or require manual specification. To overcome this limitation, we propose a data-driven approach that jointly estimates the uncertainty distribution and the corresponding KL divergence bound, which we refer to as D3ROC. To evaluate the effectiveness of our approach, we consider a car-like robot navigation task with unknown noise distributions. The experimental results show that D3ROC yields robust and effective control policies, outperforming iterative Linear Quadratic Gaussian (iLQG) control and demonstrating strong adaptability to varying noise distributions.