Data-Driven Output Regulation From Partial Noisy Measurements: An Adaptive Dynamic Programming Approach

Output regulation in dynamical systems with unknown physics, partial state measurements, and uncharacterized sensor noise remains a central challenge in robotics, aerospace, and autonomous systems. This paper investigates the optimal output regulation problem for nonlinear systems in settings where neither the system dynamics nor an admissible control policy is available in advance. Four factors distinguish the problem considered here from existing approaches: only partial state information is measurable, policy iteration cannot be initiated due to the lack of an admissible stabilizing controller, the output measurements are corrupted by noise with unknown statistics, and no belief state or observer estimate is assumed. To address these challenges, we develop a data driven adaptive dynamic programming framework that learns an optimal output regulating controller directly from streaming noisy output data. The proposed method employs an on policy value iteration scheme that uses a structured quadratic action value function together with a modified temporal difference update to refine the critic. A learned derivative feedback term provides the excitation necessary to identify the residual policy without requiring any knowledge of the system state. The effectiveness of the method is demonstrated through simulation study on a cart–pole output regulation task.