Data-Driven Internal Model Control for Output Regulation

Output regulation is a fundamental problem in control theory, extensively studied since the 1970s. Traditionally, research has primarily addressed scenarios where the system model is explicitly known, leaving the problem in the absence of a system model less explored. Leveraging recent advances in Willems et al.'s fundamental lemma, data-driven control has emerged as a powerful tool for stabilizing unknown systems. This article tackles the output regulation problem for unknown single and multiagent systems (MASs) using noisy data. Many existing data-driven approaches rely on solving data-based output regulator equations (OREs), which become inadequate for achieving zero tracking error in the presence of noisy data. To overcome this limitation, we advocate the use of a classical tool from robust output regulation, namely, the internal model principle. We first apply this idea to linear time-invariant (LTI) systems and show that exact output regulation, that is, zero tracking error, can be achieved by solving a simple data-based linear matrix inequality (LMI). The framework is then extended to the $k$ th-order output regulation problem for nonlinear systems, followed by applications to both linear and nonlinear MASs. Finally, numerical tests validate the effectiveness of the proposed data-driven controllers.