Data-driven Internal Model Control for Output Regulation

TL;DR

The paper tackles output regulation for unknown linear and nonlinear systems from noisy data by replacing data-based OREs with an internal-model design that yields zero tracking error via a data-driven LMI. It first develops a linear framework where an $n_y$-copy internal model embedded in a data-driven controller stabilizes an augmented system, then extends to nonlinear systems through a kth-order internal model and corresponding LMIs. It further generalizes the approach to cooperative output regulation in both linear and nonlinear multi-agent systems using distributed data-driven controllers with per-agent LMIs, ensuring stability and asymptotic tracking. Numerical examples validate exact tracking and demonstrate robustness to noise, highlighting practical impact for uncertain and networked control applications. Overall, the method provides a scalable, data-driven pathway to precise output regulation without explicit plant identification or solving OREs, with clear extensions to MAS settings.

Abstract

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 the recent advancements in Willems et al.'s fundamental lemma, data-driven control has emerged as a powerful tool for stabilizing unknown systems. This paper tackles the output regulation problem for unknown single and multi-agent systems (MASs) using noisy data. Previous approaches have attempted to solve data-based output regulation equations (OREs), which are inadequate for achieving zero tracking error with noisy data. To circumvent the need for solving data-based OREs, we propose an internal model-based data-driven controller that reformulates the output regulation problem into a stabilization problem. This method is first applied to linear time-invariant (LTI) systems, demonstrating exact solution capabilities, i.e., zero tracking error, through solving a straightforward data-based linear matrix inequality (LMI). Furthermore, we extend our approach to solve the $k$th-order output regulation problem for nonlinear systems. Extensions to both linear and nonlinear MASs are discussed. Finally, numerical tests validate the effectiveness and correctness of the proposed controllers.

Figures (9)

• Figure 1: Tracking performance under the controller \ref{['eq:ctrl']}.
• Figure 2: Data-driven output regulation of nonlinear systems.
• Figure 3: Data-driven local output regulation of nonlinear systems.
• Figure 4: The communication graph $\bar{\mathcal{G}}$ between the $4$ agents and the exosystem
• Figure 5: Tracking performance under the proposed data-driven control approach.

Theorems & Definitions (16)

• Remark 1
• Theorem 1
• Remark 2
• Remark 3
• Definition 1: Internal model huang2004nonlinear
• Theorem 2
• proof
• Remark 4
• Theorem 3
• Remark 5: Nonlinear exosystem