Data-driven System Interconnections and a Novel Data-enabled Internal Model Control

TL;DR

The paper addresses the gap between model-based control and data-driven BST by leveraging Willems' fundamental lemma to form data-driven interconnections between separate systems and proposing Internal Behavior Control (IBC) as a data-enabled analogue of Internal Model Control. It develops two implementation paths—component-by-component (CBC) and unified—where forward and inverse predictors or a single predictor substitute the traditional IMC blocks, preserving ideal IMC properties such as perfect tracking and disturbance rejection while avoiding explicit parametric models. The approach relies on data matrices built from offline trajectories and requires a low-rank condition to ensure admissible interconnection trajectories; simulation on a second-order SISO plant demonstrates equivalent performance to IMC with improved data efficiency in the unified approach. This work enables data-driven controller design within BST for series and feedback interconnections, with clear avenues for extension to MIMO, non-minimum-phase, and noisy data settings, and for uncertainty-aware tuning and data design.

Abstract

Over the past two decades, there has been a growing interest in control systems research to transition from model-based methods to data-driven approaches. In this study, we aim to bridge a divide between conventional model-based control and emerging data-driven paradigms grounded in Willem's fundamental lemma. Specifically, we study how input/output data from two separate systems can be manipulated to represent the behavior of interconnected systems, either connected in series or through feedback. Using these results, this paper introduces the Internal Behavior Control (IBC), a new control strategy based on the well-known Internal Model Control (IMC) but viewed under the lens of Behavioral System Theory. Similar to IMC, the IBC is easy to tune and results in perfect tracking and disturbance rejection but, unlike IMC, does not require a parametric model of the dynamics. We present two approaches for IBC implementation: a component-by-component one and a unified one. We compare the two approaches in terms of filter design, computations, and memory requirements.

Figures (6)

• Figure 1: Block diagram of the IMC structure
• Figure 2: Series interconnection given data from individual systems. In general, since ${\mathbf{y}}_1\neq {\mathbf{u}}_2$, the interconnection is not achievable. In the figure, the successful interconnection is shown with $G_2$ taking ${\mathbf{y}}_1$ as input and generating $\mathbf{y}_s$ as output.
• Figure 3: Positive feedback interconnection given data from individual systems. In general, ${\mathbf{y}}_1\neq \mathbf{u}_2$, so the interconnection is not achievable. In the figure, the successful interconnection is shown with $G_2$ taking ${\mathbf{y}}_1$ as input and generating $\check{\mathbf{y}}_2$ as output. The interconnected feedback system takes the signal from the subtraction $\mathbf{u}_1-\check{\mathbf{y}}_2$ as its input and produces ${\mathbf{y}}_1$ as its output.
• Figure 4: Simplified block diagram of the IMC structure
• Figure 5: Noise-free raw and filtered input/output data collected offline. Because the input is random, all Hankel matrices satisfy their respective low-rank conditions.

Theorems & Definitions (13)

• Remark 1
• Remark 2
• Theorem 1
• Theorem 2
• proof
• Theorem 3
• proof
• Theorem 4
• proof
• Theorem 5