Meta-learning of data-driven controllers with automatic model reference tuning: theory and experimental case study

TL;DR

A meta-learning approach to leverage prior knowledge about analogous (though not identical) systems is explored, aiming to reduce both the experimental workload and ease the tuning of the available degrees of freedom.

Abstract

Data-driven control offers a viable option for control scenarios where constructing a system model is expensive or time-consuming. Nonetheless, many of these algorithms are not entirely automated, often necessitating the adjustment of multiple hyperparameters through cumbersome trial-and-error processes and demanding significant amounts of data. In this paper, we explore a meta-learning approach to leverage potentially existing prior knowledge about analogous (though not identical) systems, aiming to reduce both the experimental workload and ease the tuning of the available degrees of freedom. We validate this methodology through an experimental case study involving the tuning of proportional, integral (PI) controllers for brushless DC (BLDC) motors with variable loads and architectures.

Figures (7)

• Figure 1: Closed-loop matching scheme, with $y(t)$ being the, possibly noisy, closed-loop output and $e(t)=r(t)-y(t)$ being the corresponding tracking error, and $\varepsilon(t)$ the matching error, for $t\geq 0$.
• Figure 2: Closed-loop matching scheme with the meta-controller. We indicate as $y(t)$ the, possibly noisy, closed-loop output, $e(t)=r(t)-y(t)$ is the corresponding tracking error, and $\varepsilon(t)$ is the matching error, for $t\geq 0$.
• Figure 3: Experimental setup for a specific configuration. Note that, the motor and the inertial load are connected through a spindle.
• Figure 4: Datasets: responses comprised in the meta dataset $\mathcal{D}^{\mathrm{meta}}$ (used to compute \ref{['eq:similarity_data']}) and the training sets $\mathcal{D}^{\mathrm{test}}$.
• Figure 5: Comparison of direct, data-driven techniques: set point (black line) and desired response (dashed red line) vs mean (colored line) and standard deviation (shaded area) of the closed-loop responses attained with different controllers across the test motors.

Theorems & Definitions (3)

• Definition 1: busetto2023meta
• Remark 1: Choice of regularization
• Remark 2: On the use of closed-loop experiments