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One controller to rule them all

Riccardo Busetto, Valentina Breschi, Marco Forgione, Dario Piga, Simone Formentin

TL;DR

This work proposes the first in-context learning-based approach to design a unique contextual controller for an entire class of dynamical systems rather than focusing on just a single instance.

Abstract

Imagine having a system to control and only know that it belongs to a certain class of dynamical systems. Would it not be amazing to simply plug in a controller and have it work as intended? With the rise of in-context learning and powerful architectures like Transformers, this might be possible, and we want to show it. In this work, within the model reference framework, we hence propose the first in-context learning-based approach to design a unique contextual controller for an entire class of dynamical systems rather than focusing on just a single instance. Our promising numerical results show the possible advantages of the proposed paradigm, paving the way for a shift from the "one-system-one-controller" control design paradigm to a new "one-class-one-controller" logic.

One controller to rule them all

TL;DR

This work proposes the first in-context learning-based approach to design a unique contextual controller for an entire class of dynamical systems rather than focusing on just a single instance.

Abstract

Imagine having a system to control and only know that it belongs to a certain class of dynamical systems. Would it not be amazing to simply plug in a controller and have it work as intended? With the rise of in-context learning and powerful architectures like Transformers, this might be possible, and we want to show it. In this work, within the model reference framework, we hence propose the first in-context learning-based approach to design a unique contextual controller for an entire class of dynamical systems rather than focusing on just a single instance. Our promising numerical results show the possible advantages of the proposed paradigm, paving the way for a shift from the "one-system-one-controller" control design paradigm to a new "one-class-one-controller" logic.

Paper Structure

This paper contains 11 sections, 17 equations, 6 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Setting and goal
  3. In-context controller design
  4. Structuring and training a contextual controller
  5. On the structure of the in-context controller
  6. How to train a contextual controller
  7. In-context control of an evaporation process: a numerical case study
  8. Meta-dataset construction
  9. Details on the contextual controller training strategy
  10. Performance analysis
  11. Conclusions and future works

Figures (6)

  • Figure 1: GPT-like decoder-only Transformer for in-context control.
  • Figure 2: Noiseless product composition over time of $20$ systems drawn at random from $\mathcal{S}$, starting from the same initial condition and subject to the same inputs.
  • Figure 3: Observed ($y$) vs predicted ($\hat{y}$) composition with the identified grey-box models for the evaporation process: averages (lines) and standard deviations (shaded areas).
  • Figure 4: Boxplots of the matching errors achieved over the $20$ performed closed-loop tests with the contextual (ctx), oracle, and identification-based (id) controllers.
  • Figure 5: Closed-loop responses attained by the contextual (ctx), oracle, and identification-based (id) controllers vs reference to be tracked and desired behavior over $3$ (randomly drawn) test out of the $20$ we have performed.
  • ...and 1 more figures

Theorems & Definitions (1)

  • remark 1: Size of the meta-dataset