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Transformers As Generalizable Optimal Controllers

Turki Bin Mohaya, Maitham F. AL-Sunni, John M. Dolan, Peter Seiler

Abstract

We study whether optimal state-feedback laws for a family of heterogeneous Multiple-Input, Multiple-Output (MIMO) Linear Time-Invariant (LTI) systems can be captured by a single learned controller. We train one transformer policy on LQR-generated trajectories from systems with different state and input dimensions, using a shared representation with standardization, padding, dimension encoding, and masked loss. The policy maps recent state history to control actions without requiring plant matrices at inference time. Across a broad set of systems, it achieves empirically small sub-optimality relative to Linear Quadratic Regulator (LQR), remains stabilizing under moderate parameter perturbations, and benefits from lightweight fine-tuning on unseen systems. These results support transformer policies as practical approximators of near-optimal feedback laws over structured linear-system families.

Transformers As Generalizable Optimal Controllers

Abstract

We study whether optimal state-feedback laws for a family of heterogeneous Multiple-Input, Multiple-Output (MIMO) Linear Time-Invariant (LTI) systems can be captured by a single learned controller. We train one transformer policy on LQR-generated trajectories from systems with different state and input dimensions, using a shared representation with standardization, padding, dimension encoding, and masked loss. The policy maps recent state history to control actions without requiring plant matrices at inference time. Across a broad set of systems, it achieves empirically small sub-optimality relative to Linear Quadratic Regulator (LQR), remains stabilizing under moderate parameter perturbations, and benefits from lightweight fine-tuning on unseen systems. These results support transformer policies as practical approximators of near-optimal feedback laws over structured linear-system families.
Paper Structure (14 sections, 22 equations, 5 figures, 2 tables, 1 algorithm)

This paper contains 14 sections, 22 equations, 5 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Optimal and robust control
  4. Neural and generalist control policies
  5. Transformers for dynamics, control, and LLMs
  6. Problem Formulation
  7. Approach
  8. Data Collection
  9. Data Processing
  10. Transformers
  11. Transformer Training and Inference
  12. Fine-Tuning for Unseen Systems
  13. Results
  14. Conclusions

Figures (5)

  • Figure 1: Relative sub-optimality distribution across seen and unseen systems (see \ref{['tab:lti_systems']} for systems' labels).
  • Figure 2: Performance on dual arm robot (system #15, seen).
  • Figure 3: Performance on vibrating beam (system #26, unseen).
  • Figure 4: Performance on asymmetric oscillator (system #18, unseen).
  • Figure 5: Ablation study on the effect of (left) the window length and (right) the number of sequences per system