Transformers As Generalizable Optimal Controllers

2026-03-16

AI Summary

This work proposes a Transformer-based universal learning controller capable of achieving near-optimal state-feedback control for a family of heterogeneous multi-input multi-output linear time-invariant (LTI) systems. The approach trains a single policy using LQR-generated trajectories, constructing a shared cross-system representation through state history encoding, dimension embedding, normalization, padding, and masked loss. During inference, the controller maps recent system states to control actions without requiring explicit knowledge of the system matrices. This study demonstrates, for the first time, that Transformers can achieve stable zero-shot generalization with performance approaching that of the optimal LQR controller across structured LTI system families. Furthermore, the model supports lightweight fine-tuning on unseen systems, significantly enhancing deployment flexibility and robustness.

Technology Category

• Search and Optimization: Learning to Search
• Multiagent Systems: Multiagent Learning
• Intelligent Robots: Behavior Learning & Control

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information

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.

Problem

• optimal control
• MIMO systems
• LTI systems
• state-feedback
• generalizable controllers

Innovation

• Transformer
• Optimal Control
• Generalizable Policy
• LQR
• MIMO LTI Systems