# Generalizable Optimal Control with Transformers: One Policy Across Diverse Systems

arXiv: https://arxiv.org/abs/2603.14910 · HTML: https://mlsanity.com/paper/2603.14910/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Mar 2026.

## Built on by (most cited first, 1 of 1)

- [Multitask LQG Control: Performance and Generalization Bounds](https://mlsanity.com/paper/2604.16730/) (2026)

## Abstract (arXiv)

Classical optimal control designs a separate controller for each plant. Even for the Linear Quadratic Regulator (LQR), every new model must be identified and its Riccati equation re-solved. We ask whether a single learned policy can instead serve an entire family of systems, and we show that one transformer can. We train the policy to imitate optimal LQR state feedback across a collection of heterogeneous Multiple-Input, Multiple-Output (MIMO) Linear Time-Invariant (LTI) systems that differ in their state and input dimensions and in their cost objectives. A shared representation lets the same parameters control every member of the family. It combines system-wise standardization, zero-padding and masking across dimensions, and an explicit encoding of the cost matrices. At run time, the policy maps a short window of recent states and the specified cost to a control action. It uses no plant matrices and identifies the dynamics implicitly from the state history. We evaluate on 28 simulated systems over 9,675 closed-loop rollouts, and no unstable rollout was observed in any of them. On the systems seen during training, it attains a median relative sub-optimality of 0.022%, even under parameter perturbations of up to ±10%. It transfers to unseen systems with lightweight fine-tuning, reaching a median sub-optimality of 0.19%. These results support transformers as generalizable near-optimal controllers for structured families of linear systems.