Transformers As Generalizable Optimal Controllers

• URL: http://arxiv.org/abs/2603.14910v1
• Date: Mon, 16 Mar 2026 07:09:21 GMT
• Title: Transformers As Generalizable Optimal Controllers
• Abstract summary: 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.<n>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.<n>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.
• Score: 14.889781937667067
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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