# Output Feedback Minimax Adaptive Control

arXiv: https://arxiv.org/abs/2409.04115 · HTML: https://mlsanity.com/paper/2409.04115/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Sep 2024.

## Built on by (most cited first, 2 of 2)

- [Efficient Spectral Control of Partially Observed Linear Dynamical Systems](https://mlsanity.com/paper/2505.20943/) (2025)
- [Consistent Model Chasing Is Minimax Optimal: The Exact Value of Scalar Adversarial Adaptive Control under Large Parametric Uncertainty](https://mlsanity.com/paper/2608.13651/) (2026)

## Abstract (arXiv)

This paper formulates adaptive controller design as a minimax dual control problem. The objective is to design a controller that minimizes the worst-case performance over a set of uncertain systems. The uncertainty is described by a set of linear time-invariant systems with unknown parameters. The main contribution is a common framework for both state feedback and output feedback control. We show that for finite uncertainty sets, the minimax dual control problem admits a finite-dimensional information state. This information state can be used to design adaptive controllers that ensure that the closed-loop has finite gain. The controllers are derived from a set of Bellman inequalities that are amenable to numerical solutions. The proposed framework is illustrated on a challenging numerical example.