# Minimax Adaptive Control for a Finite Set of Linear Systems

arXiv: https://arxiv.org/abs/2011.10814 · HTML: https://mlsanity.com/paper/2011.10814/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Nov 2020.

## Built on by (most cited first, 4 of 4)

- [Nonasymptotic Regret Analysis of Adaptive Linear Quadratic Control with Model Misspecification](https://mlsanity.com/paper/2401.00073/) (2023)
- [Sample Complexity Bounds for Linear System Identification from a Finite Set](https://mlsanity.com/paper/2409.11141/) (2024)
- [Data-Driven H-infinity Control with a Real-Time and Efficient Reinforcement Learning Algorithm: An Application to Autonomous Mobility-on-Demand Systems](https://mlsanity.com/paper/2309.08880/) (2023)
- [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)

An adaptive controller with bounded l2-gain from disturbances to errors is derived for linear time-invariant systems with uncertain parameters restricted to a finite set. The gain bound refers to the closed loop system, including the non-linear learning procedure. As a result, robustness to unmodelled dynamics (possibly nonlinear and infinite-dimensional) follows from the small gain theorem. The approach is based on a new zero-sum dynamic game formulation, which optimizes the trade-off between exploration and exploitation. An explicit upper bound on the optimal value function is stated in terms of semi-definite programming and a corresponding simple formula for an adaptive controller achieving the upper bound is given. Once the uncertain parameters have been sufficiently estimated, the controller behaves like standard H-infinity optimal control.