# Data-Driven H-infinity Control with a Real-Time and Efficient Reinforcement Learning Algorithm: An Application to Autonomous Mobility-on-Demand Systems

arXiv: https://arxiv.org/abs/2309.08880 · HTML: https://mlsanity.com/paper/2309.08880/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 35 references that are in the map.
- First posted on arXiv 16 Sep 2023.

## Builds on (most cited first, 13 of 13)

- [Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulator](https://mlsanity.com/paper/1801.05039/) (2018)
- [On the Sample Complexity of the Linear Quadratic Regulator](https://mlsanity.com/paper/1710.01688/) (2017)
- [DeepPool: Distributed Model-free Algorithm for Ride-sharing using Deep Reinforcement Learning](https://mlsanity.com/paper/1903.03882/) (2019)
- [Policy Optimization Provably Converges to Nash Equilibria in Zero-Sum Linear Quadratic Games](https://mlsanity.com/paper/1906.00729/) (2019)
- [Least-Squares Temporal Difference Learning for the Linear Quadratic Regulator](https://mlsanity.com/paper/1712.08642/) (2017)
- [Control of Robotic Mobility-On-Demand Systems: a Queueing-Theoretical Perspective](https://mlsanity.com/paper/1404.4391/) (2014)
- [Data-Driven Model Predictive Control of Autonomous Mobility-on-Demand Systems](https://mlsanity.com/paper/1709.07032/) (2017)
- [From self-tuning regulators to reinforcement learning and back again](https://mlsanity.com/paper/1906.11392/) (2019)
- [Model-Free Linear Quadratic Control via Reduction to Expert Prediction](https://mlsanity.com/paper/1804.06021/) (2018)
- [A Modular and Transferable Reinforcement Learning Framework for the Fleet Rebalancing Problem](https://mlsanity.com/paper/2105.13284/) (2021)
- [Minimax Adaptive Control for a Finite Set of Linear Systems](https://mlsanity.com/paper/2011.10814/) (2020)
- [Routing Autonomous Vehicles in Congested Transportation Networks: Structural Properties and Coordination Algorithms](https://mlsanity.com/paper/1603.00939/) (2016)
- [Recursive Least Squares with Variable-Direction Forgetting -- Compensating for the loss of persistency](https://mlsanity.com/paper/2003.03523/) (2020)

## Abstract (arXiv)

Reinforcement learning (RL) is a class of artificial intelligence algorithms being used to design adaptive optimal controllers through online learning. This paper presents a model-free, real-time, data-efficient Q-learning-based algorithm to solve the H∞ control of linear discrete-time systems. The computational complexity is shown to reduce from O(underlineq3) in the literature to O(underlineq2) in the proposed algorithm, where underlineq is quadratic in the sum of the size of state variables, control inputs, and disturbance. An adaptive optimal controller is designed and the parameters of the action and critic networks are learned online without the knowledge of the system dynamics, making the proposed algorithm completely model-free. Also, a sufficient probing noise is only needed in the first iteration and does not affect the proposed algorithm. With no need for an initial stabilizing policy, the algorithm converges to the closed-form solution obtained by solving the Riccati equation. A simulation study is performed by applying the proposed algorithm to real-time control of an autonomous mobility-on-demand (AMoD) system for a real-world case study to evaluate the effectiveness of the proposed algorithm.