# On Periodic Reference Tracking Using Batch-Mode Reinforcement Learning with Application to Gene Regulatory Network Control

arXiv: https://arxiv.org/abs/1303.2987 · HTML: https://mlsanity.com/paper/1303.2987/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Mar 2013.

## Built on by (most cited first, 3 of 3)

- [MAKO: Meta-Adaptive Koopman Operators for Learning-based Model Predictive Control of Parametrically Uncertain Nonlinear Systems](https://mlsanity.com/paper/2510.09042/) (2025)
- [External control of a genetic toggle switch via Reinforcement Learning](https://mlsanity.com/paper/2204.04972/) (2022)
- [Revolutionizing Genomics with Reinforcement Learning Techniques](https://mlsanity.com/paper/2302.13268/) (2023)

## Abstract (arXiv)

In this paper, we consider the periodic reference tracking problem in the framework of batch-mode reinforcement learning, which studies methods for solving optimal control problems from the sole knowledge of a set of trajectories. In particular, we extend an existing batch-mode reinforcement learning algorithm, known as Fitted Q Iteration, to the periodic reference tracking problem. The presented periodic reference tracking algorithm explicitly exploits a priori knowledge of the future values of the reference trajectory and its periodicity. We discuss the properties of our approach and illustrate it on the problem of reference tracking for a synthetic biology gene regulatory network known as the generalised repressilator. This system can produce decaying but long-lived oscillations, which makes it an interesting system for the tracking problem. In our companion paper we also take a look at the regulation problem of the toggle switch system, where the main goal is to drive the system's states to a specific bounded region in the state space.