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In this paper, we consider the periodic reference tracking problem in theframework of batch-mode reinforcement learning, which studies methods forsolving optimal control problems from the sole knowledge of a set oftrajectories. In particular, we extend an existing batch-mode reinforcementlearning algorithm, known as Fitted Q Iteration, to the periodic referencetracking problem. The presented periodic reference tracking algorithmexplicitly exploits a priori knowledge of the future values of the referencetrajectory and its periodicity. We discuss the properties of our approach andillustrate it on the problem of reference tracking for a synthetic biology generegulatory network known as the generalised repressilator. This system canproduce decaying but long-lived oscillations, which makes it an interestingsystem for the tracking problem. In our companion paper we also take a look atthe regulation problem of the toggle switch system, where the main goal is todrive the system's states to a specific bounded region in the state space.

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