This paper introduces two online methods for optimal periodic control (OPC) of open-loop stable plants. The first method requires knowledge of the plant structure but allows for uncertainty in plant parameters. It employs recursive least squares to estimate parameters, then uses the estimates to adapt the shape of the optimal trajectory. The second method uses a model-free extremum seeking scheme to slowly converge to the optimal input trajectory. While relevant work has been done in the area of online optimal periodic control, the existing methods either rely heavily on knowledge of the plant or they assume a known period. This work proposes methods that do not require these assumptions/limitations. The methods are tested on a drug delivery example from the existing OPC literature. Average drug efficacy values obtained in this work are comparable to the literature, even though limited information about the plant is used.