This paper presents an optimal control law policy for maximizing biogas production of anaerobicdigesters. In particular, using a simple model of the anaerobic digestion process, we derive a controllaw to maximize the biogas production over a period T using the dilution rate as the control variable.Depending on initial conditions and constraints on the actuator (the dilution rate D(·)), the search for asolution to the optimal control problem reveals very different levels of difficulty. In the present paper,we consider that there are no severe constraints on the actuator. In particular, the interval in which theinput flow rate lives includes the value which allows the biogas to be maximized at equilibrium. Forthis case, we solve the optimal control problem using classical tools of differential equations analysis.Numerical simulations illustrate the robustness of the control law with respect to several parameters,notably with respect to initial conditions. We use these results to show that the heuristic control lawproposed by Steyer et al., 1999 [20] is optimal in a certain sense. The optimal trajectories are then com-pared with those given by a purely numerical optimal control solver (i.e. the “BOCOP” toolkit) which isan open-source toolbox for solving optimal control problems. When the exact analytical solution to theoptimal control problem cannot be found, we suggest that such numerical tool can be used to intuiteroptimal solutions.