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This paper studies the control of a nonlinear electrical circuit exemplified by a Duffing equation, which contains parameter uncertainties in the right hand side of this nonlinear differential equation. Even though this type of circuit has been object of a variety of control strategies in the past, very few papers have been devoted to the design of an optimal control law with a quadratic performance index and subject to that type of uncertainties. We develop simulation examples that show that not only an optimal control strategy can be applied to such a system, in case of an optimal control strategy without uncertainties, but an optimal control of the mini-max type can also be implemented in case of the uncertainty in the model.