The application discloses an EOS-ELM-based piezoelectric driving positioning platform modeling method and system, and an EOS-ELM-based piezoelectric driving positioning platform control method. According to the application, by taking the current desired output displacement, a plurality of previous output displacements and an input driving voltage as the input values of a model, and taking the input driving voltage value of a piezoelectric driver at the current moment as an output value of the model, a hysteretic nonlinear multi-value mapping problem is solved, and a complicated model inversion process can be avoided; secondly, the weights and the threshold values between a hidden layer and an input layer are given randomly, and a conventional neural network can be transformed into a linear equation model, so that the training time of the model is shortened greatly; thirdly, an infinite differentiable function is used as a hidden layer activation function, so that an excellent training effect can be realized; additionally, just by adopting a recursive least square method, the parameter online adaptive updating can be realized, and the applicability of the model is improved; furthermore, by integrating a plurality of weak learning machines, the precision and the stability of the model can be improved.