In this paper, a hydrostatic tidal turbine (HTT) is designed and modeled, which uses more reliable hydrostatic transmission to replace existing fixed ratio gearbox transmission. The HTT dynamic model is derived by integrating governing equations of all the components of the hydraulic machine. A nonlinear observer is proposed to predict the turbine torque and tidal speeds in real time based on extreme learning machine (ELM). A sensorless double integral sliding mode controller is then designed for the HTT to achieve the maximum power extraction in the presence of large parametric uncertainties and nonlinearities. Simscape design experiments are conducted to verify the proposed design, model, and control system, which show that the proposed control system can efficiently achieve the maximum power extraction and has much better performance than conventional control. Unlike the existing works on ELM, the weights and biases in the ELM are updated online continuously. Furthermore, the overall stability of the controlled HTT system including the ELM is proved and the selection criteria for ELM learning rates are derived. The proposed sensorless control system has prominent advantages in robustness and accuracy, and is also easy to implement in practice.