In this paper, offline and online parameter estimation methods for hydraulic systems based on stochastic gradient descent are presented. In contrast to conventional approaches, the proposed methods can estimate any parameter in mathematical models based on multi-step prediction error. These advantages are achieved by calculating the gradient of the multi-step error against the estimated parameters using Lagrange multipliers and the calculus of variations, and by forming differentiable models of hydraulic systems. In experiments on a physical hydraulic system, the proposed methods with three different gradient decent methods (normal gradient descent, Nesterov’s Accelerated Gradient (NAG), and Adam) are compared with conventional least squares. In the offline experiment, the proposed method with NAG achieves estimation error about 95% lower than that of least squares. In online estimation, the proposed method with NAG produces predictive models with about 20% lower error than that of the offline method. These results suggest the proposed method is a practical alternative to more conventional parameter estimation methods.

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