This paper presents an optimal motion control scheme for a mechatronic actuator based on a dielectric elastomer membrane transducer. The optimal control problem is formulated such that a desired position set-point is reached with minimum amount of driving energy, characterized via an accurate physical model of the device. Since the considered actuator is strongly nonlinear, an approximated approach is required to practically address the design of the control system. In this work, an Adaptive Dynamic Programming based algorithm is proposed, capable of minimizing a cost function related to the energy consumption of the considered system. Simulation results are presented in order to assess the effectiveness of the proposed method, for different set-point regulation scenarios.

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