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A model-free on-off iterative adaptive controller is described for application to microscale servo systems performing repeated motions under extremely strict power constraints. The approach is motivated by the needs of piezoelectric actuators in autonomous microrobots, where power consumption in analog circuitry and/or for position sensing may be much larger than that of the actuators themselves. The control algorithm adjusts switching instances between “on” and “off” inputs to the actuator to minimize an objective function using simultaneously perturbed stochastic approximation of the gradient with just a single sensor measurement in each iteration. Convergence conditions for the gradient approximation are shown to apply when the possibility for a range of possible switching times minimizing the objective function is accounted for, while a method is proposed for avoiding local minima for plants with bounded nonlinearities. The algorithm is tested on a prototype piezoelectric microactuator.