  We introduce a novel approach to make the tracking error of a class of
nonlinear systems differentially private in addition to guaranteeing the
tracking error performance. We use funnel control to make the tracking error
evolve within a performance funnel that is pre-specified by the user. We make
the performance funnel differentially private by adding a bounded continuous
noise generated from an Ornstein-Uhlenbeck-type process. Since the funnel
controller is a function of the performance funnel, the noise adds randomized
perturbation to the control input. We show that, as a consequence of the
differential privacy of the performance funnel, the tracking error is also
differentially private. As a result, the tracking error is bounded by the noisy
funnel boundary while maintaining privacy. We show a simulation result to
demonstrate the framework.
