  Emerging systems such as smart grids or intelligent transportation systems
often require end-user applications to continuously send information to
external data aggregators performing monitoring or control tasks. This can
result in an undesirable loss of privacy for the users in exchange of the
benefits provided by the application. Motivated by this trend, this paper
introduces privacy concerns in a system theoretic context, and addresses the
problem of releasing filtered signals that respect the privacy of the user data
streams. Our approach relies on a formal notion of privacy from the database
literature, called differential privacy, which provides strong privacy
guarantees against adversaries with arbitrary side information. Methods are
developed to approximate a given filter by a differentially private version, so
that the distortion introduced by the privacy mechanism is minimized. Two
specific scenarios are considered. First, the notion of differential privacy is
extended to dynamic systems with many participants contributing independent
input signals. Kalman filtering is also discussed in this context, when a
released output signal must preserve differential privacy for the measured
signals or state trajectories of the individual participants. Second,
differentially private mechanisms are described to approximate stable filters
when participants contribute to a single event stream, extending previous work
on differential privacy under continual observation.
