  We consider cloud-based control scenarios in which clients with local control
tasks outsource their computational or physical duties to a cloud service
provider. In order to address privacy concerns in such a control architecture,
we first investigate the issue of finding an appropriate privacy measure for
clients who desire to keep local state information as private as possible
during the control operation. Specifically, we justify the use of Kramer's
notion of causally conditioned directed information as a measure of privacy
loss based on an axiomatic argument. Then we propose a methodology to design an
optimal "privacy filter" that minimizes privacy loss while a given level of
control performance is guaranteed. We show in particular that the optimal
privacy filter for cloud-based Linear-Quadratic-Gaussian (LQG) control can be
synthesized by a Linear-Matrix-Inequality (LMI) algorithm. The trade-off in the
design is illustrated by a numerical example.
