  We consider a joint sensor and controller design problem for linear Gaussian
stochastic systems in which a weighted sum of quadratic control cost and the
amount of information acquired by the sensor is minimized. This problem
formulation is motivated by situations where a control law must be designed in
the presence of sensing, communication, and privacy constraints. We show that
the optimal joint sensor-controller design is relatively easy when the sensing
policy is restricted to be linear. Namely, an explicit form of the optimal
linear sensor equation, the Kalman filter, and the certainty equivalence
controller that jointly solves the problem can be efficiently found by
semidefinite programming (SDP). Whether the linearity assumption in our design
is restrictive or not is currently an open problem.
