Chance-constrained LQG with bounded control policies

We study the finite-horizon LQG problem in which the states are required to satisfy probabilistic constraints, and the control inputs are required to satisfy hard bounds. We demonstrate that a general class of feedback policies satisfying the above constraints can be algorithmically selected via the solution to a convex optimization problem. An estimate of the region of initial conditions for which the chance constraints are feasible is also provided. Our approach relies on concentration of measure inequalities for the standard Gaussian measure.