  This work addresses the optimal covariance control problem for stochastic
discrete-time linear time-varying systems subject to chance constraints.
Covariance steering is a stochastic control problem to steer the system state
Gaussian distribution to another Gaussian distribution while minimizing a cost
function. To the best of our knowledge, covariance steering problems have never
been discussed with probabilistic chance constraints although it is a natural
extension. In this work, first we show that, unlike the case with no chance
constraints, the covariance steering with chance constraints problem cannot
decouple the mean and covariance steering sub-problems. Then we propose an
approach to solve the covariance steering with chance constraints problem by
converting it to a semidefinite programming problem. The proposed algorithm is
verified using two simple numerical simulations.
