  We address the optimal covariance steering (OCS) problem for stochastic
discrete linear systems with additive Gaussian noise under state chance
constraints and input hard constraints. Because the system state can be
unbounded due to the unbounded noise, the state constraints are formulated as
probabilistic (chance) constraints, i.e., the maximum probability of constraint
violation is constrained. In contrast, because it is hard to interpret the
appropriate control action when the control command violates the constraints,
probabilistically formulating the control constraints are difficult, and
deterministic hard constraints are preferable. In this work we introduce an OCS
approach subject to simultaneous state chance constraints and input hard
constraints and validate the approach using numerical simulations.
