  This work develops a stochastic model predictive controller~(SMPC) for
uncertain linear systems with additive Gaussian noise subject to state and
control constraints. The proposed approach is based on the recently developed
finite-horizon optimal covariance steering control theory, which steers the
mean and the covariance of the system state to prescribed target values at a
given terminal time. We call our approach covariance steering-based SMPC, or
CS-SMPC. We show that the proposed approach has several advantages over
traditional SMPC approaches in the literature. Specifically, it is shown that
the newly developed algorithm can deal with unbounded Gaussian additive noise
while ensuring stability and recursive feasibility, and incurs lower
computational cost than previous similar approaches. The effectiveness of the
proposed CS-SMPC approach is confirmed using numerical simulations.
