This presentation will discuss stochastic control from a Model Predictive Control (MPC)
perspective, focusing on the extension of some key MPC ingredients to linear systems
subject to stochastic parametric uncertainties. We will first show how properties of the
Kronecker product can be exploited to derive deterministic recursions for the covariance
dynamics. Within a tube-based framework, such recursions provide a basis for
uncertainty propagation and constitute an important step toward tractable chance-
constraint tightening. We will then address the design of reduced-size suJicient
conditions for stabilizing the covariance dynamics, with an emphasis on the trade-oJ
between computational tractability and conservatism. The presentation will
subsequently establish the connection between covariance stability and the classical
notion of mean-square stability for stochastic systems. In particular, equivalent spectral
conditions will be discussed, providing a counterpart to the classical Schur-stability
characterization of deterministic linear systems. Finally, the talk will outline some
remaining challenges and ongoing research directions.