Covariance propagation and stabilization for tube-based stochastic MPC under parametric and additive uncertainties

Overview & Synopsis

This work addresses an SMPC-oriented characterization of the error covariance dynamics for linear discrete-time systems subject to both additive and parametric stochastic uncertainties that are potentially unbounded. In contrast with the standard additive-noise case, the covariance dynamics are coupled with the nominal trajectory because the parametric uncertainty acts on the full state. Using this characterization, the problem of control design for error covariance dynamics is addressed, providing conditions that are conservative yet more tractable compared to standard necessary and sufficient ones for the same class of systems. Numerical results assess this covariance characterization by comparing it to the empirical covariance and illustrate the control design problem.