Stochastic tube MPC for LPV systems with probabilistic set inclusion conditions

The problem of controlling an LPV system subject to both hard and probabilistic constraints is considered. A necessary and sufficient condition for the inclusion of a polytope within another polytope, which is defined in terms of random variables, is given. This leads naturally to a tube MPC optimisation including linear probabilistic constraints. This can be solved approximately by considering a related problem obtained by sampling, which gives a mixed integer programming problem with a convex continuous relaxation. For fast sampling applications, we outline efficient approximate methods of solving the MIP via greedy constraint removal.