Feasibility, Stability, Convergence and Markov Chains

Abstract

This chapter considers the closed-loop properties of stochastic MPC strategies based on the predicted costs and probabilistic constraints formulated in Chap. 6. To make the analysis of closed-loop stability and performance possible, it must first be ensured that the MPC law is well-defined at all times and the most natural way to approach this is to ensure that the associated receding horizon optimization problem remains feasible whenever it is initially feasible. We therefore begin by discussing the conditions for recursive feasibility.