Stochastic MPC design Sample Clauses

Stochastic MPC design. The overapproximation described in Section 2.5.3 is used here to design a SMPC controller that exploits the measurements received at every time step to improve closed-loop performance, while guaranteeing stability. This control policy is derived from the approach presented by [149], and relies on a decoupling between stability enforcement and performance optimization. Offline, a Lyapunov function and a feedback control law which provide mean-square stability are obtained by exploiting the NCS convex overapproximation. Online, a stochastic MPC controller based on scenario enumeration is applied to optimize the performance by relying on the current state measurements and on the available stochastic information on the network uncertainty, while retaining stability. Hereafter, the different steps of the proposed control strategy design are given. k Our first goal is to compute a Lyapunov function and a control law which render the closed-loop NCS system UGMSES. Here we consider quadratic Lyapunov functions of the form V (ξk) = ξTPξk, and assume that the control law is given by a constant matrix gain K, i.e., uk = Kξk, for all k. The Lyapunov matrix P will then serve to enforce a stability constraint in the online control problem, while the existence of the gain K will be used to prove the recursive feasibility of the receding horizon policy. ∈ ∈ ∈ > >