N-Step MPC for Systems With Persistent Bounded Disturbances Under SCP

This paper is concerned with the <inline-formula> <tex-math notation="LaTeX">${N}$ </tex-math></inline-formula>-step model predictive control (MPC) problem for a class of constrained systems with persistent bounded disturbances under the stochastic communication protocol (SCP). The control signals are transmitted to the plant via a shared network subject to a prescribed SCP for the purpose of avoiding data collisions. The SCP scheduling, which is governed by a Markov chain, is applied to orchestrate the transmission order of the controller nodes. Under the SCP, only one control node is allowed to update the control signal sent to the plant at each communication instant. Our aim is to design a set of desired controllers in the framework of <inline-formula> <tex-math notation="LaTeX">${N}$ </tex-math></inline-formula>-step MPC such that the mean-square input-to-state stability of the closed-loop system is guaranteed. An optimization algorithm consisting of both off-line and online parts is developed to cope with the design problem of the <inline-formula> <tex-math notation="LaTeX">${N}$ </tex-math></inline-formula>-step controller. Finally, a numerical example is utilized to illustrate the validity of the proposed <inline-formula> <tex-math notation="LaTeX">${N}$ </tex-math></inline-formula>-step MPC strategy.