N-step model predictive control with persistent bounded disturbances under AF cooperation protocol

This paper investigates the N-step model predictive control (N-step MPC) problem for systems subject to polytopic uncertainties and persistent bounded disturbances. To this end, we introduce the amplify-and-forward cooperation protocol (AFCP) into the N-step MPC framework for the first time. Through cooperative transmission between sensor nodes and remote controller nodes, it effectively mitigates signal distortion. Since system states are usually difficult to obtain directly in practical scenarios, a Luenberger observer-based system is constructed to address this challenge. In addition, an objective function in the form of the mathematical expectation of an infinite-horizon quadratic function is designed to tackle disturbances and the randomness introduced by AFCP. Our goal is to propose an optimisation algorithm that combines offline and online components to design a set of controllers within the N-step MPC framework, while ensuring the mean-square input-to-state stability (MS-ISS) of the system. Finally, the effectiveness of the proposed N-step MPC strategy is verified through two simulation cases.