Model predictive control for polytopic uncertain systems with persistent bounded disturbances under long-distance transmission: a cooperation protocol-based approach

This paper is concerned with the robust model predictive control (RMPC) problem for a class of systems with polytopic uncertainties and persistent bounded disturbances in the long-distance transmission environment. The signal transmitted over a long distance is very likely to be destroyed by the channel fading. To address this issue, an amplify-and-forward cooperation protocol (AFCP) is adopted in the forward channel, i.e. from sensor nodes to the remote controller node, to improve the transmission quality. Considering the difficulty of obtaining the system state in practice, the dynamic output feedback control in the framework of RMPC is put forward. With respect to the parameter uncertainty, persistent bounded disturbances, and randomness of the transmission power stored in sensors and the AF relay, the objective function is defined by the mathematical expectation of a quadratic function over the infinite time horizon. Then, based on this establishment, a ‘min–max’ optimisation problem is readily formulated. Furthermore, the singular value decomposition technique is utilised to mitigate the non-convexity and formulate an auxiliary optimisation problem with the solvability, meanwhile, the sufficient criterion for the mean-square input-to-state stability of the underlying system is obtained. Finally, two simulation examples are given to illustrate the effectiveness of the proposed method.