Robust Model Predictive Control for Polytopic Uncertain Systems With Energy Harvesting Sensors Under Round-Robin Protocol

Abstract

This paper addresses the robust model predictive control problem for a class of networked control systems with polytopic uncertainties and hard constraints, where the controller design is complicated by the joint presence of an energy harvesting sensor in the forward channel and the round-robin protocol in the backward channel. In such a setting, stochastic transmission behavior caused by random energy availability, together with fixed communication scheduling and immeasurable states, makes it difficult to guarantee recursive feasibility of the online optimization and mean-square stability of the closed-loop system. To capture these features, the mathematical expectation of a quadratic function depending on both the sensor energy level and the transmission order over an infinite horizon is constructed to formulate the optimization problem. In order to cope with the terminal constraint set and the immeasurability of system states, an auxiliary optimization problem with guaranteed solvability is developed by employing inequality analysis and slack-matrix techniques, through which a sub-optimal solution is obtained. Furthermore, sufficient conditions are derived to ensure the recursive feasibility of the proposed algorithm and the mean-square stability of the resulting closed-loop system with and without hard constraints. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed method.