Robust model predictive control with probabilistic bit flips under constrained bit rate

Abstract

This paper mainly studies the model predictive control problem with probabilistic bit flips under constrained bitrate limitations. Since the bitrate required for data transmission often exceeds the maximum bitrate that the system can provide, the transmitted data needs to be quantized to meet the bitrate requirements. The quantized data is encoded into binary data streams for long-distance transmission. However, due to external interferences such as channel noise, certain bits in the binary data streams may flip between 0 and 1, causing flip errors that affect subsequent control.Therefore, this paper quantizes data into specific intervals through a uniform quantizer and establishes a mathematical model of probabilistic bit flips by incorporating the description of bit probability flips using Bernoulli distributions. By combining it with polyhedral uncertain systems, the impacts of quantization and bit flips are transformed into system uncertainties, which are then uniformly handled in model predictive control. Considering the difficulty of obtaining system states in practical scenarios, a dynamic output feedback control framework under robust model predictive control is proposed. Singular value decomposition technology is used to address the non-convexity in the system, and solvable auxiliary optimization problems are proposed. Additionally, sufficient criteria for the mean-square stability of system states are provided. Finally, the effectiveness of the proposed method is verified through two simulation cases.