The bottleneck and ceiling effects in quantized tracking control of heterogeneous multi-agent systems under DoS attacks

Abstract

In this paper, we investigate tracking control of heterogeneous multi-agent systems under Denial-of-Service (DoS) attacks and state quantization. Dynamic quantized mechanisms are designed for inter-follower communication and leader–follower communication. Zooming-in and out factors, and data rates of both mechanisms for preventing quantizer saturation are provided. Our results show that by tuning the inter-follower quantized controller, one cannot improve the resilience beyond a level determined by the data rate of leader–follower quantized communication, i.e., the ceiling effect. Otherwise, overflow of followers’ state quantizer can occur. On the other hand, if one selects a “large” data rate for leader–follower quantized communication, then the inter-follower quantized communication determines the resilience, and further increasing the data rate for leader–follower quantized communication cannot improve the resilience, i.e., the bottleneck effect. Simulation examples are provided to justify the results of our paper.