Resilient Control under Quantization and Denial-of-Service: Co-designing a Deadbeat Controller and Transmission Protocol

Abstract: This paper is concerned with the problem of stabilizing continuous-time linear time-invariant systems subject to quantization and Denial-of-Service (DoS) attacks. In this context, two DoS-induced challenges emerge with the design of resilient encoding schemes, namely, the coupling between encoding strategies of different signals, and the synchronization between the encoder and decoder. To address these challenges, a novel structure that is equipped with a deadbeat controller as well as a delicate transmission protocol for the input and output channels, co-designed leveraging the controllability index, is put forward. When both input and output channels are subject to DoS attacks and quantization, the proposed structure is shown able to decouple the encoding schemes for input, output, and estimated output signals. This property is further corroborated by designing encoding schemes as well as conditions that ensure exponential stability of the closed-loop system. On the other hand, when only the output channel is subject to network phenomenon, the proposed structure can achieve exponential stabilization without acknowledgment (ACK) signals, in contrast to existing ACK-based results. Finally, a numerical example is given to demonstrate the practical merits of the proposed approach as well as the theory.