Quantized State Feedback Stabilization of Nonlinear Systems under Denial-of-Service

TL;DR

This paper proposes a quantized state feedback control method to stabilize nonlinear systems under DoS cyber attacks, analyzing the required data bits and demonstrating practical effectiveness through simulations.

Contribution

It introduces a dynamic quantization approach for nonlinear systems under DoS attacks and characterizes the quantization bits needed for stabilization.

Findings

Quantization bits increase under DoS attacks compared to no attack scenarios.

Theoretical bounds on required bits are established.

Simulations show actual bits needed are smaller than theoretical estimates.

Abstract

This paper studies the resilient control of networked systems in the presence of cyber attacks. In particular, we consider the state feedback stabilization problem for nonlinear systems when the state measurement is sent to the controller via a communication channel that only has a finite transmitting rate and is moreover subject to cyber attacks in the form of Denial-of-Service (DoS). We use a dynamic quantization method to update the quantization range of the encoder/decoder and characterize the number of bits for quantization needed to stabilize the system under a given level of DoS attacks in terms of duration and frequency. Our theoretical result shows that under DoS attacks, the required data bits to stabilize nonlinear systems by state feedback control are larger than those without DoS since the communication interruption induced by DoS makes the quantization uncertainty expand more between two successful transmissions. Even so, in the simulation, we show that the actual quantization bits can be much smaller than the theoretical value.