Resilient Control of Uncertain Networked Systems under DoS Attacks

This paper focuses on networked control systems with parameter uncertainties in system models under Denial-of-Services (DoS) attacks. The objective is to find the coarsest quantizer for a given quadratic Lyapunov function and still maintain stability while the network for transmitting quantized control signals is disrupted by a class of DoS attacks. Our main result shows that the coarsest quantization can be analytically obtained in the form of logarithmic quantizers whose coarseness is constrained by the unstable system poles and the level of DoS attacks. This result explicitly shows that under more frequent DoS attacks, finer quantization is required to achieve stability. Furthermore, we provide a switching control method for increasing the coarseness while the system operates without much influence of attacks.