Resilient Control for Networked Switched Systems With/Without ACK: An Active Quantized Framework

This paper deals with the quantized control problem for switched systems under denial-of-service (DoS) attack. Considering the system's defensive capability and the computational resources of quantizers and controllers, four control strategies are proposed. These strategies incorporate different combinations of controllers (active and passive), quantizers (centered on the origin or custom-designed), and network configurations (with or without ACK signals). For each strategy, specific update laws for the encoder and decoder are designed to avoid quantization saturation. Furthermore, the uniformity of encoder and decoder operations is maintained by transmitting additional information to the decoder. To achieve asymptotic stability, sufficient conditions concerning the switching signal and DoS attack constraints are derived by taking into account the asynchronous behaviors. The proposed active quantization strategy with the ACK signal leverages the system model information to compute the control signal in real-time, allowing for possible convergence of the system state despite DoS attack. Additionally, a well-designed switching signal is suggested to further mitigate the impact of DoS attack. A passive quantization strategy with ACK signal is also developed as a simplified version of the active quantized control strategy, providing the foundation for a strategy without ACK signal. Inspired by time-triggered and event-triggered mechanisms, the passive quantization strategy without ACK signal is investigated, with two feasible update laws for the quantizer. Finally, two simulations are conducted to validate the effectiveness of the proposed strategies.