Variable-Bit Event-Triggered Encoding Control for Nonlinear Strict-Feedback Systems Against DoS Attacks

Abstract

This paper investigates the coded tracking control problem for nonlinear strict-feedback systems subject to denial-of-service (DoS) attacks and severe communication resource constraints. A high-gain observer is first constructed to ensure uniform ultimate boundedness of the state-estimation errors under DoS attacks. Next, a novel variable-bit event-triggered (VBET) encoding-decoding mechanism is proposed to encode the transmitted observer states. The codeword length is adjusted in real time based on both the recent DoS attack intensity and the normalized event-triggering error, thereby achieving a favorable trade-off between communication efficiency and attack resilience, while simultaneously determining the observer gain. To overcome the discontinuities in the decoded signal, a predictor-based continuous state reconstructor is then developed, which updates only at successful transmission instants and provides continuous state estimates. Subsequently, a backstepping controller is synthesized using these continuous estimates. Finally, a numerical example with several comparative simulations is provided to verify the effectiveness of the proposed approach. Note to Practitioners—In automated factories, robot systems, remote vehicles, and other cyber-physical processes, sensors and controllers typically rely on wireless networks to exchange sensor measurements and control information. However, it cannot be ignored that wireless network communication is limited and vulnerable to various attacks, resulting in service disruptions and possible closed-loop instability. Therefore, this paper focuses on variable-bit event-triggered encoding control to defend against DoS attacks in a class of nonlinear systems. Compared to the general application of event triggering to controllers, this paper designs an encoder based on event-triggering conditions, which saves communication resources and simplifies existing encoding methods that rely on various complex quantizers. Compared to fixed-bit encoding methods, the variable-bit encoding proposed in this paper automatically adjusts the codeword length according to the attack intensity and event-triggering error. The design achieves a balance between tracking performance and communication-resource consumption. The simulation comparison demonstrates the superiority of the method in terms of tracking performance, the number of event triggers, and bit consumption under different strategies. In the future, we will focus on expanding the application of this method to resource allocation problems in actual power grids.