Learning-boosted self-triggered intelligent impulsive consensus problem for multi-agent systems with encrypted communication

This paper investigates the Q-learning-based self-triggered intelligent impulsive consensus problem for multi-agent systems (MASs) under encrypted communication. Firstly, a memory-based self-triggered impulsive control (M-STIC) strategy is developed by integrating a weighted combination of historical error measurements into the triggering conditions. Secondly, to intelligently balance convergence performance and communication efficiency, the threshold selection problem is formulated as a Markov decision process (MDP), and a distributed Q-learning algorithm is introduced to enable each agent to adaptively select triggering thresholds from a pre-screened safe action set. The action set is verified to satisfy single-mode stability conditions, ensuring that learning-based adaptation does not compromise closed-loop stability. Thirdly, the chaotic stream cipher-based encryption-decryption process is explicitly modeled as a constant communication delay τ , quantifying the security-induced performance degradation. A unified stability analysis framework is established, which integrates the M-STIC mechanism, Q-learning adaptive strategy, and encrypted communication delay modeling, rigorously proving exponential consensus and the exclusion of Zeno behavior. Finally, numerical simulations demonstrate that the proposed method achieves consensus with significantly reduced communication load compared to conventional self-triggered or periodic impulsive strategies.