Heuristic Learning for Co-Design Scheme of Optimal Sequential Attack

This paper considers a novel co-design problem of the optimal $\mathit{\text{sequential}}$ attack, whose attack strategy changes with the time series, and in which the $\mathit{\text{sequential}}$ attack selection strategy and $\mathit{\text{sequential}}$ attack signal are simultaneously designed. Different from the existing attack design works that separately focus on attack subsets or attack signals, the joint design of the attack strategy poses a huge challenge due to the deep coupling relation between the $\mathit{\text{sequential}}$ attack selection strategy and $\mathit{\text{sequential}}$ attack signal. In this manuscript, we decompose the sequential co-design problem into two equivalent sub-problems. Specifically, we first derive an analytical closed-form expression between the optimal attack signal and the sequential attack selection strategy. Furthermore, we prove the finite-time inverse convergence of the critical parameters in the injected optimal attack signal by discrete-time Lyapunov analysis, which enables the efficient off-line design of the attack signal and saves computing resources. Finally, we exploit its relationship to design a heuristic two-stage learning-based joint attack algorithm (HTL-JA), which can accelerate realization of the attack target compared to the one-stage proximal-policy-optimization-based (PPO) algorithm. Extensive simulations are conducted to show the effectiveness of the injected optimal sequential attack.