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This paper considers a novel co-design problem of the optimal\textit{sequential} attack, whose attack strategy changes with the time series,and in which the \textit{sequential} attack selection strategy and\textit{sequential} attack signal are simultaneously designed. Different fromthe existing attack design works that separately focus on attack subsets orattack signals, the joint design of the attack strategy poses a huge challengedue to the deep coupling relation between the \textit{sequential} attackselection strategy and \textit{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 theoptimal attack signal and the sequential attack selection strategy.Furthermore, we prove the finite-time inverse convergence of the criticalparameters in the injected optimal attack signal by discrete-time Lyapunovanalysis, which enables the efficient off-line design of the attack signal andsaves computing resources. Finally, we exploit its relationship to design aheuristic two-stage learning-based joint attack algorithm (HTL-JA), which canaccelerate realization of the attack target compared to the one-stageproximal-policy-optimization-based (PPO) algorithm. Extensive simulations areconducted to show the effectiveness of the injected optimal sequential attack.

Heuristic Learning for Co-Design Scheme of Optimal Sequential Attack