  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 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 \textit{sequential} attack
selection 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 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.
