The adaptive control of a class of strict-feedback nonlinear system under replay attack is investigated in this paper. Durations of each attack and the resting time after each attack are analyzed and their explicit bounds are presented to ensure closed-loop stability. Two scenarios are considered. In the first scenario, it is shown that if the duration of each attack is less than a given constant, asymptotical convergence of system output is still preserved. The second scenario shows that if the resting time of each attack meets certain condition after each arbitrarily long duration of attack, closed-loop boundedness is still preserved. This shows that the system controlled under our proposed adaptive controller will not be broken down even in the presence of replay attacks. Simulation results are given to illustrate the effectiveness of the control schemes.

研究了一类具有重放攻击的严格反馈非线性系统的自适应控制。分析每次攻击的持续时间和每次攻击后的休息时间，并给出它们的明确界限，以确保闭环稳定性。考虑了两种情况。在第一种情况下，表明如果每次攻击的持续时间小于给定的常数，则仍会保留系统输出的渐近收敛。第二种情况表明，如果在每次任意长的攻击持续时间之后每次攻击的休息时间都满足一定条件，则仍将保持闭环有界性。这表明即使存在重放攻击，在我们提出的自适应控制器下控制的系统也不会崩溃。