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.
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