In this paper, the adaptive control for cyber-physical systems under injection and deception attacks is investigated, where a class of high-order strict-feedback nonlinear systems with uncertainties is considered. An adaptive control scheme is proposed and a kind of new feedback $S$-type functions with a class of new Lyapunov functions are introduced to deal with the injection and deception attacks meanwhile guarantee that regulation errors could be made arbitrarily small by adjusting control parameters. Compared with existing works whose models are linear or relatively simple, the model we consider in this paper is a class of high-order nonlinear with parametric uncertainties. Under attacks the parameters will become unknown and time-varying, which are difficult to deal with. To solve this problem, a new type of feedback control scheme is introduced. A simulation example is given to verify the effectiveness of our proposed control scheme.

本文研究了网络物理系统在注入和欺骗攻击下的自适应控制，其中考虑了一类具有不确定性的高阶严格反馈非线性系统。提出了一种自适应控制方案和一种新的反馈$秒$引入了一类新的李雅普诺夫函数的-型函数来应对注入和欺骗攻击，同时保证通过调整控制参数使调节误差可以任意小。与现有模型线性或相对简单的工作相比，本文考虑的模型是一类具有参数不确定性的高阶非线性。在攻击下，参数将变得未知且随时间变化，这很难处理。为了解决这个问题，引入了一种新型的反馈控制方案。给出了一个仿真例子来验证我们提出的控制方案的有效性。