This article presents a resilient model predictive control (MPC) framework to attenuate adverse effects of denial-of-service (DoS) attacks for cyber-physical systems (CPSs), where the system dynamics is modeled by a linear time-invariant system. A DoS attacker targets at blocking the controller to actuator (C-A) communication channel by launching adversarial jamming signals. We show that, in order to guarantee exponential stability of the closed-loop system, several conditions for resilient MPC should be satisfied. And these established conditions are explicitly related to the duration of DoS attacks and MPC parameters such as the prediction horizon and the terminal constraint. Two key techniques, including the μ-step positively invariant set and the modified initial feasible set are exploited for achieving exponential stability in the presence of DoS attacks. Moreover, the maximum allowable duration of the DoS attacker is also obtained by using the μ-step positively invariant set. Finally, the effectiveness of the proposed MPC algorithm is verified by simulated studies and comparisons.

中文翻译：

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DoS 攻击下网络物理系统的弹性模型预测控制


本文提出了一种弹性模型预测控制 (MPC) 框架，用于减轻网络物理系统 (CPS) 的拒绝服务 (DoS) 攻击的不利影响，其中系统动态由线性时不变系统建模。 DoS 攻击者的目标是通过发射对抗性干扰信号来阻塞控制器到执行器 (CA) 的通信通道。我们表明，为了保证闭环系统的指数稳定性，应该满足弹性 MPC 的几个条件。这些既定条件与 DoS 攻击的持续时间和 MPC 参数（例如预测范围和终端约束）明确相关。利用μ步正不变集和修改后的初始可行集等两项关键技术，在存在 DoS 攻击的情况下实现指数稳定性。此外，DoS攻击者的最大允许持续时间也是利用μ步正不变集得到的。最后，通过仿真研究和比较验证了所提出的MPC算法的有效性。