In recent years, SCADA (Supervisory Control and Data Acquisition) systems have increasingly become the target of cyber attacks. SCADAs are no longer isolated, as web-based applications expose strategic infrastructures to the outside world connection. In a cyber-warfare context, we propose a Model Predictive Control (MPC) architecture with adaptive resilience, capable of guaranteeing control performance in normal operating conditions and driving towards resilience against DoS (controller-actuator) attacks when needed. Since the attackers' goal is typically to maximize the system damage, we assume they solve an adversarial optimal control problem. An adaptive resilience factor is then designed as a function of the intensity function of a Hawkes process, a point process model estimating the occurrence of random events in time, trained on a moving window to estimate the return time of the next attack. We demonstrate the resulting MPC strategy's effectiveness in 2 attack scenarios on a real system with actual data, the regulated Olginate dam of Lake Como.

翻译：近年来，SCADA（监控与数据采集）系统日益成为网络攻击的目标。由于基于Web的应用将关键基础设施暴露于外部世界连接，SCADA不再孤立运行。在网络战背景下，我们提出一种具有自适应弹性的模型预测控制（MPC）架构，该架构能够在正常工况下保证控制性能，并在必要时针对拒绝服务（控制器-执行器）攻击驱动系统实现弹性。由于攻击者的目标通常是最大化系统破坏程度，我们假设其需要解决一个对抗性最优控制问题。随后设计一个自适应弹性因子，该因子是霍克斯过程强度函数的函数——霍克斯过程是一种估计随机事件发生时间点过程模型，通过滑动窗口训练以预估下一次攻击的返回时间。我们基于真实系统的实际数据，在科莫湖调节性奥尔吉纳特水坝上的两种攻击场景中，验证了所提MPC策略的有效性。