Model Predictive Control with adaptive resilience for Denial-of-Service Attacks mitigation on a Regulated Dam

TL;DR

The paper tackles DoS attacks on SCADA-controlled dam regulation by proposing an adaptive resilient MPC framework that combines two controllers, ResMPC and SafeMPC, with a Hawkes-process–based resilience factor to forecast attack likelihood. A dual optimization is formulated: ResMPC minimizes a multi-objective cost including a resilience term $\lambda \|\mathbf{u}-\mathbf{u}_{safe}\|_2$, while SafeMPC computes a one-step safe action under potential DoS, with the attacker solving a concave maximization to maximize damage via $u_{DoS}$. Attacks are modeled adversarially, and the resilience factor is online updated through a Hawkes intensity $\gamma(t)$ integrated over a horizon, trained on a moving window, enabling the controller to adapt between performance and safety. The methodology is validated on the Olginate dam using authentic 2005 data under time-varying periodic and pseudo-random attack patterns, where ARMPC outperforms both standard MPC and SafeMPC in balancing lake level safety and agricultural water demand. This work demonstrates a practical integration of Hawkes processes into MPC for cyber-attack resilience in critical infrastructure with potential wide applicability.

Abstract

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.

Figures (6)

• Figure 1: Adaptive Resilient MPC Architecture
• Figure 2: Maximum Damage control (upper panel), Lake Como level (lower panel)
• Figure 3: $\Bar{\lambda}$ sensitivity analysis for fixed resilience, Resilient MPC.
• Figure 4: Hawkes intensity function as function of return time, for different attack return times.
• Figure 5: Resilience Factor $\lambda$ and attack occurrence.