Resilient Model Predictive Control of Distributed Systems Under Attack Using Local Attack Identification

TL;DR

Novel methods for model-based identification of attacks and combine them with distributed model predictive control to obtain a resilient framework for adaptively robust control are presented.

Abstract

With the growing share of renewable energy sources, the uncertainty in power supply is increasing. In addition to the inherent fluctuations in the renewables, this is due to the threat of deliberate malicious attacks, which may become more revalent with a growing number of distributed generation units. Also in other safety-critical technology sectors, control systems are becoming more and more decentralized, causing the targets for attackers and thus the risk of attacks to increase. It is thus essential that distributed controllers are robust toward these uncertainties and able to react quickly to disturbances of any kind. To this end, we present novel methods for model-based identification of attacks and combine them with distributed model predictive control to obtain a resilient framework for adaptively robust control. The methodology is specially designed for distributed setups with limited local information due to privacy and security reasons. To demonstrate the efficiency of the method, we introduce a mathematical model for physically coupled microgrids under the uncertain influence of renewable generation and adversarial attacks, and perform numerical experiments, applying the proposed method for microgrid control.

Figures (7)

• Figure 1: If neighboring subsystems in a distributed system exchange suitable information about their local coupling variables, each subsystem can employ a local ADI method to identify suspicions about unknown local attack inputs.
• Figure 2: A scenario tree as in the multi-stage approach to robust MPC Lucia2013Multi, here shown for time $k = 0$ and $N_{\text{p}}=4$, provides a natural and computationally efficient way to approximate the reachable sets $\mathcal{X}_I^{l, [k]}$ (indicated in gray) by discrete node sets $\widetilde{\mathcal{X}}_I^{l, [k]}$ (blue) explored by the tree.
• Figure 3: Schematic overview of the model for interconnected microgrids taken from Braun2022Resilient, showing the local model components for microgrid $I$. Apart from internal states, each microgrid only requires knowledge of its neighboring couplings $(z_{LI})_{J\in \mathcal{N}_I}$. For power balance, storage units are used as a buffer.
• Figure 4: Selected state and input trajectories for microgrid i, showing all powers in kW. The microgrid is exposed to a generator attack, causing the generation $p^{\text{g}}_{\text{i}}$ to be considerably larger than planned by $u^{\text{g}}_{\text{i}}$. The different SoC trajectories, computed by adaptively robust versus nonrobust NMPC, show the benefit of the proposed resilient control framework.
• Figure 5: Actual attack value $a^{\text{g}}_{\text{i}}$ and average identified value $\mu^{[k]}_{\text{i}}$ in the first attack scenario examined, in which only dispatchable generation units are in use and microgrid i is exposed to a generator attack.