A Data-Driven Approach To Preserve Safety and Reference Tracking for Constrained Cyber-Physical Systems Under Network Attacks

Description

This repository contains the codes for "A Data-Driven Approach To Preserve Safety and Reference Tracking for Constrained Cyber-Physical Systems Under Network Attacks" by Mehran Attar and Walter Lucia which has been submitted to publish in IEEE Transactions on Automatic Control

Abstracat

This paper proposes a data-driven control architecture capable of preserving the safety and tracking performance of constrained Cyber-Physical Systems (CPSs) in the presence of network attacks. In particular, by adopting a worst-case approach, the objective is to ensure the safety of the systems under attack while minimizing any potential degradation in tracking performance. To this end, on the controller side, a data-driven robust anomaly detector is designed to detect cyber-attack occurrences. Moreover, an add-on tracking supervisor module allows safe open-loop tracking control operations in case of unreliable measurements due to cyber-attacks. On the plant side, a safety verification module and a local emergency controller are designed to manage severe attack scenarios that cannot be handled on the controller's side. These two modules resort to worst-case reachability and controllability data-driven arguments to detect potential unsafe scenarios and replace, whenever strictly needed, the tracking controller with emergency actions whose objective is to steer the plant's state trajectory in a predefined set of admissible and safe robust control invariant region until an attack-free scenario is restored. The effectiveness of the proposed solution has been demonstrated through a simulation example.

Running

1- Download CORA release 2022 and MPT3 release 2022

2- Add CORA and MPT folder and subfolders to the Matlab (in this work, MATLAB R2021-a has been used) path.

3- Add the repo folder and subfolders to the Matlab path.

Files Description

One scenario has been considered in this work.

Scenario: Attack on the measurement channel

To simulate this scenario, please run "main.m"

Function Descriptions

• "compute_AB.m": computes all possible system matrices that are consistent with the data
• "computeRPI.m": computes a model-based RCI set based on the proposed method in **"Invariant approximations of the minimal robust positively invariant set", by Rakovic et al.
• "computing_ROSC_sets.m": computes the family of ROSC sets by considering a target set $\hat{\mathcal{T}}^0$
• "compute_intersec.m": computes the intersection of polyhedrons
• "data_driven_controller.m": computes the data-driven tracking controller for a constrained discrete-time linear system
• "data_driven_safety_guard.m": checks the safety of the plant using the received control
• "one_step_ctrl.m" computes the data-driven ST-MPC control commands.
• "poly_approx.m": computes a zonotopic inner approximation of a polyhedron
• "set_index.m": computes the set membership index of a state for the data-driven ROSC sets.
• "detector_data_driven.m": simulates the data-driven anomaly detector local to the tracking controller, which is in charge of detecting anomalies caused by FDI attacks

Figures

Proposed Architecture

State trajectory: proposed solution with attacks (blue solid line) vs trajectory in attack-free scenario (purple dashed line).

State evolution: no attack, proposed approach, \cite{attar2024safety}