This repository contains the codes for "A Data-Driven Safety Preserving Control Architecture for Constrained Cyber-Physical Systems" by Mehran Attar and Walter Lucia which has been submitted to publish in International Journal of Robust and Nonlinear Control --> Arxiv link

In this work, we propose a data-driven networked control architecture for unknown constrained linear cyber-physical systems subject to bounded disturbances capable of detecting and ensuring plant safety in the presence of cyber-attacks on the communication channels. To this end, first, by using data-driven forward reachability analysis, a passive anomaly detector that is local to the controller is designed to detect network attacks. Then, to ensure that intelligent and undetectable attacks will be detected before causing safety risks, a safety verification module, which is local to the plant, is designed based on an outer approximation of the one-step evolution set at each time step. This unit is in charge of activating the emergency controller whenever the control input is deemed unsafe or under the effect of cyber-attacks. Finally, an emergency controller is designed by exploiting a family of data-driven Robust One-Step Controllable (ROSC) Sets and dual-mode set-theoretic model predictive controller to safely confine the system into the closest robust control invariant region in a finite number of steps. Numerical simulations involving a two-tank water system is performed to clarify the proposed solution's capabilities.

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.

Two scenarios have been considered in this work.

1- To simulate this scenario, please run "data_driven_architecture_attack_on_actuation.m"

2- To simulate this scenario, please run "data_driven_architecture_attack_on_measurement.m"

• "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

x_data_caseA: contains the system's trajectory with the safety modules

u_ver_caseA: contains the control signal applied to the plant

x_w_caseA: contains the system's trajectory without the safety modules

x_data_caseB: contains the system's trajectory with the safety modules

u_ver_caseB: contains the control signal applied to the plant

x_w_caseB: contains the system's trajectory without the safety modules

1- please run "animated_test_S1.m"

2- please run "animated_test_S2.m"