Sampling based Computation of Viability Domain to Prevent Safety Violations by Attackers

TL;DR

This paper introduces a sampling-based method to compute viability domains in cyber-physical systems, ensuring safety against adversarial attacks by verifying invariance conditions and iteratively designing secure initial conditions and input bounds.

Contribution

It presents a novel, efficient sampling-based approach to verify and compute viability domains for nonlinear systems under attack, including an iterative algorithm and online control synthesis.

Findings

The method effectively verifies viability domains for nonlinear systems.

It enables design of initial conditions and input bounds to prevent safety violations.

The approach is computationally efficient and suitable for online control applications.

Abstract

This paper studies the security of cyber-physical systems under attacks. Our goal is to design system parameters, such as a set of initial conditions and input bounds so that it is secure by design. To this end, we propose new sufficient conditions to guarantee the safety of a system under adversarial actuator attacks. Using these conditions, we propose a computationally efficient sampling-based method to verify whether a set is a viability domain for a general class of nonlinear systems. In particular, we devise a method of checking a modified barrier function condition on a finite set of points to assess whether a set can be rendered forward invariant. Then, we propose an iterative algorithm to compute the set of initial conditions and input constraint set to limit what an adversary can do if it compromises the vulnerable inputs. Finally, we utilize a Quadratic Program approach for online control synthesis.