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

This paper studies the security of a class of constrained nonlinear systems under attacks. Our goal is to design initial conditions, a control action and input bounds, so that the systems is secure by design. To this end, we propose novel 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. 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.