Abstract:
We present Barrier-based Simplex (Bb-Simplex), a new, provably correct design for run-time assurance of continuous dynamical systems. Bb-Simplex is centered around the Simplex
Control Architecture, which consists of a high-performance advanced controller that is not
guaranteed to maintain safety of the plant, a verified-safe baseline controller, and a deci-
sion module that switches control of the plant between the two controllers to ensure safety
without sacrificing performance. In Bb-Simplex, Barrier certificates are used to prove that
the baseline controller ensures safety. Furthermore, Bb-Simplex features a new automated
method for deriving, from the barrier certificate, the conditions for switching between the
controllers. Our method is based on the Taylor expansion of the barrier certificate and
yields computationally inexpensive switching conditions. We also extended Bb-Simplex to
use approximate dynamics. This requires modifying the definition of barrier certificate, the
definition of switching condition, and our method for deriving the barrier certificate to take
into account the error bounds for the approximate dynamics.

We consider a significant application of Bb-Simplex to a microgrid featuring an advanced
controller in the form of a neural network trained using reinforcement learning. The microgrid
is modeled in RTDS, an industry-standard high-fidelity, real-time power systems simulator.
Our results demonstrate that Bb-Simplex can automatically derive switching conditions
for complex systems, the switching conditions are not overly conservative, and Bb-Simplex
ensures safety even in the presence of adversarial attacks on the neural controller.