Robust Simulation Functions with Disturbance Refinement

Simulation functions are Lyapunov-like functions defined over the Cartesian product of state spaces of two (un)perturbed systems, a.k.a., concrete and abstract systems, to relate output trajectories of abstract systems to those of concrete ones while the mismatch between two systems remains within some guaranteed error bounds. In this work, we approximate concrete systems with abstractions with lower dimensions (reduced-order models) and develop robust simulation functions further to consider the perturbation in the abstract system by designing an interface function for the disturbance. The proposed approach allows concrete systems to have large disturbances, which is the case in many real-life applications, while noticeably reducing the closeness error between the two systems. Accordingly, this enables controller design using a reduced-order form of the concrete system and reducing the computational load required for formal synthesis. We demonstrate the efficacy of our approaches on linear control systems by synthesising a formal controller for a 9-state area of the known New England 39-Bus Test System, using only a 3-state abstract system.