  This work addresses maximally robust control synthesis under unknown
disturbances. We consider a general nonlinear system, subject to a Signal
Temporal Logic (STL) specification, and wish to jointly synthesize the maximal
possible disturbance bounds and the corresponding controllers that ensure the
STL specification is satisfied under these bounds. Many works have considered
STL satisfaction under given bounded disturbances. Yet, to the authors' best
knowledge, this is the first work that aims to maximize the permissible
disturbance set and find the corresponding controllers that ensure satisfying
the STL specification with maximum disturbance robustness. We extend the notion
of disturbance-robust semantics for STL, which is a property of a
specification, dynamical system, and controller, and provide an algorithm to
get the maximal disturbance robust controllers satisfying an STL specification
using Hamilton-Jacobi reachability. We show its soundness and provide a
simulation example with an Autonomous Underwater Vehicle (AUV).
