  In large-scale networks of uncertain dynamical systems, where communication
is limited and there is a strong interaction among subsystems, learning local
models and control policies offers great potential for designing
high-performance controllers. At the same time, the lack of safety guarantees,
here considered in the form of constraint satisfaction, prevents the use of
data-driven techniques to safety-critical distributed systems. This paper
presents a safety framework that guarantees constraint satisfaction for
uncertain distributed systems while learning. The framework considers linear
systems with coupling in the dynamics and subject to bounded parametric
uncertainty, and makes use of robust invariance to guarantee safety. In
particular, a robust non-convex invariant set, given by the union of multiple
ellipsoidal invariant sets, and a nonlinear backup control law, given by the
combination of multiple stabilizing linear feedbacks, are computed offline. In
presence of unsafe inputs, the safety framework applies the backup control law,
preventing the system to violate the constraints. As the robust invariant set
and the backup stabilizing controller are computed offline, the online
operations reduce to simple function evaluations, which enables the use of the
proposed framework on systems with limited computational resources. The
capabilities of the safety framework are illustrated by three numerical
examples.
