Safe learning for distributed systems with bounded uncertainties

Abstract

Learning in interacting dynamical systems can lead to instabilities and violations of critical safety constraints, which is limiting its application to constrained system networks. This paper introduces two safety frameworks that can be applied together with any learning method for ensuring constraint satisfaction in a network of uncertain systems, which are coupled in the dynamics and in the state constraints. The proposed techniques make use of a safe set to modify control inputs that may compromise system safety, while accepting safe inputs from the learning procedure. Two different safe sets for distributed systems are proposed by extending recent results for structured invariant sets. The sets differ in their dynamical allocation to local sets and provide different trade-offs between required communication and achieved set size. The proposed algorithms are proven to keep the system in the safe set at all times and their effectiveness and behavior is illustrated in a numerical example.