Data-Driven Safety Verification of Discrete-Time Networks: A Compositional Approach

Abstract

This letter proposes a compositional data-driven approach for safety verification of networks of discrete-time subsystems with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">formal guarantees</i> . Following a modular approach and for each subsystem, we search for a so-called sub-barrier candidate represented as a linear combination of a priori user-defined basis functions. We formulate the conditions on sub-barrier candidates as robust convex programs (RCPs) which are semi-infinite linear programs. Collecting sampled data from each subsystem, we approximate each RCP via a scenario convex program (SCP) which is a finite linear program. We provide an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">explicit</i> formula to compute the minimum number of sampled data guaranteeing a desired mismatch between the optimal value of each RCP and that of the corresponding SCP in a probabilistic sense. To ensure that the sum of the sub-barrier candidates is a barrier function for the whole network, we define a global dissipativity condition on top of the local SCPs. The local SCPs are thus related to each other via this global condition. This results in a large-scale optimization problem in a standard canonical form which is efficiently solved by the alternating direction method of multipliers (ADMM) algorithm. The effectiveness of our approach is illustrated by applying it to a room temperature control problem in a 100-room building.