Formal Control Synthesis for Stochastic Neural Network Dynamic Models

Neural networks (NNs) are emerging as powerful tools to represent the dynamics of control systems with complicated physics or black-box components. Due complexity NNs, however, existing methods unable synthesize complex behaviors guarantees for NN dynamic models (NNDMs). This work introduces a synthesis framework stochastic NNDMs performance guarantees. The focus is on specifications expressed in linear temporal logic interpreted over finite traces (LTLf), and approach based abstraction. Specifically, we leverage recent techniques convex relaxation NNs formally abstract NNDM into an interval Markov decision process (IMDP). Then, strategy that maximizes probability satisfying given specification synthesized IMDP mapped back underlying NNDM. We show abstracting IMDPs reduces set optimization problems, hence guaranteeing efficiency. also present adaptive refinement procedure makes scalable. On several case studies, illustrate our able provide non-trivial correctness architectures up 5 hidden layers hundreds neurons per layer.