Formal Control Synthesis for Stochastic Neural Network Dynamic Models

S.J.L. Adams*, Morteza Lahijanian, L. Laurenti

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

Neural networks (NNs) are emerging as powerful tools to represent the dynamics of control systems with complicated physics or black-box components. Due to complexity of NNs, however, existing methods are unable to synthesize complex behaviors with guarantees for NN dynamic models (NNDMs). This letter introduces a control synthesis framework for stochastic NNDMs with performance guarantees. The focus is on specifications expressed in linear temporal logic interpreted over finite traces (LTLf), and the approach is based on finite abstraction. Specifically, we leverage recent techniques for convex relaxation of NNs to formally abstract a NNDM into an interval Markov decision process (IMDP). Then, a strategy that maximizes the probability of satisfying a given specification is synthesized over the IMDP and mapped back to the underlying NNDM. We show that the process of abstracting NNDMs to IMDPs reduces to a set of convex optimization problems, hence guaranteeing efficiency. We also present an adaptive refinement procedure that makes the framework scalable. On several case studies, we illustrate that our framework is able to provide non-trivial guarantees of correctness for NNDMs with architectures of up to 5 hidden layers and hundreds of neurons per layer.
Original languageEnglish
Pages (from-to)2858-2863
JournalIEEE Control Systems Letters
Volume6
DOIs
Publication statusPublished - 2022

Keywords

  • Formal methods
  • interval Markov decision processes
  • neural networks
  • switched systems
  • synthesis

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