Hybrid Zonotope-Based Backward Reachability Analysis for Neural Feedback Systems With Nonlinear Plant Models

TL;DR

This paper presents a hybrid zonotope-based method for backward reachability analysis in neural feedback systems with nonlinear plants, providing closed-form over-approximations and a refinement process to reduce conservatism.

Contribution

It introduces a novel hybrid zonotope approach for backward reachability in nonlinear neural feedback systems, including a refinement procedure to improve accuracy.

Findings

Effective over-approximation of backward reachable sets demonstrated

Refinement procedure reduces conservatism in the analysis

Numerical examples validate the approach's effectiveness

Abstract

The increasing prevalence of neural networks in safety-critical control systems underscores the imperative need for rigorous methods to ensure the reliability and safety of these systems. This work introduces a novel approach employing hybrid zonotopes to compute the over-approximation of backward reachable sets for neural feedback systems with nonlinear plant models and general activation functions. Closed-form expressions as hybrid zonotopes are provided for the over-approximated backward reachable sets, and a refinement procedure is proposed to alleviate the potential conservatism of the approximation. Two numerical examples are provided to illustrate the effectiveness of the proposed approach.