Backward Reachability Analysis of Neural Feedback Systems Using Hybrid Zonotopes
- Resource Type
- Working Paper
- Authors
- Zhang, Yuhao; Zhang, Hang; Xu, Xiangru
- Source
- Subject
- Mathematics - Optimization and Control
Electrical Engineering and Systems Science - Systems and Control
- Language
The proliferation of neural networks in safety-critical applications necessitates the development of effective methods to ensure their safety. This letter presents a novel approach for computing the exact backward reachable sets of neural feedback systems based on hybrid zonotopes. It is shown that the input-output relationship imposed by a ReLU-activated neural network can be exactly described by a hybrid zonotope-represented graph set. Based on that, the one-step exact backward reachable set of a neural feedback system is computed as a hybrid zonotope in the closed form. In addition, a necessary and sufficient condition is formulated as a mixed-integer linear program to certify whether the trajectories of a neural feedback system can avoid unsafe regions in finite time. Numerical examples are provided to demonstrate the efficiency of the proposed approach.
Comment: 6 pages, 3 figures