Construction of Barrier Certificates for Neural Network Controlled Systems Based on Polynomial Abstraction
This paper discusses a polynomial-based barrier certificate construction method for verifying the safety of neural network controlled systems.First,the neural network model is abstracted using methods such as global sector constraints,local sec-tor constraints,and overlay sector constraints to obtain corresponding semi-algebraic constraints.Then,using Positivstellenstz in computational real algebraic geometry,the barrier certificate conditions are transformed into corresponding sum-of-squares constraints,which are solved by using semi-definite programming.Finally,the effects of the above different neural network abstraction methods on the ability of construct-ing the barrier certificates of the neural network controlled systems are analyzed and compared through examples.
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