基于多项式抽象的神经网络控制系统的障碍函数构造
Construction of Barrier Certificates for Neural Network Controlled Systems Based on Polynomial Abstraction
黄程 1林望1
作者信息
- 1. 浙江理工大学计算机科学与技术学院,杭州 310018
- 折叠
摘要
针对神经网络控制系统的安全性验证,提出了基于多项式抽象的障碍函数构造方法.首先,采用全局扇区约束方法、局部扇区约束方法和区域叠加约束方法等对神经网络模型进行抽象,从而得到了相应的半代数约束;然后,运用计算实代数几何中的正点定理,将障碍函数条件松弛为相应的平方和约束条件,再采用半定规划方法进行求解.最后,通过实例对上述不同的神经网络抽象方法就神经网络控制系统的障碍函数构造能力的影响进行了分析.
Abstract
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.
关键词
神经网络控制系统/障碍函数构造/多项式抽象/平方和规划Key words
Neural network controlled system/barrier certificate construction/poly-nomial abstraction/sum-of-squares programming引用本文复制引用
出版年
2024
NETL
NSTL
万方数据