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

作　　者：黄程 林望 HUANG Cheng;LIN Wang(School of Computer Science and Technology,Zhejiang Sci-Tech University,Hangzhou 310018)

机构地区：[1]浙江理工大学计算机科学与技术学院,杭州310018

出　　处：《系统科学与数学》2024年第5期1224-1240,共17页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金项目(62272416)资助课题.

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.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 sector 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 constructing 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 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]