Observer-Based Safety Monitoring of Nonlinear Dynamical Systems with Neural Networks via Quadratic Constraint Approach

TL;DR

This paper presents a novel observer-based safety monitoring method for nonlinear dynamical systems with neural network components, using quadratic constraints and Lyapunov theory to ensure accurate state estimation.

Contribution

It introduces a quadratic constraint approach combined with Lyapunov theory to design interval observers for neural network-embedded nonlinear systems.

Findings

Successfully verified via simulation on a lateral vehicle control system.

The method guarantees state estimation within acceptable error bounds.

Transforms observer design into solvable quadratic and linear programming problems.

Abstract

The safety monitoring for nonlinear dynamical systems with embedded neural network components is addressed in this paper. The interval-observer-based safety monitor is developed consisting of two auxiliary neural networks derived from the neural network components of the dynamical system. Due to the presence of nonlinear activation functions in neural networks, we use quadratic constraints on the global sector to abstract the nonlinear activation functions in neural networks. By combining a quadratic constraint approach for the activation function with Lyapunov theory, the interval observer design problem is transformed into a series of quadratic and linear programming feasibility problems to make the interval observer operate with the ability to correctly estimate the system state with estimation errors within acceptable limits. The applicability of the proposed method is verified by simulation of the lateral vehicle control system.