LFT Representation of a Class of Nonlinear Systems: A Data-Driven Approach

TL;DR

This paper presents a data-driven method to derive an uncertain linear fractional transformation (LFT) model that captures nonlinear system dynamics, using neural networks and robustness analysis, demonstrated on an unmanned aircraft system.

Contribution

It introduces a novel approach combining neural network reduction, falsification, and IQC-based robustness analysis to obtain tractable LFT models of nonlinear systems.

Findings

Successfully derived an LFT model for aircraft dynamics

Demonstrated robustness analysis for uncertain nonlinear systems

Reduced complexity of LPV representation using CFNN

Abstract

This paper focuses on developing a method to obtain an uncertain linear fractional transformation (LFT) system that adequately captures the dynamics of a nonlinear time-invariant system over some desired envelope. First, the nonlinear system is approximated as a polynomial nonlinear state-space (PNLSS) system, and a linear parameter-varying (LPV) representation of the PNLSS model is obtained. To reduce the potentially large number of scheduling parameters in the resulting LPV system, an approach based on the cascade feedforward neural network (CFNN) is proposed. We account for the approximation and reduction errors through the addition of a norm-bounded, causal, dynamic uncertainty in the LFT system. Falsification is used in a novel way to perform guided simulations for deriving a norm bound on the dynamic uncertainty and generating data for training the CFNN. Then, robustness analysis using integral quadratic constraint theory is carried out to choose an LFT representation that leads to a computationally tractable analysis problem and useful analysis results. Finally, the proposed approach is used to obtain an LFT representation for the nonlinear equations of motion of a fixed-wing unmanned aircraft system.