Nonlinear Trajectory-Based Region of Attraction Estimation for Aircraft Dynamics Analysis

TL;DR

This paper introduces an improved trajectory-based method for estimating the region of attraction in nonlinear aircraft dynamics using only simulation data, enhancing accuracy and applicability to complex systems.

Contribution

It presents a faster, more accurate algorithm for ROA estimation from trajectory data, extendable to complex and higher-dimensional nonlinear systems.

Findings

Enhanced convergence speed and accuracy of ROA estimation.

Successful application to NASA's GTM aircraft model.

Extension to systems with multiple equilibria and limit cycles.

Abstract

Current flight control validation is heavily based on linear analysis and high fidelity, nonlinear simulations. Continuing developments of nonlinear analysis tools for flight control has greatly enhanced the validation process. Many analysis tools are reliant on assuming the analytical flight dynamics but this paper proposes an approach using only simulation data. First, this paper presents improvements to a method for estimating the region of attraction (ROA) of nonlinear systems governed by ordinary differential equations (ODEs) based only on trajectory measurements. Faster and more accurate convergence to the true ROA results. These improvements make the proposed algorithm feasible in higher-dimensional and more complex systems. Next, these tools are used to analyze the four-state longitudinal dynamics of NASA's Generic Transport Model (GTM) aircraft. A piecewise polynomial model of the GTM is used to simulate trajectories and the developed analysis tools are used to estimate the ROA around a trim condition based only on this trajectory data. Finally, the algorithm presented is extended to estimate the ROA of finitely many equilibrium point systems and of general equilibrium set (arbitrary equilibrium points and limit cycles) systems.