A Probabilistic Method for Nonlinear Robustness Analysis of F-16 Controllers

TL;DR

This paper introduces a probabilistic framework for verifying the robustness of F-16 controllers, comparing LQR and gsLQR, and demonstrating the advantages of gsLQR under uncertainties using transfer operators and optimal transport methods.

Contribution

It develops a novel probabilistic approach for nonlinear robustness analysis of aircraft controllers, integrating transfer operators and optimal transport for validation.

Findings

gsLQR outperforms LQR in robustness against uncertainties

Both controllers perform similarly under initial condition uncertainties

Numerical results align with Monte Carlo simulations

Abstract

This paper presents a new framework for controller robustness verification with respect to F-16 aircraft's closed-loop performance in longitudinal flight. We compare the state regulation performance of a linear quadratic regulator (LQR) and a gain-scheduled linear quadratic regulator (gsLQR), applied to nonlinear open-loop dynamics of F-16, in presence of stochastic initial condition and parametric uncertainties, as well as actuator disturbance. We show that, in presence of initial condition uncertainties alone, both LQR and gsLQR have comparable immediate and asymptotic performances, but the gsLQR exhibits better transient performance at intermediate times. This remains true in the presence of additional actuator disturbance. Also, gsLQR is shown to be more robust than LQR, against parametric uncertainties. The probabilistic framework proposed here, leverages transfer operator based density computation in exact arithmetic and introduces optimal transport theoretic performance validation and verification (V&V) for nonlinear dynamical systems. Numerical results from our proposed method, are in unison with Monte Carlo simulations.