Optimal Transport Approach for Probabilistic Robustness Analysis of F-16 Controllers

Abstract

This paper presents a new framework for controller robustness verification with respect to an F-16 aircraft’s closed-loop performance in longitudinal flight. The state regulation performance of a linear quadratic regulator and a gain-scheduled linear quadratic regulator are compared, where both controllers are applied to nonlinear open-loop dynamics of an F-16, in the presence of stochastic initial condition and parametric uncertainties, as well as actuator disturbance. It is shown that, in the presence of initial condition uncertainties alone, both the linear quadratic regulator and gain-scheduled linear quadratic regulator have comparable immediate and asymptotic performances, but the gain-scheduled linear quadratic regulator exhibits better transient performance at intermediate times. This remains true in the presence of additional actuator disturbance. Also, the gain-scheduled linear quadratic regulator is shown to be more robust than the linear quadratic regulator 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 for nonlinear dynamical systems. Numerical results from the proposed method are in unison with Monte Carlo simulations.