Polynomial Chaos-Based Flight Control Optimization with Guaranteed Probabilistic Performance

TL;DR

This paper introduces a polynomial chaos-based control optimization method that directly manages probabilistic performance constraints, reducing failure probability and enhancing safety in flight dynamic systems.

Contribution

It presents a novel probabilistic control design approach using polynomial chaos expansion for flight systems, improving safety guarantees over traditional robust control methods.

Findings

Reduced failure probability in simulations

Guaranteed probabilistic performance

Effective uncertainty propagation and control optimization

Abstract

A probabilistic performance-oriented controller design approach based on polynomial chaos expansion and optimization is proposed for flight dynamic systems. Unlike robust control techniques where uncertainties are conservatively handled, the proposed method aims at propagating uncertainties effectively and optimizing control parameters to satisfy the probabilistic requirements directly. To achieve this, the sensitivities of violation probabilities are evaluated by the expansion coefficients and the fourth moment method for reliability analysis, after which an optimization that minimizes failure probability under chance constraints is conducted. Afterward, a time-dependent polynomial chaos expansion is performed to validate the results. With this approach, the failure probability is reduced while guaranteeing the closed-loop performance, thus increasing the safety margin. Simulations are carried out on a longitudinal model subject to uncertain parameters to demonstrate the effectiveness of this approach.