Probabilistic Multi-Objective Gain Design for Robustness Under Plant Parameter Uncertainty for VTOL Applications

This paper presents a multi-objective, probabilistic gain design approach, with the goal of achieving a robustness focused controller in presence of not-well known plant parameter uncertainties. The proposed approach seeks to minimize always the greatest single violation probability of the considered stability/robustness sub-objectives, while enforcing strict minimal acceptable performance constraints. This is motivated by the need for safe operation, in particular during abnormal condition or first flight tests, when plant parameters, such as the inertia tensor, contain significant uncertainty, yet safety is still paramount. The method uses as input probability distributions of the critical uncertain plant parameters, enabling statistical evaluation of requirement violations via Monte Carlo (sampling based) analysis. The approach framework is modular and can simply be extended to account for other/additional plant uncertainties, probability distributions, sub-goals and constraints. By always minimizing the maximum violation probability, there is no need to manually prioritize or subjectively weigh these stability and robustness related objectives. Both pattern search and Covariance Matrix Adaptation Evolution Strategy (CMA-ES) are utilized for optimizing in this context and compared for their effectiveness. The deployed methodology is general in terms of requirements and application agnostic, however in this works, the example of a manned, 3-ton MTOW class electrical vertical take-off and landing vehicle (eVTOL), currently under development, will be used to illustrate how the gap from theory to industrial application can be bridged. Finally, the paper discusses other variations, the needed future improvements of the approach and outlines the critical challenges, especially regarding the reliance of the approach on sufficiently accurate estimations of the input probability distribution of the plant parameters.