Two-Stage Probabilistic Robust Control for Aircraft Longitudinal Short-Period Dynamics Using Pareto Optimization

This paper proposes a two-stage probabilistic robust controller design framework based on Pareto optimization (TSPO) for aircraft longitudinal short-period motion subject to aerodynamic parameter uncertainties. Unlike conventional robust control approaches such as LQR, H∞, and LMI-based design, which require engineers to translate intuitive performance specifications into abstract tuning parameters, TSPO formulates the design in terms of explicit time-domain performance targets and actuator constraints. In Stage I, multi-objective Pareto optimization generates an approximate set of candidate controllers by balancing nominal tracking performance and sample-based performance variability. The elevator-deflection limit is imposed as a hard constraint under nominal parameter values. In Stage II, Monte Carlo simulation with uniform parameter sampling estimates the rates at which candidates satisfy the time-domain requirements and elevator-deflection constraint under parameter uncertainty, and these estimates are used to select a final controller. The selected controller is then evaluated on a unit-step acceleration tracking task under three parametric uncertainty distributions: truncated Gaussian, uniform, and skewed beta. Comparative results against LQR, H∞, and LMI controllers for the considered model and uncertainty cases show favorable time-domain requirement satisfaction and elevator-deflection behavior for TSPO. The proposed framework provides a practical, heuristic, and interpretable methodology for robust flight-controller design in engineering applications.