Fuzzy dynamical modeling and Nash game-theoretic optimization for multi-objective robust control of electric helicopter tail rotor

Abstract

This paper introduces a robust controller with a compensator for the Electric Helicopter Tail Rotor system, designed to handle time-varying uncertainties and nonlinearities. Unlike traditional methods, it uses fuzzy set theory to represent uncertainties as fuzzy numbers, enabling a flexible yet precise approach. By applying fuzzy arithmetic, membership functions, and $\mathcal{D}$ -operations, robust solutions are derived to account for system vagueness. A two-player Nash game framework is employed to optimize controller parameters, balancing system efficacy (e.g., steady-state speed and corner-tracking) and control effort (e.g., minimizing input current). Simulation experiments validate the efficacy of this fuzzy-enhanced robust controller paired with Nash equilibrium optimization, revealing substantial improvements in Electric Helicopter Tail Rotor system responsiveness, stability, and energy efficiency-paving the way for more reliable aerial maneuvering in uncertain environments.